jam-O6-hypercomplex {

;	Simplified version of order-6 hypercomplex number systems with various rule sets.
;	211220

;	The basis units used are 1, e1, e2, e3, e4, and e5.  For all implemented rule sets,
;		1x1=1; 1xe1 = e1x1 = e1, 1xe2 = e2x1 = e2, 1xe3 = e3x1 = e3, 1xe4 = e4x1 = e4,
;		1xe5 = e5x1 = e5.

;	In addition to the above, the other components of the unit multiplication rules are:
;	Ruleset A:	e1^2 = e2^2 = e3^2 = e4^2 = e5^2 = -1;
;				e1e2 = -e2e1 = e3, e2e3 = -e3e2 = e4, e3e4 = -e4e3 = e5,
;				e4e5 = -e5e4 = e1, e5e1 = - e1e5 = e2;
;				e1e3 = -e3e1 = -e5, e2e4 = -e4e2 = -e1, e3e5 = -e5e3 = -e2,
;				e4e1 = -e1e4 = -e3, e5e2 = -e2e5 = -e4.
;	B:			Same combination rules as above, except:

; Plotting options are the following planes:
; real-e1, real-e2, real-e3, real-e4, real-e5, e1-e2, e1-e3, e1-e4, e1-e5,
; e2-e3, e2-e4, e2-e5, e3-e4, e3-e5, and e4-e5.

; The bailout variable can be the magnitude of the hypercomplex number, h,
; or any pair of these components:  real,e1; real,e2; real,e3; real,e4; real, e5;
; e1,e2; e1,e3; e1,e4; e1, e5; e2,e3; e2,e4; e2, e5; e3,e4; e3, e5; or e4, e5,
; or, alternatively, the absolute value of any single component.

global:

init:
	complex jc = (0,0) ; Julia constant (Julia) or pixel value (Mandelbrot)
	float jcreal = float jcimag = 0.0
	float bailoutvalue = 0.0
	
	; Working variables for the iteration:
	; The hypercomplex H = h0 + h1e1 + h2e2 + h3e3 + h4e4 + h5e5, where the hs are real (scalars)
	float h0 = float h1 = float h2 = float h3 = float h4 = float h5 = 0.0
	
	; An order-6 hypercomplex when squared will generate 36 terms using the non-commutative
	; multiplication rules; after partial simplification using scalar commutativity, there are
	; 21 unique, individual coefficients.  For simplicity and
	; clarity rather than efficiency, these 21 term coefficients are defined here.
	float c0 = float c1 = float c2 = float c3 = float c4 = float c5 = 0.0
	float c6 = float c7 = float c8 = float c9 = float c10 = float c11 = float c12 = 0.0
	float c13 = float c14 = float c15 = float c16 = float c17 = float c18 = 0.0
	float c19 = float c20 = 0.0
	
	float temp = 0.0 ; scratch variable

	if @mandy
	#z = #pixel, jc = #pixel
	else ; Julia
	#z = #pixel, jc = @jconstant
	endif
	
	; jc1 and jc2 will be added to the appropriate components of the
	;	hypercomplex number corresponding to the selected plot plane.
	jcreal = real(jc)
	jcimag = imag(jc)

	; initialize the hypercomplex number
	if @plotplane == "real, e1"
		h0 = real(#z)
		h1 = imag(#z)
		h2 = @e2start
		h3 = @e3start
		h4 = @e4start
		h5 = @e5start
	elseif @plotplane == "real, e2"
		h0 = real(#z)
		h1 = @e1start
		h2 = imag(#z)
		h3 = @e3start
		h4 = @e4start
		h5 = @e5start
	elseif @plotplane == "real, e3"
		h0 = real(#z)
		h1 = @e1start
		h2 = @e2start
		h3 = imag(#z)
		h4 = @e4start
		h5 = @e5start
	elseif @plotplane == "real, e4"
		h0 = real(#z)
		h1 = @e1start
		h2 = @e2start
		h3 = @e3start
		h4 = imag(#z)
		h5 = @e5start
	elseif @plotplane == "real, e5"
		h0 = real(#z)
		h1 = @e1start
		h2 = @e2start
		h3 = @e3start
		h4 = @e4start
		h5 = imag(#z)
	elseif @plotplane == "e1, e2"
		h0 = @realstart
		h1 = real(#z)
		h2 = imag(#z)
		h3 = @e3start
		h4 = @e4start
		h5 = @e5start
	elseif @plotplane == "e1, e3"
		h0 = @realstart
		h1 = real(#z)
		h2 = @e2start
		h3 = imag(#z)
		h4 = @e4start
		h5 = @e5start
	elseif @plotplane == "e1, e4"
		h0 = @realstart
		h1 = real(#z)
		h2 = @e2start
		h3 = @e3start
		h4 = imag(#z)
		h5 = @e5start
	elseif @plotplane == "e1, e5"
		h0 = @realstart
		h1 = real(#z)
		h2 = @e2start
		h3 = @e3start
		h4 = @e4start
		h5 = imag(#z)
	elseif @plotplane == "e2, e3"
		h0 = @realstart
		h1 = @e1start
		h2 = real(#z)
		h3 = imag(#z)
		h4 = @e4start
		h5 = @e5start
	elseif @plotplane == "e2, e4"
		h0 = @realstart
		h1 = @e1start
		h2 = real(#z)
		h3 = @e3start
		h4 = imag(#z)
		h5 = @e5start
	elseif @plotplane == "e2, e5"
		h0 = @realstart
		h1 = @e1start
		h2 = real(#z)
		h3 = @e3start
		h4 = @e4start
		h5 = imag(#z)
	elseif @plotplane == "e3, e4"
		h0 = @realstart
		h1 = @e1start
		h2 = @e2start
		h3 = real(#z)
		h4 = imag(#z)
		h5 = @e5start
	elseif @plotplane == "e3, e5"
		h0 = @realstart
		h1 = @e1start
		h2 = @e2start
		h3 = real(#z)
		h4 = @e4start
		h5 = imag(#z)
	elseif @plotplane == "e4, e5"
		h0 = @realstart
		h1 = @e1start
		h2 = @e2start
		h3 = @e3start
		h4 = real(#z)
		h5 = imag(#z)
	endif ; @plotplane

loop:
	; Iterate the hypercomplex number according to the chosen ruleset,
	; h(n+1) = h(n)^2 + jc = h0^2 + h1^2 e1^2 + h2^2 e2^2 + h3^2 e3^2 + h4^2 e4^2
	; + h5^2 e5^2 + 2h0h1 e1 + 2h0h2 e2 + 2h0h3 e3 + 2h0h4 e4 + 2h0h5 e5 + h1h2 e1e2
	; + h1h2 e2e1 + h1h3 e1e3 + h1h3 e3e1 + + h1h4 e1e4 + h1h4 e4e1 + h1h5 e1e5 + h1h5 e5e1
	; + h2h3 e2e3 + h2h3 e3e2 + h2h4 e2e4 + h2h4 e4e2 + h2h5 e2e5 + h2h5 e5e2 +
	; h3h4 e3e4 + h3h4 e4e3 + h3h5 e3e5 + h3h5 e5e3 + h4h5 e4e5 + h4h5 e5e4 + jc

	; First, calculate all 21 independent coefficients c0,...,c20
	c0 = sqr(h0)
	c1 = sqr(h1)
	c2 = sqr(h2)
	c3 = sqr(h3)
	c4 = sqr(h4)
	c5 = sqr(h5)
	temp = 2 * h0
	c6 = temp * h1
	c7 = temp * h2
	c8 = temp * h3
	c9 = temp * h4
	c10 = temp * h5
	c11 = h1 * h2
	c12 = h1 * h3
	c13 = h1 * h4
	c14 = h1 * h5
	c15 = h2 * h3
	c16 = h2 * h4
	c17 = h2 * h5
	c18 = h3 * h4
	c19 = h3 * h5
	c20 = h4 * h5
	
	; Second, combine the coefficients according to the current ruleset.
	if @ruleset == "A"
		h0 = c0 - c1 - c2 - c3 - c4 -c5
		h1 = c6
		h2 = c7
		h3 = c8
		h4 = c9
		h5 = c10
;	elseif @ruleset == "B"
	endif ; @ruleset
	
	; Next, add the Julia constant or #pixel value to the hypercomplex number
	if @plotplane == "real, e1"
		h0 = h0 + jcreal
		h1 = h1 + jcimag
		#z = h0 + flip(h1)
	elseif @plotplane == "real, e2"
		h0 = h0 + jcreal
		h2 = h2 + jcimag
		#z = h0 + flip(h2)
	elseif @plotplane == "real, e3"
		h0 = h0 + jcreal
		h3 = h3 + jcimag
		#z = h0 + flip(h3)
	elseif @plotplane == "real, e4"
		h0 = h0 + jcreal
		h4 = h4 + jcimag
		#z = h0 + flip(h4)
	elseif @plotplane == "real, e5"
		h0 = h0 + jcreal
		h5 = h5 + jcimag
		#z = h0 + flip(h5)
	elseif @plotplane == "e1, e2"
		h1 = h1 + jcreal
		h2 = h2 + jcimag
		#z = h1 + flip(h2)
	elseif @plotplane == "e1, e3"
		h1 = h1 + jcreal
		h3 = h3 + jcimag
		#z = h1 + flip(h3)
	elseif @plotplane == "e1, e4"
		h1 = h1 + jcreal
		h4 = h4 + jcimag
		#z = h1 + flip(h4)
	elseif @plotplane == "e1, e5"
		h1 = h1 + jcreal
		h5 = h5 + jcimag
		#z = h1 + flip(h5)
	elseif @plotplane == "e2, e3"
		h2 = h2 + jcreal
		h3 = h3 + jcimag
		#z = h2 + flip(h3)
	elseif @plotplane == "e2, e4"
		h2 = h2 + jcreal
		h4 = h4 + jcimag
		#z = h2 + flip(h4)
	elseif @plotplane == "e2, e5"
		h2 = h2 + jcreal
		h5 = h5 + jcimag
		#z = h2 + flip(h5)
	elseif @plotplane == "e3, e4"
		h3 = h3 + jcreal
		h4 = h4 + jcimag
		#z = h3 + flip(h4)
	elseif @plotplane == "e3, e5"
		h3 = h3 + jcreal
		h5 = h5 + jcimag
		#z = h3 + flip(h5)
	elseif @plotplane == "e4, e5"
		h4 = h4 + jcreal
		h5 = h5 + jcimag
		#z = h4 + flip(h5)
	endif ; @plotplane

	; Calculate the value used in the bailout test
	if @bailvar == "hypercomplex norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1) + sqr(h2) + sqr(h3) + sqr(h4) + sqr(h5))
	elseif @bailvar == "real, e1 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1))
	elseif @bailvar == "real, e2 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h2))
	elseif @bailvar == "real, e3 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h3))
	elseif @bailvar == "real, e4 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h4))
	elseif @bailvar == "real, e5 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h5))
	elseif @bailvar == "e1, e2 norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h2))
	elseif @bailvar == "e1, e3 norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h3))
	elseif @bailvar == "e1, e4 norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h4))
	elseif @bailvar == "e1, e5 norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h5))
	elseif @bailvar == "e2, e3 norm"
		bailoutvalue = sqrt(sqr(h2) + sqr(h3))
	elseif @bailvar == "e2, e4 norm"
		bailoutvalue = sqrt(sqr(h2) + sqr(h4))
	elseif @bailvar == "e2, e5 norm"
		bailoutvalue = sqrt(sqr(h2) + sqr(h5))
	elseif @bailvar == "e3, e4 norm"
		bailoutvalue = sqrt(sqr(h3) + sqr(h4))
	elseif @bailvar == "e3, e5 norm"
		bailoutvalue = sqrt(sqr(h3) + sqr(h5))
	elseif @bailvar == "e4, e5 norm"
		bailoutvalue = sqrt(sqr(h4) + sqr(h5))
	elseif @bailvar == "|real|"
		bailoutvalue = abs(h0)
	elseif @bailvar == "|e1|"
		bailoutvalue = abs(h1)
	elseif @bailvar == "|e2|"
		bailoutvalue = abs(h2)
	elseif @bailvar == "|e3|"
		bailoutvalue = abs(h3)
	elseif @bailvar == "|e4|"
		bailoutvalue = abs(h4)
	elseif @bailvar == "|e5|"
		bailoutvalue = abs(h5)
	endif ; @bailvar

bailout:
	bailoutvalue < @bail

default:
	title = "Order-6 Hypercomplex Streamlined"
	center = (0,0)
	maxiter = 500
	method = multipass
	periodicity = 0

heading
	text = "A sampling of order-6 hypercomplex number systems"
endheading

param ruleset
	caption = "Multiplication Ruleset"
	enum = "A"
	default = 0
	hint = "This parameter determines how the basis units of the hypercomplex system \
		combine when multiplied.  The different rules are listed in the comments at \
		the top of the formula entry.  Set 'F' are Olariu's polar 5-complex numbers."
endparam
param plotplane
	caption = "Plot Plane"
	enum = "real, e1" "real, e2" "real, e3" "real, e4" "real, e5" "e1, e2" "e1, e3" "e1, e4" \
		"e1, e5" "e2, e3" "e2, e4" "e2, e5" "e3, e4" "e3, e5" "e4, e5"
	default = 0
	hint = "This parameter determines which components of the hypercomplex iterate \
		are plotted on the screen."
endparam
param bailvar
	caption = "Bailout Variable"
	enum = "hypercomplex norm" "real, e1 norm" "real, e2 norm" "real, e3 norm" "real, e4 norm" \
		"real, e5 norm" "e1, e2 norm" "e1, e3 norm" "e1, e4 norm" "e1, e5 norm" "e2, e3 norm" \
		"e2, e4 norm" "e2, e5 norm" "e3, e4 norm" "e3, e5 norm" "e4, e5 norm" "|real|" "|e1|" \
		"|e2|" "|e3|" "|e4|" "|e5|"
	default = 0
	hint = "This setting determines which magnitude value is used in the bailout test. \
		The norm of the selected quantities is tested."
endparam
param realstart
	caption = "Real Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve the real axis, then this parameter sets the \
		initial value of the real component of the hypercomplex number."
	visible = !((@plotplane == "real, e1") || (@plotplane == "real, e2") || (@plotplane == "real, e3") \
		|| (@plotplane == "real, e4") || (@plotplane == "real, e5"))
endparam
param e1start
	caption = "e1 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e1, then this parameter sets the \
		initial value of the e1 component of the hypercomplex number."
	visible = !((@plotplane == "real, e1") || (@plotplane == "e1, e2") || (@plotplane == "e1, e3") \
		|| (@plotplane == "e1, e4") || (@plotplane == "e1, e5"))
endparam
param e2start
	caption = "e2 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e2, then this parameter sets the \
		initial value of the e2 component of the hypercomplex number."
	visible = !((@plotplane == "real, e2") || (@plotplane == "e1, e2") || (@plotplane == "e2, e3") \
		|| (@plotplane == "e2, e4") || (@plotplane == "e2, e5"))
endparam
param e3start
	caption = "e3 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e3, then this parameter sets the \
		initial value of the e3 component of the hypercomplex number."
	visible = !((@plotplane == "real, e3") || (@plotplane == "e1, e3") || (@plotplane == "e2, e3") \
		|| (@plotplane == "e3, e4") || (@plotplane == "e3, e5"))
endparam
param e4start
	caption = "e4 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e4, then this parameter sets the \
		initial value of the e4 component of the hypercomplex number."
	visible = !((@plotplane == "real, e4") || (@plotplane == "e1, e4") || (@plotplane == "e2, e4") \
		|| (@plotplane == "e3, e4") || (@plotplane == "e4, e5"))
endparam
param e5start
	caption = "e5 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e5, then this parameter sets the \
		initial value of the e5 component of the hypercomplex number."
	visible = !((@plotplane == "real, e5") || (@plotplane == "e1, e5") || (@plotplane == "e2, e5") \
		|| (@plotplane == "e3, e5") || (@plotplane == "e4, e5"))
endparam
param bail
    caption = "Bailout Value"
    default = 16.0
    hint = "Value needed to 'escape' to infinity"
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types"
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
	type = "jam-O6-hypercomplex"
	ruleset = ruleset
	plotplane = plotplane
	bailvar = bailvar
	realstart = realstart
	e1start = e1start
	e2start = e2start
	e3start = e3start
	e4start = e4start
	e5start = e5start
	jconstant = #pixel
	bail = bail
	mandy = julia
	julia = mandy
}

jam-O2-hypercomplex {

; If not indicated otherwise below, implemented multiplication rules
; for the basis units 1, i include:
;		1x1=1; 1i = i1 = i.

;	Additional multiplication rules implemented for the imaginary unit i are:
;	Ruleset A:	i^2 = 1 (double numbers)
;	B:			i^2 = 0 (dual numbers)
;	C:			i^2 = 1 + i
;	D:			i^2 = 1 - i
;	E:			i^2 = i - 1
;	F:			i^2 = -1 - i
;	G:			i^2 = -1 (complex numbers, for completeness)

; The bailout variable can be the magnitude of the hypercomplex number, h,
; or, alternatively, the absolute value of any single component.

global:

init:
	complex jc = (0,0) ; Julia constant (Julia) or pixel value (Mandelbrot)
	float h0 = float h1 = 0.0 ; hypercomplex components
	float bailoutvalue = 0.0
	
	; working variables for the iteration
	; An order-2 hypercomplex when squared will generate 3 terms after
	; partial simplification using the multiplication rules.
	
	; (h0 + h1 i)^2 = h0^2 + 2 h0h1 i + h1^2 i^2
	
	float c1 = float c2 = float c3 = 0.0

	if @mandy
	#z = #pixel, jc = #pixel
	else ; Julia
	#z = #pixel, jc = @jconstant
	endif
	
	; initialize the hypercomplex number
	h0 = real(#z)
	h1 = imag(#z)

loop:
	; Iterate the hypercomplex number according to the chosen ruleset,
	; h(n+1) = h(n)^2 + jc

	; First, calculate the 3 coefficients
	c1 = h0 * h0
	c2 = 2 * h0 * h1
	c3 = h1 * h1
	
	; Second, combine the coefficients according to the current ruleset.

	if @ruleset == "A" ; i^2 = 1 (double numbers)
		h0 = c1 + c3
		h1 = c2
	elseif @ruleset == "B" ; i^2 = 0 (dual numbers)
		h0 = c1
		h1 = c2
	elseif @ruleset == "C" ; i^2 = 1 + i
		h0 = c1 + c3
		h1 = c2 + c3
	elseif @ruleset == "D" ; i^2 = 1 - i
		h0 = c1 + c3
		h1 = c2 - c3
	elseif @ruleset == "E" ; i^2 = i - 1
		h0 = c1 - c3
		h1 = c2 + c3
	elseif @ruleset == "F" ; i^2 = -1 - i
		h0 = c1 - c3
		h1 = c2 - c3
	elseif @ruleset == "G" ; i^2 = -1 (standard complex numbers)
		h0 = c1 - c3
		h1 = c2
	endif ; @ruleset
	
	; Next, add the Julia constant or #pixel value to the hypercomplex number
	h0 = h0 + real(jc)
	h1 = h1 + imag(jc)
	#z = h0 + flip(h1)

	; Calculate the value used in the bailout test
	if @bailvar == "hypercomplex norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1))
	elseif @bailvar == "|real|"
		bailoutvalue = abs(h0)
	elseif @bailvar == "|i|"
		bailoutvalue = abs(h1)
	endif ; @bailvar

bailout:
	bailoutvalue < @bail

default:
	title = "Order-2 Hypercomplex Streamlined"
	center = (0,0)
	maxiter = 2500
	method = multipass
	periodicity = 0

heading
	text = "A sampling of order-2 hypercomplex number systems"
endheading

param ruleset
	caption = "Multiplication Ruleset"
	enum = "A" "B" "C" "D" "E" "F" "G"
	default = 0
	hint = "This parameter determines how the basis units of the hypercomplex system \
		combine when multiplied.  The different rules are listed in the comments at \
		the top of the formula entry.  'A' is the Double Numbers, 'B' the Dual Numbers, \
		and 'G' the standard complex numbers."
endparam
param bailvar
	caption = "Bailout Variable"
	enum = "hypercomplex norm" "|real|" "|i|"
	default = 0
	hint = "This setting determines which magnitude value is used in the bailout test. \
		The norm of the selected quantities is tested."
endparam
param bail
    caption = "Bailout Value"
    default = 16.0
    hint = "Value needed to 'escape' to infinity"
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types"
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
	type = "jam-O2-hypercomplex"
	ruleset = ruleset
	bailvar = bailvar
	jconstant = #pixel
	bail = bail
	mandy = julia
	julia = mandy
}

jam-O5-hypercomplex {

;	Simplified version of jam-quintonions with additional rule sets.
;	211206

;	The basis units used are 1, e1, e2, e3, and e4.  For all implemented rule sets,
;		1x1=1; 1xe1 = e1x1 = e1, 1xe2 = e2x1 = e2, 1xe3 = e3x1 = e3, 1xe4 = e4x1 = e4.

;	In addition to the above, the other components of the unit multiplication rules are:
;	Ruleset A:	e1^2 = e2^2 = e3^2 = e4^2 = -1; e1e2 = e3, e2e3 = e4, e3e4 = e1,
;				e4e1 = e2; e2e1 = -e3, e3e2 = -e4, e4e3 = -e1, e1e4 = -e2;
;				e1e3 = e3e1 = e2e4 = e4e2 = 1.
;	B:			Same combination rules as above, except the last line becomes:
;				e1e3 = e3e1 = e2e4 = e4e2 = 0.
;	C:			Same, except e1e3 = e3e1 = e2e4 = e4e2 = -1.
;	D:			Same, except e1e3 = -e3e1 = -1, e2e4 = -e4e2 = 1. [Same as B]
;	E:			Same, except e1e3 = e2+e4, e3e1 = e2-e4, e2e4 = e1+e3, e4e2 = e1-e3.
;	F:			e1^2 = e2, e2^2 = e4, e3^2 = e1, e4^2 = e3; e1e2 = e2e1 = e3;
;					e1e3 = e3e1 = e4; e1e4 = e4e1 = 1; e2e3 = e3e2 = 1;
;					e2e4 = e4e2 = e1; e3e4 = e4e3 = e2 (Olariu's polar 5-complex numbers).
;	G:			e1^2 = e2^2 = e3^2 = e4^2 = -1; e1e2 = e3, e2e3 = e4, e3e4 = e1,
;					e4e1 = e2; e2e1 = -e3, e3e2 = -e4, e4e3 = -e1, e1e4 = -e2;
;					e1e3 = -e3e1 = -e4, e2e4 = -e4e2 = -e1. [Same as B]
;	H:			e1^2 = e2, e2^2 = e3, e3^2 = e4, e4^2 = e1;
;					e1e2 = -e2e1 = e4, e2e3 = -e3e2 = e1, e3e4 = - e4e3 = e2;
;					e1e4 = e4e1 = -1; e1e3 = e3e1 = 1; e2e4 = 1, e4e2 = -1.

; Plotting options are the following planes:
; real-e1, real-e2, real-e3, real-e4, e1-e2, e1-e3, e1-e4, e2-e3, e2-e4, and e3-e4.

; The bailout variable can be the magnitude of the hypercomplex number, h,
; or any pair of these components:  real,e1; real,e2; real,e3; real,e4; e1,e2; e1,e3;
; e1,e4; e2,e3; e2,e4; or e3,e4,
; or, alternatively, the absolute value of any single component.

global:

init:
	complex jc = (0,0) ; Julia constant (Julia) or pixel value (Mandelbrot)
	float jcreal = float jcimag = 0.0
	float bailoutvalue = 0.0
	
	; Working variables for the iteration:
	; The hypercomplex H = h0 + h1e1 + h2e2 + h3e3 + h4e4, where the hs are real (scalars)
	float h0 = float h1 = float h2 = float h3 = float h4 = 0.0
	
	; An order-5 hypercomplex when squared will generate 25 terms before
	; simplification using the multiplication rules.
	; After partial simplification using scalar commutativity, there are
	; 21 individual coefficients.  For simplicity and
	; clarity rather than efficiency, these 21 term coefficients are defined here.
	float c0 = float c1 = float c2 = float c3 = float c4 = float c5 = 0.0
	float c6 = float c7 = float c8 = float c9 = float c10 = float c11 = float c12 = 0.0
	float c13 = float c14 = float c15 = float c16 = float c17 = float c18 = 0.0
	float c19 = float c20 = 0.0
	
	float temp = 0.0

	if @mandy
	#z = #pixel, jc = #pixel
	else ; Julia
	#z = #pixel, jc = @jconstant
	endif
	
	; jc1 and jc2 will be added to the appropriate components of the
	;	hypercomplex number corresponding to the selected plot plane.
	jcreal = real(jc)
	jcimag = imag(jc)

	; initialize the hypercomplex number
	if @plotplane == "real, e1"
		h0 = real(#z)
		h1 = imag(#z)
		h2 = @e2start
		h3 = @e3start
		h4 = @e4start
	elseif @plotplane == "real, e2"
		h0 = real(#z)
		h1 = @e1start
		h2 = imag(#z)
		h3 = @e3start
		h4 = @e4start
	elseif @plotplane == "real, e3"
		h0 = real(#z)
		h1 = @e1start
		h2 = @e2start
		h3 = imag(#z)
		h4 = @e4start
	elseif @plotplane == "real, e4"
		h0 = real(#z)
		h1 = @e1start
		h2 = @e2start
		h3 = @e3start
		h4 = imag(#z)
	elseif @plotplane == "e1, e2"
		h0 = @realstart
		h1 = real(#z)
		h2 = imag(#z)
		h3 = @e3start
		h4 = @e4start
	elseif @plotplane == "e1, e3"
		h0 = @realstart
		h1 = real(#z)
		h2 = @e2start
		h3 = imag(#z)
		h4 = @e4start
	elseif @plotplane == "e1, e4"
		h0 = @realstart
		h1 = real(#z)
		h2 = @e2start
		h3 = @e3start
		h4 = imag(#z)
	elseif @plotplane == "e2, e3"
		h0 = @realstart
		h1 = @e1start
		h2 = real(#z)
		h3 = imag(#z)
		h4 = @e4start
	elseif @plotplane == "e2, e4"
		h0 = @realstart
		h1 = @e1start
		h2 = real(#z)
		h3 = @e3start
		h4 = imag(#z)
	elseif @plotplane == "e3, e4"
		h0 = @realstart
		h1 = @e1start
		h2 = @e2start
		h3 = real(#z)
		h4 = imag(#z)
	endif ; @plotplane

loop:
	; Iterate the hypercomplex number according to the chosen ruleset,
	; h(n+1) = h(n)^2 + jc = h0^2 + h1^2 e1^2 + h2^2 e2^2 + h3^2 e3^2 + h4^2 e4^2 +
	; 2h0h1 e1 + 2h0h2 e2 + 2h0h3 e3 + 2h0h4 e4 + h1h2 e1e2 + h1h2 e2e1 + 
	; h1h3 e1e3 + h1h3 e3e1 + + h1h4 e1e4 + h1h4 e4e1 + h2h3 e2e3 + h2h3 e3e2 + 
	; h2h4 e2e4 + h2h4 e4e2 + h3h4 e3e4 + h3h4 e4e3 + jc

	; First, calculate all 21 independent coefficients c0,...,c20
	c0 = sqr(h0)
	temp = 2 * h0
	c1 = sqr(h1)
	c2 = sqr(h2)
	c3 = sqr(h3)
	c4 = sqr(h4)
	c5 = temp * h1
	c6 = temp * h2
	c7 = temp * h3
	c8 = temp * h4
	c9 = h1 * h2
	c10 = c9
	c11 = h1 * h3
	c12 = c11
	c13 = h1 * h4
	c14 = c13
	c15 = h2 * h3
	c16 = c15
	c17 = h2 * h4
	c18 = c17
	c19 = h3 * h4
	c20 = c19
	
	; Second, combine the coefficients according to the current ruleset.
	if @ruleset == "A"
		h0 = c0 - c1 - c2 - c3 - c4 + c11 + c12 + c17 + c18
		h1 = c5
		h2 = c6
		h3 = c7
		h4 = c8
	elseif @ruleset == "B"
		h0 = c0 - c1 - c2 - c3 - c4
		h1 = c5
		h2 = c6
		h3 = c7
		h4 = c8
	elseif @ruleset == "C"
		h0 = c0 - c1 - c2 - c3 - c4 - c11 - c12 - c17 - c18
		h1 = c5
		h2 = c6
		h3 = c7
		h4 = c8
	elseif @ruleset == "D"
		h0 = c0 - c1 - c2 - c3 - c4
		h1 = c5
		h2 = c6
		h3 = c7
		h4 = c8
	elseif @ruleset == "E"
		h0 = c0 - c1 - c2 - c3 - c4
		h1 = c5 + c17 + c18
		h2 = c6 + c11 + c12
		h3 = c7
		h4 = c8
	elseif @ruleset == "F" ; Olariu's polar 5-complex numbers
		h0 = c0 + c13 + c14 + c15 + c16
		h1 = c5 + c3 + c17 + c18
		h2 = c6 + c1 + c19 + c20
		h3 = c7 + c4 + c9 + c10
		h4 = c8 + c2 + c11 + c12
	elseif @ruleset == "G"
		h0 = c0 - c1 - c2 - c3 - c4
		h1 = c5
		h2 = c6
		h3 = c7
		h4 = c8
	elseif @ruleset == "H"
		h0 = c0 + c11 - c13 + c12 - c14
		h1 = c5 + c4
		h2 = c6 + c1
		h3 = c7 + c2
		h4 = c8 + c3
	endif ; @ruleset
	
	; Next, add the Julia constant or #pixel value to the hypercomplex number
	if @plotplane == "real, e1"
		h0 = h0 + jcreal
		h1 = h1 + jcimag
		#z = h0 + flip(h1)
	elseif @plotplane == "real, e2"
		h0 = h0 + jcreal
		h2 = h2 + jcimag
		#z = h0 + flip(h2)
	elseif @plotplane == "real, e3"
		h0 = h0 + jcreal
		h3 = h3 + jcimag
		#z = h0 + flip(h3)
	elseif @plotplane == "real, e4"
		h0 = h0 + jcreal
		h4 = h4 + jcimag
		#z = h0 + flip(h4)
	elseif @plotplane == "e1, e2"
		h1 = h1 + jcreal
		h2 = h2 + jcimag
		#z = h1 + flip(h2)
	elseif @plotplane == "e1, e3"
		h1 = h1 + jcreal
		h3 = h3 + jcimag
		#z = h1 + flip(h3)
	elseif @plotplane == "e1, e4"
		h1 = h1 + jcreal
		h4 = h4 + jcimag
		#z = h1 + flip(h4)
	elseif @plotplane == "e2, e3"
		h2 = h2 + jcreal
		h3 = h3 + jcimag
		#z = h2 + flip(h3)
	elseif @plotplane == "e2, e4"
		h2 = h2 + jcreal
		h4 = h4 + jcimag
		#z = h2 + flip(h4)
	elseif @plotplane == "e3, e4"
		h3 = h3 + jcreal
		h4 = h4 + jcimag
		#z = h3 + flip(h4)
	endif ; @plotplane

	; Calculate the value used in the bailout test
	if @bailvar == "hypercomplex norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1) + sqr(h2) + sqr(h3) + sqr(h4))
	elseif @bailvar == "real, e1 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1))
	elseif @bailvar == "real, e2 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h2))
	elseif @bailvar == "real, e3 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h3))
	elseif @bailvar == "real, e4 norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h4))
	elseif @bailvar == "e1, e2 norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h2))
	elseif @bailvar == "e1, e3 norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h3))
	elseif @bailvar == "e1, e4 norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h4))
	elseif @bailvar == "e2, e3 norm"
		bailoutvalue = sqrt(sqr(h2) + sqr(h3))
	elseif @bailvar == "e2, e4 norm"
		bailoutvalue = sqrt(sqr(h2) + sqr(h4))
	elseif @bailvar == "e3, e4 norm"
		bailoutvalue = sqrt(sqr(h3) + sqr(h4))
	elseif @bailvar == "|real|"
		bailoutvalue = abs(h0)
	elseif @bailvar == "|e1|"
		bailoutvalue = abs(h1)
	elseif @bailvar == "|e2|"
		bailoutvalue = abs(h2)
	elseif @bailvar == "|e3|"
		bailoutvalue = abs(h3)
	elseif @bailvar == "|e4|"
		bailoutvalue = abs(h4)
	endif ; @bailvar

bailout:
	bailoutvalue < @bail

default:
	title = "Order-5 Hypercomplex Streamlined"
	center = (0,0)
	maxiter = 2500
	method = multipass
	periodicity = 0

heading
	text = "A sampling of order-5 hypercomplex number systems"
endheading

param ruleset
	caption = "Multiplication Ruleset"
	enum = "A" "B" "C" "D" "E" "F" "G" "H"
	default = 0
	hint = "This parameter determines how the basis units of the hypercomplex system \
		combine when multiplied.  The different rules are listed in the comments at \
		the top of the formula entry.  Set 'F' are Olariu's polar 5-complex numbers."
endparam
param plotplane
	caption = "Plot Plane"
	enum = "real, e1" "real, e2" "real, e3" "real, e4" "e1, e2" "e1, e3" "e1, e4" \
		"e2, e3" "e2, e4" "e3, e4"
	default = 0
	hint = "This parameter determines which components of the hypercomplex iterate \
		are plotted on the screen."
endparam
param bailvar
	caption = "Bailout Variable"
	enum = "hypercomplex norm" "real, e1 norm" "real, e2 norm" "real, e3 norm" "real, e4 norm" \
		"e1, e2 norm" "e1, e3 norm" "e1, e4 norm" "e2, e3 norm" "e2, e4 norm" "e3, e4 norm" \
		"|real|" "|e1|" "|e2|" "|e3|" "|e4|"
	default = 0
	hint = "This setting determines which magnitude value is used in the bailout test. \
		The norm of the selected quantities is tested."
endparam
param realstart
	caption = "Real Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve the real axis, then this parameter sets the \
		initial value of the real component of the hypercomplex number."
	visible = (@plotplane == "e1, e2") || (@plotplane == "e1, e3") || (@plotplane == "e1, e4") \
		|| (@plotplane == "e2, e3") || (@plotplane == "e2, e4") || (@plotplane == "e3, e4")
endparam
param e1start
	caption = "e1 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e1, then this parameter sets the \
		initial value of the e1 component of the hypercomplex number."
	visible = (@plotplane == "real, e2") || (@plotplane == "real, e3") || (@plotplane == "real, e4") \
		|| (@plotplane == "e2, e3") || (@plotplane == "e2, e4") || (@plotplane == "e3, e4")
endparam
param e2start
	caption = "e2 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e2, then this parameter sets the \
		initial value of the e2 component of the hypercomplex number."
	visible = (@plotplane == "real, e1") || (@plotplane == "real, e3") || (@plotplane == "real, e4") \
		|| (@plotplane == "e1, e3") || (@plotplane == "e1, e4") || (@plotplane == "e3, e4")
endparam
param e3start
	caption = "e3 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e3, then this parameter sets the \
		initial value of the e3 component of the hypercomplex number."
	visible = (@plotplane == "real, e1") || (@plotplane == "real, e2") || (@plotplane == "real, e4") \
		|| (@plotplane == "e1, e2") || (@plotplane == "e1, e4") || (@plotplane == "e2, e4")
endparam
param e4start
	caption = "e4 Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve e4, then this parameter sets the \
		initial value of the e4 component of the hypercomplex number."
	visible = (@plotplane == "real, e1") || (@plotplane == "real, e2") || (@plotplane == "real, e3") \
		|| (@plotplane == "e1, e2") || (@plotplane == "e1, e3") || (@plotplane == "e2, e3")
endparam
param bail
    caption = "Bailout Value"
    default = 16.0
    hint = "Value needed to 'escape' to infinity"
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types"
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
	type = "jam-O5-hypercomplex"
	ruleset = ruleset
	plotplane = plotplane
	bailvar = bailvar
	realstart = realstart
	e1start = e1start
	e2start = e2start
	e3start = e3start
	e4start = e4start
	jconstant = #pixel
	bail = bail
	mandy = julia
	julia = mandy
}

jam-O4-hypercomplex {

;	Simplified version of jam-quaternions with additional rule sets.
;	211201

;	All implemented multiplication rules for the basis units 1, i, j, k include:
;		1x1=1; 1i = i1 = i; 1j = j1 = j; 1k = k1 = k.

;	Additional multiplication rules implemented for the imaginary units i, j and k are:
;	Ruleset A:	i^2 = j^2 = k^2 = -1; ij = -ji = k, jk = -kj = i, ki = -ik = j (quaternions)
;	B:			i^2 = -1; j^2 = k^2 = 1; ij = -ji = k, jk = -kj = -i; ki = -ik = j (split quaternions)
;	C:			i^2 = -1; j^2 = k^2 = 0; ij = -ji = k, jk = kj = 0, ki = -ik = j (dual complex)
;	D:			i^2 = k^2 = -1, j^2 = 1; ij = ji = k, jk = kj = i, ki = ik = -j (bicomplex/tessarines)
;	E:			i^2 = j^2 = -1; k^2 = 0; ij = -ji = k, jk = -kj = i, ki = -ik = j
;	F:			i^2 = -1; j^2 = 1; k^2 = 0; ij = -ji = k, jk = -kj = i, ki = -ik = j
;	G:			i^2 = k^2 = -1; j^2 = 1; ij = -ji = k, jk = -kj = i, ki = -ik = j
;	H:			i^2 = -1; j^2 = k^2 = 1; ij = -ji = k, jk = -kj = i, ki = -ik = j
;	I:			i^2 = j^2 = k^2 = -1; ij = -ji = k; jk = -kj = i + 1; ki = -ik = j
;	J:			i^2 = -1; j^2 = i + k; k^2 = i - j; ij = -ji = k, jk = -kj = i, ki = -ik = j
;	K:			i^2 = j - 1; j^2 = k - 1; k^2 = i - 1; ij = -ji = k, jk = -kj = i, ki = -ik = j
;	L:			i^2 = j^2 = k^2 = 1; ij = ji = k, ik = ki = j, jk = kj = i (Olariu hyperbolic 4-complex)
;	M:			i^2 = -k^2 = j; j^2 = -1; ij = ji = k, jk = kj = -i, ik = ki = -1 (Olariu planar 4-complex)
;	N:			i^2 = k^2 = j; j^2 = 1; ij = ji = k, jk = kj = i, ik = ki = -1 (Olariu polar 4-complex)

; Plotting options are the real-i, real-j, real-k, i-j, j-k, or ki planes.

; The bailout variable can be the magnitude of the hypercomplex number, h,
; or any pair of these components:  real,i; real,j; real,k; i,j; j,k; or k,i,
; or, alternatively, the absolute value of any single component.

global:

init:
	complex jc = (0,0) ; Julia constant (Julia) or pixel value (Mandelbrot)
	float jcreal = float jcimag = 0.0
	float bailoutvalue = 0.0
	
	; Working variables for the iteration:
	; The hypercomplex H = h0 + h1i + h2j + h3k, where the hs are real (scalars)
	float h0 = float h1 = float h2 = float h3 = 0.0
	
	; An order-4 hypercomplex when squared will generate 16 terms before
	; simplification using the multiplication rules.
	; After partial simplification using scalar commutativity, there are
	; 13 individual coefficients.  For simplicity and
	; clarity rather than efficiency, these 13 term coefficients are defined here.
	
	; h^2 = h0^2 + 2h0h1 i + 2h0h2 j + 2h0h3 k + h1^2 i^2 + h2^2 j^2 + h3^2 k^2 +
	;		h1h2 ij + h1h2 ji + h1h3 ik + h1h3 ki + h2h3 jk + h2h3 kj
	
	float c0 = float c1 = float c2 = float c3 = float c4 = float c5 = 0.0
	float c6 = float c7 = float c8 = float c9 = float c10 = float c11 = float c12 = 0.0
	
	float temp = 0.0

	if @mandy
	#z = #pixel, jc = #pixel
	else ; Julia
	#z = #pixel, jc = @jconstant
	endif
	
	; jcreal and jcimag will be added to the appropriate components of the
	;	hypercomplex number corresponding to the selected plot plane.
	jcreal = real(jc)
	jcimag = imag(jc)

	; initialize the hypercomplex number
	if @plotplane == "real, i"
		h0 = real(#z)
		h1 = imag(#z)
		h2 = @jstart
		h3 = @kstart
	elseif @plotplane == "real, j"
		h0 = real(#z)
		h1 = @istart
		h2 = imag(#z)
		h3 = @kstart
	elseif @plotplane == "real, k"
		h0 = real(#z)
		h1 = @istart
		h2 = @jstart
		h3 = imag(#z)
	elseif @plotplane == "i, j"
		h0 = @realstart
		h1 = real(#z)
		h2 = imag(#z)
		h3 = @kstart
	elseif @plotplane == "j, k"
		h0 = @realstart
		h1 = @istart
		h2 = real(#z)
		h3 = imag(#z)
	elseif @plotplane == "k, i"
		h0 = @realstart
		h1 = imag(#z)
		h2 = @jstart
		h3 = real(#z)
	endif ; @plotplane

loop:
	; Iterate the hypercomplex number according to the chosen ruleset,
	; h(n+1) = h(n)^2 + jc = h0^2 + 2h0h1i + 2h0h2j + 2h0h3k + h1^2i^2 +
	; h2^2j^2 + h3^2k^2 + h1h2ij + h1h2ji + h1h3ik + h1h3ki +
	; h2h3jk + h2h3kj + jc

	; First, calculate all 13 independent coefficients c0,...,c12
	c0 = sqr(h0)
	temp = 2 * h0
	c1 = temp * h1
	c2 = temp * h2
	c3 = temp * h3
	c4 = sqr(h1)
	c5 = sqr(h2)
	c6 = sqr(h3)
	c7 = h1 * h2
	c8 = c7
	c9 = h1 * h3
	c10 = c9
	c11 = h2 * h3
	c12 = c11
	
	; Second, combine the coefficients according to the current ruleset.
	if @ruleset == "A" ; quaternions
		h0 = c0 - c4 - c5 - c6
		h1 = c1
		h2 = c2
		h3 = c3
	elseif @ruleset == "B" ; split quaternions
		h0 = c0 + c5 + c6 - c4
		h1 = c1
		h2 = c2
		h3 = c3
	elseif @ruleset == "C" ; dual complex numbers
		h0 = c0 - c4
		h1 = c1
		h2 = c2
		h3 = c3
	elseif @ruleset == "D" ; bicomplex numbers/tessarines
		h0 = c0 + c5 - c4 - c6
		h1 = c1 + c11 + c12
		h2 = c2 - c9 - c10
		h3 = c3 + c7 + c8
	elseif @ruleset == "E"
		h0 = c0 - c4 - c5
		h1 = c1
		h2 = c2
		h3 = c3
	elseif @ruleset == "F"
		h0 = c0 - c4 + c5
		h1 = c1
		h2 = c2
		h3 = c3
	elseif @ruleset == "G"
		h0 = c0 - c4 + c5 - c6
		h1 = c1
		h2 = c2
		h3 = c3
	elseif @ruleset == "H"
		h0 = c0 - c4 + c5 + c6
		h1 = c1
		h2 = c2
		h3 = c3
	elseif @ruleset == "I"
		h0 = c0 - c4 - c5 - c6 + c11 - c12
		h1 = c1
		h2 = c2
		h3 = c3
	elseif @ruleset == "J"
		h0 = c0 - c4
		h1 = c1 + c5 + c6
		h2 = c2 - c6
		h3 = c3
	elseif @ruleset == "K"
		h0 = c0 - c4 - c5 - c6
		h1 = c1 + c6
		h2 = c2 + c4
		h3 = c3 + c5
	elseif @ruleset == "L" ; Olariu hyperbolic 4-complex
		h0 = c0 + c4 + c5 + c6
		h1 = c1 + c11 + c12
		h2 = c2 + c9 + c10
		h3 = c3 + c7 + c8
	elseif @ruleset == "M"; Olariu planar 4-complex
		h0 = c0 - c5 - c9 - c10
		h1 = c1 - c11 - c12
		h2 = c2 + c4 - c6
		h3 = c3 + c7 + c8
	elseif @ruleset == "N"; Olariu planar 4-complex
		h0 = c0 + c5 - c9 - c10
		h1 = c1 + c11 + c12
		h2 = c2 + c4 + c6
		h3 = c3 + c7 + c8
	endif ; @ruleset
	
	; Next, add the Julia constant or #pixel value to the hypercomplex number
	if @plotplane == "real, i"
		h0 = h0 + jcreal
		h1 = h1 + jcimag
		#z = h0 + flip(h1)
	elseif @plotplane == "real, j"
		h0 = h0 + jcreal
		h2 = h2 + jcimag
		#z = h0 + flip(h2)
	elseif @plotplane == "real, k"
		h0 = h0 + jcreal
		h3 = h3 + jcimag
		#z = h0 + flip(h3)
	elseif @plotplane == "i, j"
		h1 = h1 + jcreal
		h2 = h2 + jcimag
		#z = h1 + flip(h2)
	elseif @plotplane == "j, k"
		h2 = h2 + jcreal
		h3 = h3 + jcimag
		#z = h2 + flip(h3)
	elseif @plotplane == "k, i"
		h3 = h3 + jcreal
		h1 = h1 + jcimag
		#z = h3 + flip(h1)
	endif ; @plotplane

	; Calculate the value used in the bailout test
	if @bailvar == "hypercomplex norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1) + sqr(h2) + sqr(h3))
	elseif @bailvar == "real, i norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1))
	elseif @bailvar == "real, j norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h2))
	elseif @bailvar == "real, k norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h3))
	elseif @bailvar == "i, j norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h2))
	elseif @bailvar == "j, k norm"
		bailoutvalue = sqrt(sqr(h2) + sqr(h3))
	elseif @bailvar == "k, i norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h3))
	elseif @bailvar == "|real|"
		bailoutvalue = abs(h0)
	elseif @bailvar == "|i|"
		bailoutvalue = abs(h1)
	elseif @bailvar == "|j|"
		bailoutvalue = abs(h2)
	elseif @bailvar == "|k|"
		bailoutvalue = abs(h3)
	endif ; @bailvar

bailout:
	bailoutvalue < @bail

default:
	title = "Order-4 Hypercomplex Streamlined"
	center = (0,0)
	maxiter = 2500
	method = multipass
	periodicity = 0

heading
	text = "A sampling of order-4 hypercomplex number systems"
endheading

param ruleset
	caption = "Multiplication Ruleset"
	enum = "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N"
	default = 0
	hint = "This parameter determines how the basis units of the hypercomplex system \
		combine when multiplied.  The different rules are listed in the comments at \
		the top of the formula entry.  Set A are the quaternions, B the split quaternions, \
		C the dual complex numbers, D the bicomplex numbers (tessarines).  Olariu's \
		hyperbolic, planar, and polar 4-complex numbers are sets L, M, and N, respectively."
endparam
param plotplane
	caption = "Plot Plane"
	enum = "real, i" "real, j" "real, k" "i, j" "j, k" "k, i"
	default = 0
	hint = "This parameter determines which components of the hypercomplex iterate \
		are plotted on the screen."
endparam
param bailvar
	caption = "Bailout Variable"
	enum = "hypercomplex norm" "real, i norm" "real, j norm" "real, k norm" "i, j norm" \
		"j, k norm" "k, i norm" "|real|" "|i|" "|j|" "|k|"
	default = 0
	hint = "This setting determines which magnitude value is used in the bailout test. \
		The norm of the selected quantities is tested."
endparam
param realstart
	caption = "Real Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve the real axis, then this parameter sets the \
		initial value of the real component of the hypercomplex number."
	visible = (@plotplane == "i, j") || (@plotplane == "j, k") || (@plotplane == "k, i")
endparam
param istart
	caption = "i Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve i, then this parameter sets the \
		initial value of the i component of the hypercomplex number."
	visible = (@plotplane == "real, j") || (@plotplane == "real, k") || (@plotplane == "j, k")
endparam
param jstart
	caption = "j Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve j, then this parameter sets the \
		initial value of the j component of the hypercomplex number."
	visible = (@plotplane == "real, i") || (@plotplane == "real, k") || (@plotplane == "k, i")
endparam
param kstart
	caption = "k Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' does not involve k, then this parameter sets the \
		initial value of the k component of the hypercomplex number."
	visible = (@plotplane == "real, i") || (@plotplane == "real, j") || (@plotplane == "i, j")
endparam
param bail
    caption = "Bailout Value"
    default = 16.0
    hint = "Value needed to 'escape' to infinity"
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types"
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
	type = "jam-O4-hypercomplex"
	ruleset = ruleset
	plotplane = plotplane
	bailvar = bailvar
	kstart = kstart
	jstart = jstart
	istart = istart
	realstart = realstart
	jconstant = #pixel
	bail = bail
	mandy = julia
	julia = mandy
}

jam-O3-hypercomplex {

;	Simplified version of jam-teronions with expanded rule sets.
;	211201

;	If not indicated otherwise below, implemented multiplication rules
; for the basis units 1, i, j include:
;		1x1=1; 1i = i1 = i; 1j = j1 = j; i^2 = j^2 = -1.

;	Additional multiplication rules implemented for the imaginary units i and j are:
;	Ruleset A:	ij = ji = -1
;	B:			ij = -1; ji = 1
;	C:			ij = 1/2; ji = 1/2
;	D:			ij = j; ji = i
;	E:			ij = -j; ji = i
;	F:			ij = i+j; ji = i-j
;	G:			ij = ji = i+j
;	H:			ij = 1/2 + i; ji = -1/2 + j
;	I:			ij = 1/2 + i; ji = 1/2 + j
;	J:			ij = 1/2 + i; ji = 1/2 - j
;	K:			ij = ji = 0 [Same as B]
; 	L:			j^2 = ij = ji = 0
;	M:			j^2 = 1; ij = i; ji = j
;	N:			j^2 = 1; ij = ji = -1
;	O:			j^2 = 1; ij = j; ji = -i
;	P:			j^2 = 1; ij = -1; ji = 1
;	Q:			j^2 = 1; ij = ji = i + j
;	R:			j^2 = 1; ij = i - j; ji = i + j
;	S:			j^2 = 1; ij = ji = 0 [Same as P]
;	T:			j^2 = 1; ij = i + j; ji = -i - j [Same as P]
;	U:			ij = i + j; ji = -i - j [Same as B]
;	V:			i^2 = j, j^2 = i; ij = ji = 1 (polar hypercomplex (tricomplex) ---
;												see Olariu (2000))
;	W:			ij = ji = 1 + i + j

; Plotting options are the real-i, real-j, or i-j planes.

; The bailout variable can be the magnitude of the hypercomplex number, h,
; or any pair of these components:  real,i; real,j; or i,j, or, alternatively,
; the absolute value of any single component.

global:

init:
	complex jc = (0,0) ; Julia constant (Julia) or pixel value (Mandelbrot)
	float h0 = float h1 = float h2 = 0.0 ; hypercomplex components
	float jc1 = float jc2 = 0.0
	float bailoutvalue = 0.0
	
	; working variables for the iteration
	; An order-3 hypercomplex when squared will generate 9 terms before
	; simplification using the multiplication rules.  For simplicity and
	; clarity rather than efficiency, these 9 term coefficients are defined here.
	
	; (h0 + h1e1 + h2e2)^2 = h0^2 + h0h1e1 + h0h2e2 + h0h1e1 + h1^2e1^2 + 
	;							h1h2e1e2 + h0h2e2 + h1h2e2e1 + h2^2e2^2
	
	float c1 = float c2 = float c3 = float c4 = float c5 = 0.0
	float c6 = float c7 = float c8 = float c9 = 0.0

	if @mandy
	#z = #pixel, jc = #pixel
	else ; Julia
	#z = #pixel, jc = @jconstant
	endif
	
	; jc1 and jc2 will be added to the appropriate components of the
	;	hypercomplex number corresponding to the selected plot plane.
	jc1 = real(jc)
	jc2 = imag(jc)

	; initialize the hypercomplex number
	if @plotplane == "real, i"
		h0 = real(#z)
		h1 = imag(#z)
		h2 = @jstart
	elseif @plotplane == "real, j"
		h0 = real(#z)
		h1 = @istart
		h2 = imag(#z)
	elseif @plotplane == "i, j"
		h0 = @realstart
		h1 = real(#z)
		h2 = imag(#z)
	endif ; @plotplane

loop:
	; Iterate the hypercomplex number according to the chosen ruleset,
	; h(n+1) = h(n)^2 + jc
	; h(n)^2 = h0^2 + h0h1e1 + h0h2e2 + h0h1e1 + h1^2e1^2 +	h1h2e1e2 + h0h2e2 + h1h2e2e1 + h2^2e2^2

	; First, calculate all the 9 coefficients
	c1 = h0 * h0
	c2 = h0 * h1
	c3 = h0 * h2
	c4 = c2 ; scalar multiplication is commutative
	c5 = h1 * h1
	c6 = h1 * h2
	c7 = c3
	c8 = c6
	c9 = h2 * h2
	
	; Second, combine the coefficients according to the current ruleset.
	; Since most rule sets only differ in the ij and ji terms, the other
	; terms can be calculated first.
	h0 = c1 - c5 - c9
	h1 = c2 + c4
	h2 = c3 + c7

	; Now calculate the ij/ji terms and combine appropriately
	if @ruleset == "A" ; ij = ji = -1
		h0 = h0 - c6 - c8
;	elseif @ruleset == "B" ; ij = -1, ji = 1; nothing to do
	elseif @ruleset == "C" ; ij = 1/2, ji = 1/2
		h0 = h0 + (0.5 * (c6 + c8))
	elseif @ruleset == "D" ; ij = j, ji = i
		h2 = h2 + c6
		h1 = h1 + c8
	elseif @ruleset == "E" ; ij = -j, ji = i
		h2 = h2 - c6
		h1 = h1 + c8
	elseif @ruleset == "F" ; ij = i+j, ji = i-j
		h1 = h1 + c6 + c8
		h2 = h2
	elseif @ruleset == "G" ; ij = i+j, ji = i+j
		h1 = h1 + c6 + c8
		h2 = h2 + c6 + c8
	elseif @ruleset == "H" ; ij = 1/2 + i, ji = -1/2 + j
		h1 = h1 + c6
		h2 = h2 + c8
	elseif @ruleset == "I" ; ij = 1/2 + i, ji = 1/2 + j
		h0 = h0 + 0.5 * (c6 + c8)
		h1 = h1 + c6
		h2 = h2 + c8
	elseif @ruleset == "J" ; ij = 1/2 + i, ji = 1/2 - j
		h0 = h0 + 0.5 * (c6 + c8)
		h1 = h1 + c6
		h2 = h2 - c8
;	elseif @ruleset == "K" --- ij = 0, ji = 0, so nothing to do [same as B]
	elseif @ruleset == "L" ; j^2 = ij = ji = 0
		h2 = 0
	elseif @ruleset == "M" ; j^2 = 1; ij = i; ji = j
		h0 = c1 - c5 + c9
		h1 = h1 + c6
		h2 = h2 + c8
	elseif @ruleset == "N" ; j^2 = 1; ij = ji = -1
		h0 = c1 - c5 + c9 - c6 - c8
	elseif @ruleset == "O" ; j^2 = 1; ij = j; ji = -i
		h0 = c1 - c5 + c9
		h1 = h1 - c8
		h2 = h2 + c6
	elseif @ruleset == "P" ; j^2 = 1; ij = -1; ji = 1
		h0 = c1 - c5 + c9
	elseif @ruleset == "Q" ; j^2 = 1; ij = ji = i + j
		h0 = c1 - c5 + c9
		h1 = h1 + c6 + c8
		h2 = h2 + c6 + c8
	elseif @ruleset == "R" ; j^2 = 1; ij = i - j; ji = i + j
		h0 = c1 - c5 + c9
		h1 = h1 + c6 + c8
	elseif @ruleset == "S" ; j^2 = 1; ij = ji = 0 [same as P]
		h0 = c1 - c5 + c9
	elseif @ruleset == "T" ; j^2 = 1; ij = i + j; ji = -i - j [same as P]
		h0 = c1 - c5 + c9
;	elseif @ruleset == "U" ; ij = i + j; ji = -i - j ; [same as B]
	elseif @ruleset == "V" ; i^2 = j, j^2 = 1, ij = ji = 1 (polar hypercomplex)
		h0 = c1 + c6 + c8
		h1 = h1 + c9
		h2 = h2 + c5
	elseif @ruleset == "W" ; i^2 = j^2 = -1, ij = ji = 1 + i + j
		h0 = h0 + c6 + c8
		h1 = h1 + c6 + c8
		h2 = h2 + c6 + c8
	endif ; @ruleset
	
	; Next, add the Julia constant or #pixel value to the hypercomplex number
	if @plotplane == "real, i"
		h0 = h0 + jc1
		h1 = h1 + jc2
		#z = h0 + flip(h1)
	elseif @plotplane == "real, j"
		h0 = h0 + jc1
		h2 = h2 + jc2
		#z = h0 + flip(h2)
	elseif @plotplane == "i, j"
		h1 = h1 + jc1
		h2 = h2 + jc2
		#z = h1 + flip(h2)
	endif ; @plotplane

	; Calculate the value used in the bailout test
	if @bailvar == "hypercomplex norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1) + sqr(h2))
	elseif @bailvar == "real, i norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h1))
	elseif @bailvar == "real, j norm"
		bailoutvalue = sqrt(sqr(h0) + sqr(h2))
	elseif @bailvar == "i, j norm"
		bailoutvalue = sqrt(sqr(h1) + sqr(h2))
	elseif @bailvar == "|real|"
		bailoutvalue = abs(h0)
	elseif @bailvar == "|i|"
		bailoutvalue = abs(h1)
	elseif @bailvar == "|j|"
		bailoutvalue = abs(h2)
	endif ; @bailvar

bailout:
	bailoutvalue < @bail

default:
	title = "Order-3 Hypercomplex Streamlined"
	center = (0,0)
	maxiter = 2500
	method = multipass
	periodicity = 0

heading
	text = "A sampling of order-3 hypercomplex number systems"
endheading

param ruleset
	caption = "Multiplication Ruleset"
	enum = "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" \
		"O" "P" "Q" "R" "S" "T" "U" "V" "W"
	default = 0
	hint = "This parameter determines how the basis units of the hypercomplex system \
		combine when multiplied.  The different rules are listed in the comments at \
		the top of the formula entry."
endparam
param plotplane
	caption = "Plot Plane"
	enum = "real, i" "real, j" "i, j"
	default = 0
	hint = "This parameter determines which components of the hypercomplex iterate \
		are plotted on the screen."
endparam
param bailvar
	caption = "Bailout Variable"
	enum = "hypercomplex norm" "real, i norm" "real, j norm" "i, j norm" "|real|" "|i|" "|j|"
	default = 0
	hint = "This setting determines which magnitude value is used in the bailout test. \
		The norm of the selected quantities is tested."
endparam
param jstart
	caption = "j Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' = 'real, i', then this parameter sets the \
		initial value of the j component of the hypercomplex number."
	visible = @plotplane == "real, i"
endparam
param istart
	caption = "i Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' = 'real, j', then this parameter sets the \
		initial value of the i component of the hypercomplex number."
	visible = @plotplane == "real, j"
endparam
param realstart
	caption = "Real Component Value"
	default = 0.1
	hint = "If parameter 'Plot Plane' = 'i, j', then this parameter sets the \
		initial value of the real component of the hypercomplex number."
	visible = @plotplane == "i, j"
endparam
param bail
    caption = "Bailout Value"
    default = 16.0
    hint = "Value needed to 'escape' to infinity"
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types"
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
	type = "jam-O3-hypercomplex"
	ruleset = ruleset
	plotplane = plotplane
	bailvar = bailvar
	jstart = jstart
	istart = istart
	realstart = realstart
	jconstant = #pixel
	bail = bail
	mandy = julia
	julia = mandy
}

jam-catseye {

  ; jam 8/12/2017
  ; based on the Xaos Catseye formula as deduced from the
  ; source code

init:

	complex jc = (0,0)
	float zreal = float zimag = float pixreal = float piximag = 0.0
	float realpart = float imagpart = 0.0
	float zdenom = 0.0
	float pixdenom = 0.0

	if @mandy
	#z = #pixel, jc = #pixel
	else ; Julia
	#z = #pixel, jc = @jconstant
	endif
	
	pixreal = real(jc), piximag = imag(jc)
	pixdenom = 1/(sqr(pixreal) + sqr(piximag))

loop:

	zdenom = 1/(sqr(real(#z)) + sqr(imag(#z)))
	realpart = (pixreal * real(#z) + piximag * imag(#z)) * zdenom
	imagpart = (-pixreal * imag(#z) + piximag * real(#z)) * zdenom
	
	zreal = (real(#z) * pixreal + imag(#z) * piximag) * pixdenom + realpart
	zimag = (-real(#z) * piximag + imag(#z) * pixreal) * pixdenom + imagpart
	
	realpart = sqr(zreal)
	imagpart = sqr(zimag)
	
	#z = zreal + flip(zimag)

bailout:
  (realpart + imagpart) < @bail + 0.0001

default:
  title = "Xaos Catseye"
  center = (0,0)
  maxiter = 1000
  method = multipass
  periodicity = 0

param bail
    caption = "Bailout Value"
    default = 4.0
    hint = "Value needed to 'escape' to infinity"
  endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types"
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
type = "jam-catseye"
jconstant = #pixel
bail = bail
mandy = julia
julia = mandy
}

jam-factorials { ; jam 030309
  ; Mandelbrot/Julia based on power series incorporating generalized factorials,
  ;        ___
  ; f(z) = \     [(-1)^n]  *  a(n) * z^n / n! .
  ;        /__
  ;         n
  ; The factorial denominator can be a normal factorial, double factorial,
  ; or generalized triple, quadruple, etc. factorials.  Examples:  for double
  ; factorials, 8!! = 8 x 6 x 4 x 2, and 7!! = 7 x 5 x 3 x 1; for triple
  ; factorials, 12!!! = 12 x 9 x 6 x 3, 13!!! = 13 x 10 x 7 x 4 x 1, and
  ; 14!!! = 14 x 11 x 8 x 5 x 2; etc.  The terms of the series so defined may
  ; optionally alternate sign, and the coefficients a(n), exponents n, and
  ; factorial denominator n! (or n!!, n!!!, etc) may depend simply and directly
  ; on n, or each may independently be defined by a function of the form
  ;
  ; coefficient/exponent/factorial = kn + m ,
  ;
  ; where the constants k and m are user-specified.  The starting value of n,
  ; normally 0, may also be specified.  For purposes of this formula, negative
  ; factorials are defined = 1.
  ;
  ; The function is implemented either as a static Taylor series expansion about
  ; z=0 using a fixed, user-specified number of terms (minimally 1 term),
  ; or dynamically using an indefinite number of terms based on the current
  ; iteration count. The z argument may be modified before or after passage to
  ; the series by another overall function, and/or the series terms may be
  ; multiplied by an overall constant.

  ; Some of the options are based on techniques of Dave Makin, as are some of the
  ; series based on simple factorials.  Thanks, Dave!

  ; Contact Joe Maddry (maddry@sri.org) with comments/questions.  Enjoy!

  global:
  ; initialize arrays/variables that will be needed (static mode)
  complex numcoeffs[@staticterms] ; numerator coefficients and final coefficients
  complex exponents[@staticterms] ; the z power
  float lastfactvalues[@factorialorder] ; holds value of last-computed factorial
                                      ; in each factorial series
  int lastfactindexes[@factorialorder] ; holds the integer used to compute the
                                      ; last factorial value in each series
  int sloop = int sloop2 = 0
  int stempint = int stempindex = int scurrentterm = 0

  ; figure the amount each index should be adjusted for computation of
  ; the next factorial
  if @factorialstart == "kn+m"
    int sincrement = @factmultiplier * @factorialorder
  else
    int sincrement = @factorialorder
  endif ; @factorialstart
  bool sfirstset = TRUE ; the first time thru the factorial values array, we have
                        ; to calculate the starting value; after that, we just
                        ; add on to what's already there

  if @mode == "static"
    ; set up the factorials computation
    ; first, set the initial index
    sloop = 0
    while sloop < @factorialorder
      stempindex = (sloop + @firstterm) % @factorialorder
      if stempindex < 0
        stempindex = stempindex + @factorialorder
      endif ; stempindex

      ; increment is subtracted to set the array indexes to the position
      ; immediately before the desired starting index; this index will
      ; then be incremented to the desired starting index later, by the
      ; normal factorial calculation code
      if @factorialstart == "n"
        lastfactindexes[stempindex] = sloop + @firstterm - sincrement
      elseif @factorialstart == "n+1"
        lastfactindexes[stempindex] = sloop + @firstterm + 1 - sincrement
      elseif @factorialstart == "n-1"
        lastfactindexes[stempindex] = sloop + @firstterm - 1 - sincrement
      else ; @factorialstart == "kn+m"
        lastfactindexes[stempindex] = @factmultiplier * (sloop + @firstterm) \
                                  + @factoffset - sincrement
      endif ; @factorialstart
      lastfactvalues[sloop] = 1.0 ; all begin with value = 1
      sloop = sloop + 1
    endwhile ; sloop

    ; compute coefficients for static series
    sloop = 0
    while sloop < @staticterms
      scurrentterm = sloop + @firstterm
      if @coeffnum == "1"
        numcoeffs[sloop] = (1.0,0)
      elseif @coeffnum == "n"
        numcoeffs[sloop] = scurrentterm
      elseif @coeffnum == "n+1"
        numcoeffs[sloop] = scurrentterm + 1
      elseif @coeffnum == "n-1"
        numcoeffs[sloop] = scurrentterm - 1
      elseif @coeffnum == "kn+m"
        numcoeffs[sloop] = @nummultiplier * scurrentterm + @numoffset
      else ; @coeff == 1/n
        if scurrentterm == 0
          numcoeffs[sloop] = 1
        else
          numcoeffs[sloop] = 1/scurrentterm
        endif ; scurrentterm
      endif ; @coeffnum

      ; apply any specified function to the numerator coefficient
      if @coefffunc == "power"
        numcoeffs[sloop] = numcoeffs[sloop]^@numpower
      endif ; @coefffunc
      if @multconst
        if @constpower == (1,0)
          numcoeffs[sloop] = @seriesconst * numcoeffs[sloop]
        elseif @constpower == (0,0)
          numcoeffs[sloop] = @seriesconst^scurrentterm * numcoeffs[sloop]
        elseif @constpower == (-1,0)
          numcoeffs[sloop] = @seriesconst^(@nummultiplier * scurrentterm + @numoffset) * numcoeffs[sloop]
        else ;
          numcoeffs[sloop] = @seriesconst^@constpower * numcoeffs[sloop]
        endif ; @constpower
      endif ; multconst
      if @altsign
        if abs(scurrentterm % 2) == 1
          numcoeffs[sloop] = -numcoeffs[sloop]
        endif ; abs()
      endif ; @altsign

      if @zexponent == "n"
        exponents[sloop] = scurrentterm
      elseif @zexponent == "n+1"
        exponents[sloop] = scurrentterm + 1
      elseif @zexponent == "n-1"
        exponents[sloop] = scurrentterm - 1
      else ; @zexponent == "kn+m"
        exponents[sloop] = @expmultiplier * scurrentterm + @expoffset
      endif ; @zexponent

      ; now calculate the factorial based on the factorial index and the
      ; factorial order
      stempindex = scurrentterm % @factorialorder
      if stempindex < 0
        stempindex = stempindex + @factorialorder
      endif ; stempindex

      ; save old index, calculate next index
      stempint = lastfactindexes[stempindex]
      if sfirstset || (stempint < 1)
        stempint = 1
      endif ; stempint
      lastfactindexes[stempindex] = lastfactindexes[stempindex] + sincrement

      ; calculate next factorial value
      if lastfactindexes[stempindex] > 1
        if lastfactindexes[stempindex] <= @factorialorder
          lastfactvalues[stempindex] = lastfactindexes[stempindex]
        else
          sloop2 = lastfactindexes[stempindex]
          while sloop2 > stempint
            lastfactvalues[stempindex] = lastfactvalues[stempindex] * sloop2
            sloop2 = sloop2 - @factorialorder
          endwhile ; sloop2
        endif ; lastfactindex[]
      endif ; lastfactindex[]

      ; compute final coefficient for current term
      numcoeffs[sloop] = numcoeffs[sloop]/lastfactvalues[stempindex]

      ; move on to next term
      sloop = sloop + 1
      if sloop == @factorialorder
        sfirstset = FALSE ; make sure we don't recalculate each term from beginning
      endif ; sloop
    endwhile ; sloop

  endif ; @static

  init:
  if @mandy
    z = @jconstant, jc = #pixel
  else ; Julia
    z = #pixel, jc = @jconstant
  endif

  ; general variables
  complex ztemp = complex zextra = complex zorig = (0,0)
  complex zsum = @sumconst, complex zprod = @prodconst
  float tempx = float tempy = 0.0
  float vcreal = real(@vectconst), float vcimag = imag(@vectconst)
  int seed = @randseed

  ; declare vars for powers of z
  complex zpower[@staticterms]

  ; initialize arrays/variables that will be needed (dynamic mode)
  complex numcoeff = (0,0); numerator coefficients and final coefficients
  complex exponent = (0,0); the z exponent
  float lastfactvalue[@factorialorder] ; holds value of last-computed factorial
                                      ; in each factorial series
  int lastfactindex[@factorialorder] ; holds the integer used to compute the
                                      ; last factorial value in each series
  int dloop = int dloop2 = 0
  int dtempint = int dtempindex = int dcurrentterm = 0

  ; figure the amount each index should be adjusted for computation of
  ; the next factorial
  if @factorialstart == "kn+m"
    int dincrement = @factmultiplier * @factorialorder
  else
    int dincrement = @factorialorder
  endif ; @factorialstart

  bool dfirstset = TRUE ; the first time thru the factorial values array, we have
                        ; to calculate the starting value; after that, we just
                        ; add on to what's already there

  if @mode == "dynamic"
    ; set up the factorials computation
    ; first, set the initial index
    dloop = 0
    while dloop < @factorialorder
      dtempindex = (dloop + @firstterm) % @factorialorder
      if dtempindex < 0
        dtempindex = dtempindex + @factorialorder
      endif ; dtempindex

      ; increment is subtracted to set the array indexes to the position
      ; immediately before the desired starting index; this index will
      ; then be incremented to the desired starting index later, by the
      ; normal factorial calculation code
      if @factorialstart == "n"
        lastfactindex[dtempindex] = dloop + @firstterm - dincrement
      elseif @factorialstart == "n+1"
        lastfactindex[dtempindex] = dloop + @firstterm + 1 - dincrement
      elseif @factorialstart == "n-1"
        lastfactindex[dtempindex] = dloop + @firstterm - 1 - dincrement
      else ; @factorialstart == "kn+m"
        lastfactindex[dtempindex] = @factmultiplier * (dloop + @firstterm) \
                                  + @factoffset - dincrement
      endif ; @factorialstart
      lastfactvalue[dloop] = 1.0 ; all begin with value = 1
      dloop = dloop + 1
    endwhile ; dloop

    ; compute initial coefficient for dynamic series
    dloop = 0
    if @coeffnum == "1"
      numcoeff = (1.0,0)


    elseif @coeffnum == "n"
      numcoeff = @firstterm
    elseif @coeffnum == "n+1"
      numcoeff = @firstterm + 1
    elseif @coeffnum == "n-1"
      numcoeff = @firstterm - 1
    elseif @coeffnum == "kn+m"
      numcoeff = @nummultiplier * @firstterm + @numoffset
    else
      if @firstterm == 0
        numcoeff = 1
      else
        numcoeff = 1/@firstterm
      endif ; @firstterm
    endif ; @coeffnum

    ; apply any specified function to the numerator coefficient
    if @coefffunc == "power"
      numcoeff = numcoeff^@numpower
    endif ; @coefffunc
    if @multconst
      if @constpower == (1,0)
        numcoeff = @seriesconst * numcoeff
      elseif @constpower == (0,0)
        numcoeff = @seriesconst^@firstterm * numcoeff
      elseif @constpower == (-1,0)
        numcoeff = @seriesconst^(@nummultiplier * @firstterm + @numoffset) * numcoeff
      else ;
        numcoeff = @seriesconst^@constpower * numcoeff
      endif ; @constpower
    endif ; multconst
    if @altsign
      if abs(@firstterm % 2) == 1
        numcoeff = -numcoeff
      endif ; abs()
    endif ; @altsign

    if @zexponent == "n"
      exponent = @firstterm
    elseif @zexponent == "n+1"
      exponent = @firstterm + 1
    elseif @zexponent == "n-1"
      exponent = @firstterm - 1
    else ; @zexponent == "kn+m"
      exponent = @expmultiplier * @firstterm + @expoffset
    endif ; @zexponent

    ; now calculate the factorial based on the factorial index and the
    ; factorial order
    dtempindex = @firstterm % @factorialorder
    if dtempindex < 0
      dtempindex = dtempindex + @factorialorder
    endif ; dtempindex

    ; save old index, calculate next index
    dtempint = lastfactindex[dtempindex]
    if dfirstset || (dtempint < 1)
      dtempint = 1
    endif ; dtempint
    lastfactindex[dtempindex] = lastfactindex[dtempindex] + dincrement

    ; calculate next factorial value
    if lastfactindex[dtempindex] > 1
      if lastfactindex[dtempindex] <= @factorialorder
        lastfactvalue[dtempindex] = lastfactindex[dtempindex]
      else
        dloop2 = lastfactindex[dtempindex]
        while dloop2 > dtempint
          lastfactvalue[dtempindex] = lastfactvalue[dtempindex] * dloop2
          dloop2 = dloop2 - @factorialorder
        endwhile ; dloop2
      endif ; lastfactindex[]
    endif ; lastfactindex[]

    ; compute final coefficient for current term
    numcoeff = numcoeff/lastfactvalue[dtempindex]

    ; move on to next term
    dloop = dloop + 1
    if dloop == @factorialorder
      dfirstset = FALSE ; make sure we don't recalculate each term from beginning
    endif ; dloop

  else ; @mode == "static"
    int loopcount = 0 ; to store iteration count
  endif ; @mode

  ; Pixel/constant initialization section
  if @pixelformula == 1
    jc = jc * jc
  elseif  @pixelformula == 2
    jc = jc * jc * jc
  elseif  @pixelformula == 3
    zextra = jc * jc
    jc = zextra * zextra
  elseif  @pixelformula == 4
    jc = jc ^ @ppower
  elseif  @pixelformula == 5
    jc = 1/jc
  elseif  @pixelformula == 6
    jc = sqrt(jc)
  elseif  @pixelformula == 7
    jc = 1 / ( jc * jc )
  elseif  @pixelformula == 8
    jc = log(jc)
  elseif  @pixelformula == 9
    jc = exp( jc)
  elseif  @pixelformula == 10
    jc = jc^jc
  elseif  @pixelformula == 11
    jc = sin( jc )
  elseif  @pixelformula == 12
    jc = cos( jc )
  elseif  @pixelformula == 13
    jc = tan( jc )
  elseif  @pixelformula == 14
    jc = asin( jc )
  elseif  @pixelformula == 15
    jc = acos( jc )
  elseif  @pixelformula == 16
    jc = atan( jc )
  elseif  @pixelformula == 17
    jc = sinh( jc )
  elseif  @pixelformula == 18
    jc = cosh( jc )
  elseif  @pixelformula == 19
    jc = tanh( jc )
  elseif  @pixelformula == 20
    jc = asinh( jc )
  elseif  @pixelformula == 21
    jc = acosh( jc )
  elseif  @pixelformula == 22
    jc = atanh( jc )
  elseif  @pixelformula == 23
    jc = log( 1/jc )
  elseif  @pixelformula == 24
    jc = log( log( jc ))
  elseif  @pixelformula == 25
    jc = exp( -jc )
  elseif  @pixelformula == 26
    jc = exp( 1/jc )
  elseif  @pixelformula == 27
    jc = jc^(-jc)
  elseif  @pixelformula == 28
    zextra = sin( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 29
    zextra = cos( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 30
    zextra = tan( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 31
    jc = cotan( jc )
  elseif  @pixelformula == 32
    jc = 1/cos( jc )
  elseif  @pixelformula == 33
    jc = 1/sin( jc )
  elseif  @pixelformula == 34
    zextra = cotan( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 35
    zextra = 1/cos( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 36
    zextra = 1/sin( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 37
    zextra = jc^(jc)
    jc = jc^zextra
  elseif  @pixelformula == 38
    zextra = jc^(jc)
    jc = 1/( jc^zextra )
  elseif  @pixelformula == 39
    jc = log(-jc)
  elseif  @pixelformula == 40
    jc = 1/log( jc )
  elseif  @pixelformula == 41
    jc = jc * log( jc )
  elseif  @pixelformula == 42
    jc = sin( jc ) / jc
  elseif  @pixelformula == 43
    jc = cos( jc ) / jc
  elseif  @pixelformula == 44
    jc = sin( jc ) * cos( jc )
  elseif  @pixelformula == 45
    jc = sin( jc^2 )
  elseif  @pixelformula == 46
    jc = exp( -1/jc )
  elseif  @pixelformula == 47
    jc = jc * exp( jc )
  elseif  @pixelformula == 48
    jc = jc * exp( -jc )
  elseif  @pixelformula == 49
    jc = jc * exp( 1/jc )
  elseif  @pixelformula == 50
    jc = jc * exp( -1/jc )
  elseif  @pixelformula == 51
    jc = jc * jc * jc
  elseif  @pixelformula == 52
    jc = 1 / ( jc * jc * jc )
  elseif  @pixelformula == 53
    jc = atan( 1 / jc )
  elseif  @pixelformula == 54
    jc = acos( 1 / jc )
  elseif  @pixelformula == 55
    jc = asin( 1 / jc )
  elseif  @pixelformula == 56
    jc = tan( jc ) / jc
  elseif  @pixelformula == 57
    jc = cotan( jc ) / jc
  elseif  @pixelformula == 58
    jc = 1 / ( jc * cos( jc ))
  elseif  @pixelformula == 59
    jc = 1 / ( jc * sin( jc ))
  elseif  @pixelformula == 60
    jc = jc * sin( jc )
  elseif  @pixelformula == 61
    jc = jc * cos( jc )
  elseif  @pixelformula == 62
    jc = jc * tan( jc )
  elseif  @pixelformula == 63
    jc = jc * cotan( jc )
  elseif  @pixelformula == 64
    jc = jc/cos( jc )
  elseif  @pixelformula == 65
    jc = jc/sin( jc )
  elseif  @pixelformula == 66
    jc = sin( 1/jc )
  elseif  @pixelformula == 67
    jc = cos( 1/jc )
  elseif  @pixelformula == 68
    jc = tan( 1/jc )
  elseif  @pixelformula == 69
    jc = cotan( 1/jc )
  elseif  @pixelformula == 70
    jc = 1/cos( 1/jc )
  elseif  @pixelformula == 71
    jc = 1/sin( 1/jc )
  elseif  @pixelformula == 72
    jc = cotanh( jc )
  elseif  @pixelformula == 73
    jc = 1/cosh( jc )
  elseif  @pixelformula == 74
    jc = 1/sinh( jc )
  elseif  @pixelformula == 75
    jc = atanh( 1/jc )
  elseif  @pixelformula == 76
    jc = acosh( 1/jc )
  elseif  @pixelformula == 77
    jc = asinh( 1/jc )
  elseif @pixelformula == 78
    jc = @coeffpa * jc^@exponentpa + @coeffpb * jc^@exponentpb + \
        @coeffpc * jc^@exponentpc
  elseif  @pixelformula == 79
    zextra = sinh(#z)
    jc = zextra * zextra
  elseif  @pixelformula == 80
    zextra = cosh( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 81
    zextra = tanh(jc)
    jc = zextra * zextra
  elseif  @pixelformula == 82
    zextra = cotanh( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 83
    zextra = (1,0)/cosh(jc)
    jc = zextra * zextra
  elseif  @pixelformula == 84
    zextra = (1,0) / sinh( jc )
    jc = zextra * zextra
  elseif  @pixelformula == 85
    jc = sinh(1/jc)
  elseif  @pixelformula == 86
    jc = cosh(1/jc)
  elseif  @pixelformula == 87
    jc = tanh(1/jc)
  elseif  @pixelformula == 88
    jc = cotanh(1/jc)
  elseif  @pixelformula == 89
    jc = (1,0)/cosh(1/jc)
  elseif  @pixelformula == 90
    jc = (1,0)/sinh(1/jc)
  elseif  @pixelformula == 91
    jc = sin( jc ) * tan(jc)
  elseif  @pixelformula == 92
    jc = sinh(jc) * tanh(jc)
  elseif  @pixelformula == 93
    jc = sinh(jc) * cosh(jc)
  elseif  @pixelformula == 94
    ztemp = sinh(jc), zextra = cosh(jc)
    jc = ztemp*ztemp*zextra*zextra
  elseif  @pixelformula == 95
    ztemp = sin(jc), zextra = cos(jc)
    jc = ztemp*ztemp*zextra*zextra
  elseif  @pixelformula == 96
    zextra = 1/jc
    jc = sin(zextra)*cos(zextra)
  elseif  @pixelformula == 97
    zextra = sin( 1/jc )
    jc = zextra*zextra
  elseif  @pixelformula == 98
    jc = sin(jc) * cos(1/jc)
  elseif  @pixelformula == 99
    jc = sin(jc) * sin(1/jc)
  elseif  @pixelformula == 100
    zextra = log(jc)
    jc = zextra*zextra
  elseif  @pixelformula == 101
    jc = sin(jc) * sin(2*jc)
  elseif @pixelformula == 102
    jc = exp(2*jc)
  elseif  @pixelformula == 103
    jc = exp(-2*jc)
  elseif  @pixelformula == 104
    zextra = 1/jc
    jc = sinh(zextra)*cosh(zextra)
  elseif  @pixelformula == 105
    zextra = sinh( 1/jc )
    jc = zextra*zextra
  elseif  @pixelformula == 106
    jc = sinh(jc) * cosh(1/jc)
  elseif  @pixelformula == 107
    jc = sinh(jc) * sinh(1/jc)
  elseif  @pixelformula == 108
    jc = sin(jc) * sinh(jc)
  elseif  @pixelformula == 109
    jc = sin(jc) * cosh(jc)
  elseif  @pixelformula == 110
    zextra = sin(jc), ztemp = sinh(jc)
    jc = ztemp*ztemp*zextra*zextra
  elseif  @pixelformula == 111
    jc = sin(jc)*exp(jc)
  elseif  @pixelformula == 112
    jc = cos(jc)*exp(jc)
  elseif  @pixelformula == 113
    jc = sinh(jc)*exp(jc)
  elseif  @pixelformula == 114
    jc = cosh(jc)*exp(jc)
  elseif  @pixelformula == 115
    jc = sin(jc)*log(jc)
  elseif  @pixelformula == 116
    jc = cos(jc)*log(jc)
  elseif  @pixelformula == 117
    jc = sinh(jc)*log(jc)
  elseif @pixelformula == 118
    jc = cosh(jc)*log(jc)
  endif ; @pixelformula = 1

  loop:
  if @pmode != 0
    z = z + jc
  endif ; pmode

  zorig = z

  if (@func1app == "prefunction") || (@func1app == "both")
    if @function1 == 1
      z = z * z
    elseif  @function1 == 2
      z = z * z * z
    elseif  @function1 == 3
      zextra = z * z
      z = zextra * zextra
    elseif  @function1 == 4
      z = z ^ @f1power
    elseif  @function1 == 5
      z = 1/z
    elseif  @function1 == 6
      z = sqrt(z)
    elseif  @function1 == 7
      z = 1 / ( z * z )
    elseif  @function1 == 8
      z = log(z)
    elseif  @function1 == 9
      z = exp( z)
    elseif  @function1 == 10
      z = z^z
    elseif  @function1 == 11
      z = sin( z )
    elseif  @function1 == 12
      z = cos( z )
    elseif  @function1 == 13
      z = tan( z )
    elseif  @function1 == 14
      z = asin( z )
    elseif  @function1 == 15
      z = acos( z )
    elseif  @function1 == 16
      z = atan( z )
    elseif  @function1 == 17
      z = sinh( z )
    elseif  @function1 == 18
      z = cosh( z )
    elseif  @function1 == 19
      z = tanh( z )
    elseif  @function1 == 20
      z = asinh( z )
    elseif  @function1 == 21
      z = acosh( z )
    elseif  @function1 == 22
      z = atanh( z )
    elseif  @function1 == 23
      z = log( 1/z )
    elseif  @function1 == 24
      z = log( log( z ))
    elseif  @function1 == 25
      z = exp( -z )
    elseif  @function1 == 26
      z = exp( 1/z )
    elseif  @function1 == 27
      z = z^(-z)
    elseif  @function1 == 28
      zextra = sin( z )
      z = zextra * zextra
    elseif  @function1 == 29
      zextra = cos( z )
      z = zextra * zextra
    elseif  @function1 == 30
      zextra = tan( z )
      z = zextra * zextra
    elseif  @function1 == 31
      z = cotan( z )
    elseif  @function1 == 32
      z = 1/cos( z )
    elseif  @function1 == 33
      z = 1/sin( z )
    elseif  @function1 == 34
      zextra = cotan( z )
      z = zextra * zextra
    elseif  @function1 == 35
      zextra = 1/cos( z )
      z = zextra * zextra
    elseif  @function1 == 36
      zextra = 1/sin( z )
      z = zextra * zextra
    elseif  @function1 == 37
      zextra = z^(z)
      z = z^zextra
    elseif  @function1 == 38
      zextra = z^(z)
      z = 1/( z^zextra )
    elseif  @function1 == 39
      z = log(-z)
    elseif  @function1 == 40
      z = 1/log( z )
    elseif  @function1 == 41
      z = z * log( z )
    elseif  @function1 == 42
      z = sin( z ) / z
    elseif  @function1 == 43
      z = cos( z ) / z
    elseif  @function1 == 44
      z = sin( z ) * cos( z )
    elseif  @function1 == 45
      z = sin( z^2 )
    elseif  @function1 == 46
      z = exp( -1/z )
    elseif  @function1 == 47
      z = z * exp( z )
    elseif  @function1 == 48
      z = z * exp( -z )
    elseif  @function1 == 49
      z = z * exp( 1/z )
    elseif  @function1 == 50
      z = z * exp( -1/z )
    elseif  @function1 == 51
      z = z * z * z
    elseif  @function1 == 52
      z = 1 / ( z * z * z )
    elseif  @function1 == 53
      z = atan( 1 / z )
    elseif  @function1 == 54
      z = acos( 1 / z )
    elseif  @function1 == 55
      z = asin( 1 / z )
    elseif  @function1 == 56
      z = tan( z ) / z
    elseif  @function1 == 57
      z = cotan( z ) / z
    elseif  @function1 == 58
      z = 1 / ( z * cos( z ))
    elseif  @function1 == 59
      z = 1 / ( z * sin( z ))
    elseif  @function1 == 60
      z = z * sin( z )
    elseif  @function1 == 61
      z = z * cos( z )
    elseif  @function1 == 62
      z = z * tan( z )
    elseif  @function1 == 63
      z = z * cotan( z )
    elseif  @function1 == 64
      z = z/cos( z )
    elseif  @function1 == 65
      z = z/sin( z )
    elseif  @function1 == 66
      z = sin( 1/z )
    elseif  @function1 == 67
      z = cos( 1/z )
    elseif  @function1 == 68
      z = tan( 1/z )
    elseif  @function1 == 69
      z = cotan( 1/z )
    elseif  @function1 == 70
      z = 1/cos( 1/z )
    elseif  @function1 == 71
      z = 1/sin( 1/z )
    elseif  @function1 == 72
      z = cotanh( z )
    elseif  @function1 == 73
      z = 1/cosh( z )
    elseif  @function1 == 74
      z = 1/sinh( z )
    elseif  @function1 == 75
      z = atanh( 1/z )
    elseif  @function1 == 76
      z = acosh( 1/z )
    elseif  @function1 == 77
      z = asinh( 1/z )
    elseif @function1 == 78
      z = exp(z*z)
    elseif  @function1 == 79
      zextra = sinh(#z)
      z = zextra * zextra
    elseif  @function1 == 80
      zextra = cosh( z )
      z = zextra * zextra
    elseif  @function1 == 81
      zextra = tanh(z)
      z = zextra * zextra
    elseif  @function1 == 82
      zextra = cotanh( z )
      z = zextra * zextra
    elseif  @function1 == 83
      zextra = (1,0)/cosh(z)
      z = zextra * zextra
    elseif  @function1 == 84
      zextra = (1,0) / sinh( z )
      z = zextra * zextra
    elseif  @function1 == 85
      z = sinh(1/z)
    elseif  @function1 == 86
      z = cosh(1/z)
    elseif  @function1 == 87
      z = tanh(1/z)
    elseif  @function1 == 88
      z = cotanh(1/z)
    elseif  @function1 == 89
      z = (1,0)/cosh(1/z)
    elseif  @function1 == 90
      z = (1,0)/sinh(1/z)
    elseif  @function1 == 91
      z = sin( z ) * tan(z)
    elseif  @function1 == 92
      z = sinh(z) * tanh(z)
    elseif  @function1 == 93
      z = sinh(z) * cosh(z)
    elseif  @function1 == 94
      ztemp = sinh(z), zextra = cosh(z)
      z = ztemp*ztemp*zextra*zextra
    elseif  @function1 == 95
      ztemp = sin(z), zextra = cos(z)
      z = ztemp*ztemp*zextra*zextra
    elseif  @function1 == 96
      zextra = 1/z
      z = sin(zextra)*cos(zextra)
    elseif  @function1 == 97
      zextra = sin( 1/z )
      z = zextra*zextra
    elseif  @function1 == 98
      z = sin(z) * cos(1/z)
    elseif  @function1 == 99
      z = sin(z) * sin(1/z)
    elseif  @function1 == 100
      zextra = log(z)
      z = zextra*zextra
    elseif  @function1 == 101
      z = sin(z) * sin(2*z)
    elseif @function1 == 102
      z = exp(2*z)
    elseif  @function1 == 103
      z = exp(-2*z)
    elseif  @function1 == 104
      zextra = 1/z
      z = sinh(zextra)*cosh(zextra)
    elseif  @function1 == 105
      zextra = sinh( 1/z )
      z = zextra*zextra
    elseif  @function1 == 106
      z = sinh(z) * cosh(1/z)
    elseif  @function1 == 107
      z = sinh(z) * sinh(1/z)
    elseif  @function1 == 108
      z = sin(z) * sinh(z)
    elseif  @function1 == 109
      z = sin(z) * cosh(z)
    elseif  @function1 == 110
      zextra = sin(z), ztemp = sinh(z)
      z = ztemp*ztemp*zextra*zextra
    elseif  @function1 == 111
      z = sin(z)*exp(z)
    elseif  @function1 == 112
      z = cos(z)*exp(z)
    elseif  @function1 == 113
      z = sinh(z)*exp(z)
    elseif  @function1 == 114
      z = cosh(z)*exp(z)
    elseif  @function1 == 115
      z = sin(z)*log(z)
    elseif  @function1 == 116
      z = cos(z)*log(z)
    elseif  @function1 == 117
      z = sinh(z)*log(z)
    elseif @function1 == 118
      z = cosh(z)*log(z)
    elseif @function1 == 119
      z = exp(-z*z)
    elseif @function1 == 120
      z = exp(1/(z*z))
    elseif @function1 == 121
      z = exp(-1/(z*z))
    endif ; @function1
  endif ; @func1app

  if @summode
    z = z + zsum
    zsum = z
  endif ; @summode

  if @prodmode
    if z != (0,0)
      z = z * zprod
      zprod = z
    endif ; z
  endif ; @prodmode

  if @matrixmode
    tempx = @matconst11 * real(z) + @matconst12 * imag(z)
    tempy = @matconst21 * real(z) + @matconst22 * imag(z)
    z = tempx + flip(tempy)
  endif ; @matrixmode

  if @vectormode
    z = z + vcreal + flip(vcimag)
    if @vectperturb
      seed = random(seed)
      tempx = @vperturbamt * seed / #randomrange
      vcreal = vcreal + tempx * vcreal
      vcimag = vcimag + tempx * vcimag
    endif ; @vectperturb
  endif ; @vectormode

  ztemp = (0,0)
  if @mode == "static" ; standard Taylor series expansion
    loopcount = 0
    while loopcount < @staticterms
      zpower[loopcount] = z^exponents[loopcount]
      ztemp = ztemp + numcoeffs[loopcount] * zpower[loopcount]
      loopcount = loopcount + 1
    endwhile ; loopcount
  else ; @mode == dynamic; number of terms based on iteration count
    ; calculate the next term in the series
    zpower[0] = z^exponent
    ztemp = numcoeff * zpower[0]

    ; now update coeffs, factorials, exponents for next iteration
    ; loop is now the number of the current iteration
    dcurrentterm = dloop + @firstterm
    if @coeffnum == "1"
      numcoeff = (1.0,0)
    elseif @coeffnum == "n"
      numcoeff = dcurrentterm
    elseif @coeffnum == "n+1"
      numcoeff = dcurrentterm + 1
    elseif @coeffnum == "n-1"
      numcoeff = dcurrentterm - 1
    elseif @coeffnum == "kn+m"
      numcoeff = @nummultiplier * dcurrentterm + @numoffset
    else
      if dcurrentterm == 0
        numcoeff = 1
      else
        numcoeff = 1/dcurrentterm
      endif ; dcurrentterm
    endif ; @coeffnum

    ; apply any specified function to the numerator coefficient
    if @coefffunc == "power"
      numcoeff = numcoeff^@numpower
    endif ; @coefffunc
    if @multconst
      numcoeff = @seriesconst * numcoeff
      if @constpower == (1,0)
        numcoeff = @seriesconst * numcoeff
      elseif @constpower == (0,0)
        numcoeff = @seriesconst^dcurrentterm * numcoeff
      elseif @constpower == (-1,0)
        numcoeff = @seriesconst^(@nummultiplier * dcurrentterm + @numoffset) * numcoeff
      else ;
        numcoeff = @seriesconst^@constpower * numcoeff
      endif ; @constpower
    endif ; multconst
    if @altsign
      if abs(dcurrentterm % 2) == 1
        numcoeff = -numcoeff
      endif ; abs()
    endif ; @altsign

    if @zexponent == "n"
      exponent = dcurrentterm
    elseif @zexponent == "n+1"
      exponent = dcurrentterm + 1
    elseif @zexponent == "n-1"
      exponent = dcurrentterm - 1
    else ; @zexponent == "kn+m"
      exponent = @expmultiplier * dcurrentterm + @expoffset
    endif ; @zexponent

    ; now calculate the next factorial based on the factorial index and the
    ; factorial order
    dtempindex = dcurrentterm % @factorialorder
    if dtempindex < 0
      dtempindex = dtempindex + @factorialorder
    endif ; dtempindex

    ; save old index, calculate next index
    dtempint = lastfactindex[dtempindex]
    if dfirstset || (dtempint < 1)
      dtempint = 1
    endif ; dtempint
    lastfactindex[dtempindex] = lastfactindex[dtempindex] + dincrement

    ; calculate next factorial value
    if lastfactindex[dtempindex] > 1
      if lastfactindex[dtempindex] <= @factorialorder
        lastfactvalue[dtempindex] = lastfactindex[dtempindex]
      else
        dloop2 = lastfactindex[dtempindex]
        while dloop2 > dtempint
          lastfactvalue[dtempindex] = lastfactvalue[dtempindex] * dloop2
          dloop2 = dloop2 - @factorialorder
        endwhile ; dloop2
      endif ; lastfactindex[]
    endif ; lastfactindex[]

    ; compute final coefficient for current term
    numcoeff = numcoeff/lastfactvalue[dtempindex]

    ; move on to next term
    dloop = dloop + 1
    if dloop == @factorialorder
      dfirstset = FALSE ; make sure we don't recalculate each term from beginning
    endif ; dloop
  endif ; @mode
  z = ztemp

  if (@func1app == "postfunction") || (@func1app == "both")
    if @function1 == 1
      z = z * z
    elseif  @function1 == 2
      z = z * z * z
    elseif  @function1 == 3
      zextra = z * z
      z = zextra * zextra
    elseif  @function1 == 4
      z = z ^ @f1power
    elseif  @function1 == 5
      z = 1/z
    elseif  @function1 == 6
      z = sqrt(z)
    elseif  @function1 == 7
      z = 1 / ( z * z )
    elseif  @function1 == 8
      z = log(z)
    elseif  @function1 == 9
      z = exp( z)
    elseif  @function1 == 10
      z = z^z
    elseif  @function1 == 11
      z = sin( z )
    elseif  @function1 == 12
      z = cos( z )
    elseif  @function1 == 13
      z = tan( z )
    elseif  @function1 == 14
      z = asin( z )
    elseif  @function1 == 15
      z = acos( z )
    elseif  @function1 == 16
      z = atan( z )
    elseif  @function1 == 17
      z = sinh( z )
    elseif  @function1 == 18
      z = cosh( z )
    elseif  @function1 == 19
      z = tanh( z )
    elseif  @function1 == 20
      z = asinh( z )
    elseif  @function1 == 21
      z = acosh( z )
    elseif  @function1 == 22
      z = atanh( z )
    elseif  @function1 == 23
      z = log( 1/z )
    elseif  @function1 == 24
      z = log( log( z ))
    elseif  @function1 == 25
      z = exp( -z )
    elseif  @function1 == 26
      z = exp( 1/z )
    elseif  @function1 == 27
      z = z^(-z)
    elseif  @function1 == 28
      zextra = sin( z )
      z = zextra * zextra
    elseif  @function1 == 29
      zextra = cos( z )
      z = zextra * zextra
    elseif  @function1 == 30
      zextra = tan( z )
      z = zextra * zextra
    elseif  @function1 == 31
      z = cotan( z )
    elseif  @function1 == 32
      z = 1/cos( z )
    elseif  @function1 == 33
      z = 1/sin( z )
    elseif  @function1 == 34
      zextra = cotan( z )
      z = zextra * zextra
    elseif  @function1 == 35
      zextra = 1/cos( z )
      z = zextra * zextra
    elseif  @function1 == 36
      zextra = 1/sin( z )
      z = zextra * zextra
    elseif  @function1 == 37
      zextra = z^(z)
      z = z^zextra
    elseif  @function1 == 38
      zextra = z^(z)
      z = 1/( z^zextra )
    elseif  @function1 == 39
      z = log(-z)
    elseif  @function1 == 40
      z = 1/log( z )
    elseif  @function1 == 41
      z = z * log( z )
    elseif  @function1 == 42
      z = sin( z ) / z
    elseif  @function1 == 43
      z = cos( z ) / z
    elseif  @function1 == 44
      z = sin( z ) * cos( z )
    elseif  @function1 == 45
      z = sin( z^2 )
    elseif  @function1 == 46
      z = exp( -1/z )
    elseif  @function1 == 47
      z = z * exp( z )
    elseif  @function1 == 48
      z = z * exp( -z )
    elseif  @function1 == 49
      z = z * exp( 1/z )
    elseif  @function1 == 50
      z = z * exp( -1/z )
    elseif  @function1 == 51
      z = z * z * z
    elseif  @function1 == 52
      z = 1 / ( z * z * z )
    elseif  @function1 == 53
      z = atan( 1 / z )
    elseif  @function1 == 54
      z = acos( 1 / z )
    elseif  @function1 == 55
      z = asin( 1 / z )
    elseif  @function1 == 56
      z = tan( z ) / z
    elseif  @function1 == 57
      z = cotan( z ) / z
    elseif  @function1 == 58
      z = 1 / ( z * cos( z ))
    elseif  @function1 == 59
      z = 1 / ( z * sin( z ))
    elseif  @function1 == 60
      z = z * sin( z )
    elseif  @function1 == 61
      z = z * cos( z )
    elseif  @function1 == 62
      z = z * tan( z )
    elseif  @function1 == 63
      z = z * cotan( z )
    elseif  @function1 == 64
      z = z/cos( z )
    elseif  @function1 == 65
      z = z/sin( z )
    elseif  @function1 == 66
      z = sin( 1/z )
    elseif  @function1 == 67
      z = cos( 1/z )
    elseif  @function1 == 68
      z = tan( 1/z )
    elseif  @function1 == 69
      z = cotan( 1/z )
    elseif  @function1 == 70
      z = 1/cos( 1/z )
    elseif  @function1 == 71
      z = 1/sin( 1/z )
    elseif  @function1 == 72
      z = cotanh( z )
    elseif  @function1 == 73
      z = 1/cosh( z )
    elseif  @function1 == 74
      z = 1/sinh( z )
    elseif  @function1 == 75
      z = atanh( 1/z )
    elseif  @function1 == 76
      z = acosh( 1/z )
    elseif  @function1 == 77
      z = asinh( 1/z )
    elseif @function1 == 78
      z = exp(z*z)
    elseif  @function1 == 79
      zextra = sinh(#z)
      z = zextra * zextra
    elseif  @function1 == 80
      zextra = cosh( z )
      z = zextra * zextra
    elseif  @function1 == 81
      zextra = tanh(z)
      z = zextra * zextra
    elseif  @function1 == 82
      zextra = cotanh( z )
      z = zextra * zextra
    elseif  @function1 == 83
      zextra = (1,0)/cosh(z)
      z = zextra * zextra
    elseif  @function1 == 84
      zextra = (1,0) / sinh( z )
      z = zextra * zextra
    elseif  @function1 == 85
      z = sinh(1/z)
    elseif  @function1 == 86
      z = cosh(1/z)
    elseif  @function1 == 87
      z = tanh(1/z)
    elseif  @function1 == 88
      z = cotanh(1/z)
    elseif  @function1 == 89
      z = (1,0)/cosh(1/z)
    elseif  @function1 == 90
      z = (1,0)/sinh(1/z)
    elseif  @function1 == 91
      z = sin( z ) * tan(z)
    elseif  @function1 == 92
      z = sinh(z) * tanh(z)
    elseif  @function1 == 93
      z = sinh(z) * cosh(z)
    elseif  @function1 == 94
      ztemp = sinh(z), zextra = cosh(z)
      z = ztemp*ztemp*zextra*zextra
    elseif  @function1 == 95
      ztemp = sin(z), zextra = cos(z)
      z = ztemp*ztemp*zextra*zextra
    elseif  @function1 == 96
      zextra = 1/z
      z = sin(zextra)*cos(zextra)
    elseif  @function1 == 97
      zextra = sin( 1/z )
      z = zextra*zextra
    elseif  @function1 == 98
      z = sin(z) * cos(1/z)
    elseif  @function1 == 99
      z = sin(z) * sin(1/z)
    elseif  @function1 == 100
      zextra = log(z)
      z = zextra*zextra
    elseif  @function1 == 101
      z = sin(z) * sin(2*z)
    elseif @function1 == 102
      z = exp(2*z)
    elseif  @function1 == 103
      z = exp(-2*z)
    elseif  @function1 == 104
      zextra = 1/z
      z = sinh(zextra)*cosh(zextra)
    elseif  @function1 == 105
      zextra = sinh( 1/z )
      z = zextra*zextra
    elseif  @function1 == 106
      z = sinh(z) * cosh(1/z)
    elseif  @function1 == 107
      z = sinh(z) * sinh(1/z)
    elseif  @function1 == 108
      z = sin(z) * sinh(z)
    elseif  @function1 == 109
      z = sin(z) * cosh(z)
    elseif  @function1 == 110
      zextra = sin(z), ztemp = sinh(z)
      z = ztemp*ztemp*zextra*zextra
    elseif  @function1 == 111
      z = sin(z)*exp(z)
    elseif  @function1 == 112
      z = cos(z)*exp(z)
    elseif  @function1 == 113
      z = sinh(z)*exp(z)
    elseif  @function1 == 114
      z = cosh(z)*exp(z)
    elseif  @function1 == 115
      z = sin(z)*log(z)
    elseif  @function1 == 116
      z = cos(z)*log(z)
    elseif  @function1 == 117
      z = sinh(z)*log(z)
    elseif @function1 == 118
      z = cosh(z)*log(z)
    elseif @function1 == 119
      z = exp(-z*z)
    elseif @function1 == 120
      z = exp(1/(z*z))
    elseif @function1 == 121
      z = exp(-1/(z*z))
    endif ; @function1
  endif ; @func1app

  if @blend
    z = @weight1*z + @weight2*zorig^@blendpower
  endif ; @blend

  if @pmode != 1
    z = z + jc
  endif ; pmode

  bailout:
  |z| < @bail

  default:
  title = "zFactorial Fun"
  center = (0,0)
  maxiter = 100
  method = multipass
  periodicity = 0
  magn = 0.75
  
  heading
  	caption = "There is a newer version of this formula"
  endheading

  param factorialorder
    caption = "Factorial Order"
    default = 1
    min = 1
    hint = "This value defines how the factorial denominator is defined.  1 = \
          normal factorials, 2 = double factorials (2x4x6x... or 1x3x5x...), \
          3 = triple factorials (3x6x9x... or 2x5x8x... or 1x4x7x...), etc.  \
          Integers >= 1 only"
  endparam
  param firstterm
    caption = "First Term (n)"
    default = 0
    hint = "This value sets the initial value of n, the index for the Taylor \
          series.  It is used in defining the factorial values, coefficients, \
          and z exponents.  Integers only"
  endparam
  param factorialstart
    caption = "Factorial Index"
    enum = "n" "n+1" "n-1" "kn+m"
    default = 0
    hint = "This parameter defines how the factorial index is computed from \
          the Taylor series index, 'First Term (n).  For 'kn+m', also set \
          parameters 'Factorial Multiplier' and 'Factorial Offset' (k and m, \
          respectively)"
  endparam
  param factmultiplier
    caption = "Factorial Multiplier k"
    default = 1
    hint = "If param 'Factorial Index' is set to 'kn+m', then this value \
          is the multiplier, k.  Integers only"
    visible = @factorialstart == "kn+m"
  endparam
  param factoffset
    caption = "Factorial Offset m"
    default = 0
    hint = "If param 'Factorial Index' is set to 'kn+m', then this value \
          is the offset, m.  Integers only"
    visible = @factorialstart == "kn+m"
  endparam
  param coeffnum
    caption = "Coefficient"
    enum = "1" "n" "n+1" "n-1" "kn+m" "1/n"
    default = 0
    hint = "This parameter defines the coefficient of each term in the series \
          (except for the factorial denominator), in terms of the series index, \
          n.  For 'kn+m', also set params 'Coeff Multiplier' (k) and 'Coeff \
          Offset' (m)"
  endparam
  param nummultiplier
    caption = "Coeff Multiplier k"
    default = (2,0)
    hint = "If param 'Coefficient' is set to 'kn+m', then this value \
          is the multiplier, k.  Complex value"
    visible = (@coeffnum == "kn+m") || (@constpower == (-1,0))
  endparam
  param numoffset
    caption = "Coeff Offset m"
    default = (1,0)
    hint = "If param 'Coefficient' is set to 'kn+m', then this value \
          is the offset, m.  Complex value"
    visible = @coeffnum == "kn+m"
  endparam
  param coefffunc
    caption = "Coeff Function"
    enum = "none" "power"
    default = 0
    hint = "Each term coefficient can be fed to this function.  The function \
          is executed before optional sign alternation and multiplication by \
          a constant are applied"
  endparam
  param numpower
    caption = "Coeff Power"
    default = (2,0)
    hint = "If param 'Coeff Function' is set to 'power', then this value is \
          used as the exponent.  Complex value"
    visible = @coefffunc == "power"
  endparam
  param multconst
    caption = "Mult Coeff?"
    default = FALSE
    hint = "If enabled, then each coefficient term will be multiplied by \
          a complex constant value, set by param 'Series Multiplier'.  The \
          multiplication is done after application of 'Coeff Function'"
  endparam
  param seriesconst
    caption = "Series Multiplier"
    default = (-1,0)
    hint = "If 'Mult Coeff?' is enabled, then this value is multiplied \
          by each term's coefficient in the series.  Complex value. \
          This multiplier can optionally be raised to a power by setting \
          the exponent param 'Constant Power'"
    visible = @multconst == TRUE
  endparam
  param constpower
    caption = "Constant Power"
    default = (1,0)
    hint = "If 'Mult Coeff' is enabled, then the constant 'Series Multiplier' \
          is raised to this power before being multiplied by the series.  \
          The special value of (0,0) can be used to set the exponent of \
          'Series Multiplier' to 'n', the current series term; the special \
          value (-1,0) sets the multiplier exponent to the current value of \
          the coeeficient 'kn+m'.  Complex value"
    visible = @multconst == TRUE
  endparam
  param zexponent
    caption = "Exponent Index"
    enum = "n" "n+1" "n-1" "kn+m"
    default = 0
    hint = "This parameter defines the z exponent of each term in the series, \
          in terms of the series index, n.  For 'kn+m', also set params 'Exponent \
          Multiplier' (k) and 'Exponent Offset' (m)"
  endparam
  param expmultiplier
    caption = "Exp Multiplier k"
    default = (2,0)
    hint = "If param 'Exponent Index' is set to 'kn+m', then this value \
          is the multiplier, k.  Complex value"
    visible = @zexponent == "kn+m"
  endparam
  param expoffset
    caption = "Exp Offset m"
    default = (1,0)
    hint = "If param 'Exponent Index' is set to 'kn+m', then this value \
          is the offset, m.  Complex value"
    visible = @zexponent == "kn+m"
  endparam
  param mode
    caption = "Iteration Mode"
    default = 0
    enum = "static" "dynamic"
    hint = "This parameter determines how the series is iterated.  If 'static', \
          then each iteration sends the current z to a partial Taylors series \
          employing a fixed number of terms, as set by param 'Static Terms'.  If \
          'dynamic' is set, then each iteration uses z to compute just a single \
          term in the series (the term corresponding to the next n)"
  endparam
  param staticterms
    caption = "Static Terms"
    default = 8
    min = 1
    hint = "If param 'Iteration Mode' is set to 'static', then this value \
          determines how many terms of the series are used in the iteration.  \
          Integers >= 1 only"
    visible = @mode == "static"
  endparam
  param altsign
    caption = "Alternate Terms?"
    default = TRUE
    hint = "If enabled, the terms of the Taylor series will alternate in sign; \
          otherwise, all terms are of the same sign"
  endparam
  param summode
    caption = "Sumarize?"
    default = FALSE
    hint = "Like Dave Makin's 'iterate the sum' option.  If enabled, set param \
          'Sumarize Constant'"
  endparam
  param sumconst
    caption = "Sumarize Const"
    default = (0,0)
    hint = "Initial constant for 'Sumarize'.  Complex value"
    visible = @summode == TRUE
  endparam
  param prodmode
    caption = "Multiprize?"
    default = FALSE
    hint = "Like Dave Makin's 'iterate the product' option.  If enabled, set \
          param 'Multiprize Constant'"
  endparam
  param prodconst
    caption = "Multiprize Const"
    default = (1,0)
    hint = "Initial constant for 'Multiprize'.  Complex value"
    visible = @prodmode == TRUE
  endparam
  param matrixmode
    caption = "Matricize?"
    default = FALSE
    hint = "z can be multipled by a general 2x2 matrix before iteration.  If \
          enabled, set the 4 constants 'Matricize 1,1', 'Matricize 1,2', \
          'Matricize 2,1', and 'Matricize 2,2'"
  endparam
  param matconst11
    caption = "Matricize 1,1"
    default = 0.866025403784438646763723170752936
    hint = "Row 1, Column 1 constant for 'Matricize'.  Float value"
    visible = @matrixmode == TRUE
  endparam
  param matconst12
    caption = "Matricize 1,2"
    default = -0.5
    hint = "Row 1, Column 2 constant for 'Matricize'.  Float value"
    visible = @matrixmode == TRUE
  endparam
  param matconst21
    caption = "Matricize 2,1"
    default = 0.5
    hint = "Row 2, Column 1 constant for 'Matricize'.  Float value"
    visible = @matrixmode == TRUE
  endparam
  param matconst22
    caption = "Matricize 2,2"
    default = 0.866025403784438646763723170752936
    hint = "Row 2, Column 2 constant for 'Matricize'.  Float value"
    visible = @matrixmode == TRUE
  endparam
  param vectormode
    caption = "Vectorize?"
    default = FALSE
    hint = "z can be translated by a general 2D vector before iteration.  If \
          enabled, set param 'Vectorize Const'"
  endparam
  param vectconst
    caption = "Vectorize Constant"
    default = (1,-1)
    hint = "X- (real) and Y- (imag) components of initial constant for \
          'Vectorrize'.  Complex value"
    visible = @vectormode == TRUE
  endparam
  param vectperturb
    caption = "Perturb Vector?"
    default = FALSE
    hint = "If enabled, then each iteration the value of 'Vectorize Constant' \
          is modified based on the value of param 'Perturb Strength'"
    visible = @vectormode == TRUE
  endparam
  param vperturbamt
    caption = "Perturb Strength"
    default = 0.1
    hint = "If 'Perturb Vector' is enabled, this value is the amount of \
          perturbation each iteration.  Float value"
    visible = @vectperturb == TRUE
  endparam
  param randseed
    caption = "Random Seed"
    default = 1111
    hint = "If 'Perturb Vector' is enabled, this number initializes the \
          random number generator.  Integers only"
    visible = @vectperturb == TRUE
  endparam
  param func1app
    caption = "Function 1 Usage"
    default = 0
    enum = "none" "prefunction" "postfunction" "both"
    hint = "Function 1 can be applied at various stages of the calculation, \
          depending upon this setting.  'prefunction' means z is fed to \
          Function 1 each iteration before other options are applied; \
          'postfunction' means the function is applied to the new z at the \
          end of each iteration; and 'argument' means that Function 1 is applied \
          to the modified z before being fed to the Taylor series"
  endparam
  param function1
    caption = "Function 1"
    enum = "z" "z^2" "z^3" "z^4" "z^power" \
          "1/z" "sqrt(z)" "1/z^2" "log(z)" "e^z" \
          "z^z" "sin(z)" "cos(z)" "tan(z)" "asin(z)" \
          "acos(z)" "atan(z)" "sinh(z)" "cosh(z)" "tanh(z)" \
          "asinh(z)" "acosh(z)" "atanh(z)" "log(1/z)" "log(log(z))" \
          "e^-z" "e^(1/z)" "z^-z" "sin(z)^2" "cos(z)^2" \
          "tan(z)^2" "cot(z)" "sec(z)" "csc(z)" "cot(z)^2" \
          "sec(z)^2" "csc(z)^2" "z^z^z" "1/z^z^z" "log(-z)" \
          "1/log(z)" "zlog(z)" "sin(z)/z" "cos(z)/z" "sin(z)*cos(z)" \
          "sin(z^2)" "e^(-1/z)" "ze^z" "ze^-z" "ze^(1/z)" \
          "ze^(-1/z)" "z^3" "1/z^3" "acot(z)" "asec(z)" \
          "acsc(z)" "tan(z)/z" "cot(z)/z" "sec(z)/z" "csc(z)/z" \
          "zsin(z)" "zcos(z)" "ztan(z)" "zcot(z)" "zsec(z)" \
          "zcsc(z)" "sin(1/z)" "cos(1/z)" "tan(1/z)" "cot(1/z)" \
          "sec(1/z)" "csc(1/z)" "cotanh(z)" "sech(z)" "cosech(z)" \
          "acoth(z)" "asech(z)" "acosech(z)" "e^(z^2)" "sinh(z)^2" \
          "cosh(z)^2" "tanh(z)^2" "cotanh(z)^2" "sech(z)^2" "cosech(z)^2" \
          "sinh(1/z)" "cosh(1/z)" "tanh(1/z)" "cotanh(1/z)" "sech(1/z)" \
          "cosech(1/z)" "sin(z)tan(z)" "sinh(z)tanh(z)" "sinh(z)cosh(z)" \
          "sinh(z)^2*cosh(z)^2" \
          "sin(z)^2*cos(z)^2" "sin(1/z)*cos(1/z)" "sin(1/z)^2" "sin(z)cos(1/z)" \
          "sin(z)sin(1/z)" \
          "log(z)^2" "sin(z)sin(2z)" "e^2z" "e^-2z" "sinh(1/z)cosh(1/z)" \
          "sinh(1/z)^2" "sinh(z)cosh(1/z)" "sinh(z)sinh(1/z)" "sin(z)sinh(z)" \
          "sin(z)cosh(z)" \
          "sin(z)^2*sinh(z)^2" "sin(z)e^z" "cos(z)e^z" "sinh(z)e^z" "cosh(z)e^z" \
          "sin(z)log(z)" "cos(z)log(z)" "sinh(z)log(z)" "cosh(z)log(z)" \
          "e^(-z^2)" \
          "e^(1/z^2)" "e^(-1/z^2)"
    default = 0
    hint = "This function is applied in the manner specified by param \
          'Function 1 Usage'"
    visible = @func1app != "none"
  endparam
  param f1power
    caption = "Func 1 Power"
    default = (5,0)
    hint = "This is the power used if param 'Function 1' is set to 'z^power'.  \
          Complex value"
    visible = @function1 == "z^power"
  endparam
  param pixelformula
    caption = "Pixel Formula"
    enum = "p" "p^2" "p^3" "p^4" "p^power" "1/p" "sqrt(p)" "1/p^2" "log(p)" "e^p" \
          "p^p" "sin(p)" "cos(p)" \
          "tan(p)" "asin(p)" "acos(p)" "atan(p)" "sinh(p)" "cosh(p)" "tanh(p)" \
          "asinh(p)" "acosh(p)" "atanh(p)" "log(1/p)" "log(log(p))" "e^-p" \
          "e^(1/p)" "p^-p" "sin(p)^2" "cos(p)^2" "tan(p)^2" "cot(p)" "sec(p)" \
          "csc(p)" "cot(p)^2" "sec(p)^2" "csc(p)^2" "p^p^p" "1/p^p^p" "log(-p)" \
          "1/log(p)" "plog(p)" "sin(p)/p" "cos(p)/p" "sin(p)*cos(p)" "sin(p^2)" \
          "e^(-1/p)" "pe^p" "pe^-p" "pe^(1/p)" "pe^(-1/p)" "p^3" "1/p^3" \
          "acot(p)" "asec(p)" "acsc(p)" "tan(p)/p" "cot(p)/p" "sec(p)/p" \
          "csc(p)/p" "psin(p)" "pcos(p)" "ptan(p)" "pcot(p)" "psec(p)" "pcsc(p)" \
          "sin(1/p)" "cos(1/p)" "tan(1/p)" "cot(1/p)" "sec(1/p)" "csc(1/p)" \
          "cotanh(p)" "sech(p)" "cosech(p)" "acoth(p)" "asech(p)" "acosech(p)" \
          "3-term polynomial" "sinh(p)^2" "cosh(p)^2" "tanh(p)^2" "cotanh(p)^2" \
          "sech(p)^2" "cosech(p)^2" "sinh(1/p)" "cosh(1/p)" "tanh(1/p)" \
          "cotanh(1/p)" "sech(1/p)" "cosech(1/p)" "sin(p)tan(p)" "sinh(p)tanh(p)" \
          "sinh(p)cosh(p)" "sinh(p)^2*cosh(p)^2" "sin(p)^2*cos(p)^2" \
          "sin(1/p)*cos(1/p)" "sin(1/p)^2" "sin(p)cos(1/p)" "sin(p)sin(1/p)" \
          "log(p)^2" "sin(p)sin(2p)" "e^2p" "e^-2p" "sinh(1/p)cosh(1/p)" \
          "sinh(1/p)^2" "sinh(p)cosh(1/p)" "sinh(p)sinh(1/p)" "sin(p)sinh(p)" \
          "sin(p)cosh(p)" "sin(p)^2*sinh(p)^2" "sin(p)e^p" "cos(p)e^p" \
          "sinh(p)e^p" "cosh(p)e^p" "sin(p)log(p)" "cos(p)log(p)" "sinh(p)log(p)" \
          "cosh(p)log(p)"
    default = 0
    hint = "Pixel value (Mand) or seed (Julia) can be initialized \
        before iterating. For 'p^power', set parameter 'Pixel Power'; \
        for '3-term polynomial', set 'Coeff Pa', 'Exponent Pa', 'Coeff Pb', \
        'Exponent Pb', 'Coeff Pc', 'Exponent Pc'. 'p' results in normal \
        initialization"
  endparam
  param ppower
    caption = "Pixel Power"
    default = (5,0)
    hint = "This is the power used if param 'Pixel Formula' is set to 'p^power'.  \
          Complex value"
    visible = @pixelformula == "p^power"
  endparam
  param coeffpa
    caption = "Coeff Pa"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the \
        coefficient of the 1st term.  Complex value"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param exponentpa
    caption = "Exponent Pa"
    default = (6,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 1st term.  Complex value"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param coeffpb
    caption = "Coeff Pb"
    default = (-1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the \
        coefficient of the 2nd term.  Complex value"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param exponentpb
    caption = "Exponent Pb"
    default = (4,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 2nd term.  Complex value"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param coeffpc
    caption = "Coeff Pc"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the \
        coefficient of the 3rd term.  Complex value"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param exponentpc
    caption = "Exponent Pc"
    default = (2,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 3rd term.  Complex value"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param blend
    caption = "Blend Z^Power"
    default = FALSE
    hint = "If true, then the factorial function is blended with a normal \
            z^powerMandelbrot/Julia, z = c1*factorial(z) + c2*z^power.  Set the \
            weight coefficients c1 & c2 with params 'Factorial Weight' and 'Z^Power \
            Weight'.  The exponent is set with param 'Blend Power'"
  endparam
  param weight1
    caption = "Factorial Weight"
    default = -0.1
    hint = "If 'Blend Z^Power' is enabled (TRUE), then this coefficient sets the \
            relative proportion of the factorial function that is blended \
            with z^power each iteration to obtain the final z"
  endparam
  param weight2
    caption = "Z^Power Weight"
    default = 1.0
    hint = "If 'Blend Z^Power' is enabled (TRUE), then this coefficient sets the \
            relative proportion of the z^power function that is blended \
            with the factorial function each iteration to obtain the final z"
  endparam
  param blendpower
    caption = "Blend Power"
    default = (2,0)
    hint = "If 'Blend Z^Power' is enabled (TRUE), then this parameter sets the \
          exponent for the z^power function (i.e., this is the power)"
  endparam
  param pmode
    caption = "Pixel Mode"
    default = 0
    enum = "Post-add" "Pre-add" "Both"
    hint = "If 'Post-add', the formula is executed, then pixel/constant is added \
        to the result (normal Mandelbrot/Julia behavior); if 'Pre-add', then \
        the pixel/constant is added to z before any formulas are executed.  \
        'Both' results in a pixel/constant addition, formula execution, then \
        another pixel/constant addition to the result each iteration"
  endparam
  param jconstant
    caption = "Seed/Perturbation"
    default = (0,0)
    hint = "This is the seed constant for Julia-type fractals, or the initial \
          perturbation for Mandelbrot-types.  Complex value"
  endparam
  param bail
    caption = "Bailout Value"
    default = 1024.0
    hint = "Value needed to 'escape' to infinity.  Float value"
  endparam
  param mandy
    caption = "Mandelbrot flag"
    default = TRUE
    hint = "Works in combination with the Julia flag for switching"
  endparam
  param julia
    caption = "Julia flag"
    default = FALSE
    hint = "Works in combination with the Mandelbrot flag for switching"
  endparam

  switch:
  type = "jam-factorials"
  jconstant = #pixel
  factorialorder = factorialorder
  firstterm = firstterm
  factorialstart = factorialstart
  factmultiplier = factmultiplier
  factoffset = factoffset
  coeffnum = coeffnum
  nummultiplier = nummultiplier
  numoffset = numoffset
  coefffunc = coefffunc
  numpower = numpower
  multconst = multconst
  constpower = constpower
  seriesconst = seriesconst
  zexponent = zexponent
  expmultiplier = expmultiplier
  expoffset = expoffset
  mode = mode
  staticterms = staticterms
  altsign = altsign
  summode = summode
  sumconst = sumconst
  prodmode = prodmode
  prodconst = prodconst
  matrixmode = matrixmode
  matconst11 = matconst11
  matconst12 = matconst12
  matconst21 = matconst21
  matconst22 = matconst22
  vectormode = vectormode
  vectconst = vectconst
  vectperturb = vectperturb
  vperturbamt = vperturbamt
  randseed = randseed
  func1app = func1app
  function1 = function1
  f1power = f1power
  bail = bail
  pixelformula = pixelformula
  ppower = ppower
  coeffpa = coeffpa
  exponentpa = exponentpa
  coeffpb = coeffpb
  exponentpb = exponentpb
  coeffpc = coeffpc
  exponentpc = exponentpc
  blend = blend
  weight1 = weight1
  weight2 = weight2
  blendpower = blendpower
  pmode = pmode
  mandy = julia
  julia = mandy
}

jam-hypergeometricPFQ { ; jam 030309
  ; Mandelbrot/Julia based on the generalized hypergeometric function pFq,
  ; pFq(a1,a2,...,ap;b1,b2,...,bq;z) = 1 + (a1*a2*...*ap/(b1*b2*...*bq*1!))z +
  ; (a1*[a1+1]*a2*[a2+2]*...*ap*[ap+1]/(b1*[b1+1]*b2*[b2+1]*...*bq*[bq+1]*2!))z^2
  ; + ...
  ; The function is implemented either as a static, 11-term series expansion about
  ; z=0, or using an indefinite number of terms based on the current iteration
  ; count; z argument may be modified before passage to the hypergeometric
  ; function, and the HG function may also be multiplied by 1 or 2 other functions.

  ; Thanks to Dave Makin for comments and testing, and particularly for ideas
  ; relating to the dynamic iteration method.

  ; Contact Joe Maddry (maddry@sri.org) with comments/questions.  Enjoy!

  init:
  if @mandy
    z = @jconstant, jc = #pixel
  else ; Julia
    z = #pixel, jc = @jconstant
  endif

  complex zextra = complex ztemp = (0,0) ; temp/spare scratch variables
  complex zarg = complex zpre1 = complex zpre2 = (0,0)

  ; declare vars for powers of z
  complex z2 = complex z3 = complex z4 = complex z5 = complex z6 = (0,0)
  complex z7 = complex z8 = complex z9 = (0,0)

  ; compute coefficients for series
  ; start with the numerator and denominator input parameters (the a's & b's)
  complex a1_1 = @a1, complex a2_1 = @a2, complex a3_1 = @a3, complex a4_1 = @a4
  complex b1_1 = @b1, complex b2_1 = @b2, complex b3_1 = @b3, complex b4_1 = @b4
  complex a5_1 = @a5, complex b5_1 = @b5
  ; initialize all the other variables, to eliminate annoying warning messages
  complex a1_2 = complex a1_3 = complex a1_4 = complex a1_5 = (0,0)
  complex a1_6 = complex a1_7 = complex a1_8 = complex a1_9 = complex a1_10 = (0,0)
  complex a2_2 = complex a2_3 = complex a2_4 = complex a2_5 = (0,0)
  complex a2_6 = complex a2_7 = complex a2_8 = complex a2_9 = complex a2_10 = (0,0)
  complex a3_2 = complex a3_3 = complex a3_4 = complex a3_5 = (0,0)
  complex a3_6 = complex a3_7 = complex a3_8 = complex a3_9 = complex a3_10 = (0,0)
  complex a4_2 = complex a4_3 = complex a4_4 = complex a4_5 = (0,0)
  complex a4_6 = complex a4_7 = complex a4_8 = complex a4_9 = complex a4_10 = (0,0)
  complex a5_2 = complex a5_3 = complex a5_4 = complex a5_5 = (0,0)
  complex a5_6 = complex a5_7 = complex a5_8 = complex a5_9 = complex a5_10 = (0,0)
  complex b1_2 = complex b1_3 = complex b1_4 = complex b1_5 = (0,0)
  complex b1_6 = complex b1_7 = complex b1_8 = complex b1_9 = complex b1_10 = (0,0)
  complex b2_2 = complex b2_3 = complex b2_4 = complex b2_5 = (0,0)
  complex b2_6 = complex b2_7 = complex b2_8 = complex b2_9 = complex b2_10 = (0,0)
  complex b3_2 = complex b3_3 = complex b3_4 = complex b3_5 = (0,0)
  complex b3_6 = complex b3_7 = complex b3_8 = complex b3_9 = complex b3_10 = (0,0)
  complex b4_2 = complex b4_3 = complex b4_4 = complex b4_5 = (0,0)
  complex b4_6 = complex b4_7 = complex b4_8 = complex b4_9 = complex b4_10 = (0,0)
  complex b5_2 = complex b5_3 = complex b5_4 = complex b5_5 = (0,0)
  complex b5_6 = complex b5_7 = complex b5_8 = complex b5_9 = complex b5_10 = (0,0)
  complex coeff0 = complex coeff1 = (1,0)
  complex coeff2 = complex coeff3 = (1,0)
  complex coeff4 = complex coeff5 = (1,0)
  complex coeff6 = complex coeff7 = (1,0)
  complex coeff8 = complex coeff9 = (1,0)
  complex coeff10 = (1,0)
  complex numerator1 = complex numerator2 = complex numerator3 = (1,0)
  complex numerator4 = complex numerator5 = complex numerator6 = (1,0)
  complex numerator7 = complex numerator8 = complex numerator9 = (1,0)
  complex numerator10 = (1,0)
  int iter = -1, float sign = 1.0

  if @static ; using 11-term Taylor series expansion
    ; now define the coefficient numerator constants
    if @p == 0 ; nothing more to do to the numerator
      coeff0 = coeff0 ; but we have to do something to avoid a UF error
    else ; p must be at least 1
      a1_2 =  a1_1+@ca1, a1_3 = a1_2+@ca1
      a1_4 = a1_3+@ca1, a1_5 = a1_4+@ca1, a1_6 = a1_5+@ca1
      a1_7 = a1_6+@ca1, a1_8 = a1_7+@ca1, a1_9 = a1_8+@ca1
      a1_10 = a1_9+@ca1
      if @p > 1 ; p must be at least 2
        a2_2 =  a2_1+@ca2, a2_3 = a2_2+@ca2
        a2_4 = a2_3+@ca2, a2_5 = a2_4+@ca2, a2_6 = a2_5+@ca2
        a2_7 = a2_6+@ca2, a2_8 = a2_7+@ca2, a2_9 = a2_8+@ca2
        a2_10 = a2_9+@ca2
      endif ; @p
      if @p > 2 ; p must be at least 3
        a3_2 =  a3_1+@ca3, a3_3 = a3_2+@ca3
        a3_4 = a3_3+@ca3, a3_5 = a3_4+@ca3, a3_6 = a3_5+@ca3
        a3_7 = a3_6+@ca3, a3_8 = a3_7+@ca3, a3_9 = a3_8+@ca3
        a3_10 = a3_9+@ca3
      endif ; @p
      if @p > 3 ; p must be at least 4
        a4_2 =  a4_1+@ca4, a4_3 = a4_2+@ca4
        a4_4 = a4_3+@ca4, a4_5 = a4_4+@ca4, a4_6 = a4_5+@ca4
        a4_7 = a4_6+@ca4, a4_8 = a4_7+@ca4, a4_9 = a4_8+@ca4
        a4_10 = a4_9+@ca4
      endif ; @p
      if @p > 4 ; p must be at least 5
        a5_2 =  a5_1+@ca5, a5_3 = a5_2+@ca5
        a5_4 = a5_3+@ca5, a5_5 = a5_4+@ca5, a5_6 = a5_5+@ca5
        a5_7 = a5_6+@ca5, a5_8 = a5_7+@ca5, a5_9 = a5_8+@ca5
        a5_10 = a5_9+@ca5
      endif ; @p
    endif ; @p
    ; define the coefficient denominator constants
    if @q == 0 ; nothing more to do to the denominator
      coeff0 = coeff0 ; but we have to do something to avoid a UF error
    else ; q must be at least 1
      b1_2 =  b1_1+@cb1, b1_3 = b1_2+@cb1
      b1_4 = b1_3+@cb1, b1_5 = b1_4+@cb1, b1_6 = b1_5+@cb1
      b1_7 = b1_6+@cb1, b1_8 = b1_7+@cb1, b1_9 = b1_8+@cb1
      b1_10 = b1_9+@cb1
      if @q > 1 ; q must be at least 2
        b2_2 =  b2_1+@cb2, b2_3 = b2_2+@cb2
        b2_4 = b2_3+@cb2, b2_5 = b2_4+@cb2, b2_6 = b2_5+@cb2
        b2_7 = b2_6+@cb2, b2_8 = b2_7+@cb2, b2_9 = b2_8+@cb2
        b2_10 = b2_9+@cb2
      endif ; @q
      if @q > 2 ; q must be at least 3
        b3_2 =  b3_1+@cb3, b3_3 = b3_2+@cb3
        b3_4 = b3_3+@cb3, b3_5 = b3_4+@cb3, b3_6 = b3_5+@cb3
        b3_7 = b3_6+@cb3, b3_8 = b3_7+@cb3, b3_9 = b3_8+@cb3
        b3_10 = b3_9+@cb3
      endif ; @q
      if @q > 3 ; q must be at least 4
        b4_2 =  b4_1+@cb4, b4_3 = b4_2+@cb4
        b4_4 = b4_3+@cb4, b4_5 = b4_4+@cb4, b4_6 = b4_5+@cb4
        b4_7 = b4_6+@cb4, b4_8 = b4_7+@cb4, b4_9 = b4_8+@cb4
        b4_10 = b4_9+@cb4
      endif ; @q
      if @q > 4 ; q must be at least 5
        b5_2 =  b5_1+@cb5, b5_3 = b5_2+@cb5
        b5_4 = b5_3+@cb5, b5_5 = b5_4+@cb5, b5_6 = b5_5+@cb5
        b5_7 = b5_6+@cb5, b5_8 = b5_7+@cb5, b5_9 = b5_8+@cb5
        b5_10 = b5_9+@cb5
      endif ; @q
    endif ; @q
    ; now put them all together, in the process converting the factorials to their
    ; reciprocals.  We are doing it the long way, to minimize the number of divisions
    if @q == 1
      coeff1 = coeff0*b1_1
      coeff2 = coeff1*b1_2
      coeff3 = coeff2*b1_3
      coeff4 = coeff3*b1_4
      coeff5 = coeff4*b1_5
      coeff6 = coeff5*b1_6
      coeff7 = coeff6*b1_7
      coeff8 = coeff7*b1_8
      coeff9 = coeff8*b1_9
      coeff10 = coeff9*b1_10
    elseif @q == 2
      coeff1 = coeff0*b1_1*b2_1
      coeff2 = coeff1*b1_2*b2_2
      coeff3 = coeff2*b1_3*b2_3
      coeff4 = coeff3*b1_4*b2_4
      coeff5 = coeff4*b1_5*b2_5
      coeff6 = coeff5*b1_6*b2_6
      coeff7 = coeff6*b1_7*b2_7
      coeff8 = coeff7*b1_8*b2_8
      coeff9 = coeff8*b1_9*b2_9
      coeff10 = coeff9*b1_10*b2_10
    elseif @q == 3
      coeff1 = coeff0*b1_1*b2_1*b3_1
      coeff2 = coeff1*b1_2*b2_2*b3_2
      coeff3 = coeff2*b1_3*b2_3*b3_3
      coeff4 = coeff3*b1_4*b2_4*b3_4
      coeff5 = coeff4*b1_5*b2_5*b3_5
      coeff6 = coeff5*b1_6*b2_6*b3_6
      coeff7 = coeff6*b1_7*b2_7*b3_7
      coeff8 = coeff7*b1_8*b2_8*b3_8
      coeff9 = coeff8*b1_9*b2_9*b3_9
      coeff10 = coeff9*b1_10*b2_10*b3_10
    elseif @q == 4
      coeff1 = coeff0*b1_1*b2_1*b3_1*b4_1
      coeff2 = coeff1*b1_2*b2_2*b3_2*b4_2
      coeff3 = coeff2*b1_3*b2_3*b3_3*b4_3
      coeff4 = coeff3*b1_4*b2_4*b3_4*b4_4
      coeff5 = coeff4*b1_5*b2_5*b3_5*b4_5
      coeff6 = coeff5*b1_6*b2_6*b3_6*b4_6
      coeff7 = coeff6*b1_7*b2_7*b3_7*b4_7
      coeff8 = coeff7*b1_8*b2_8*b3_8*b4_8
      coeff9 = coeff8*b1_9*b2_9*b3_9*b4_9
      coeff10 = coeff9*b1_10*b2_10*b3_10*b4_10
    elseif @q == 5
      coeff1 = coeff0*b1_1*b2_1*b3_1*b4_1*b5_1
      coeff2 = coeff1*b1_2*b2_2*b3_2*b4_2*b5_2
      coeff3 = coeff2*b1_3*b2_3*b3_3*b4_3*b5_3
      coeff4 = coeff3*b1_4*b2_4*b3_4*b4_4*b5_4
      coeff5 = coeff4*b1_5*b2_5*b3_5*b4_5*b5_5
      coeff6 = coeff5*b1_6*b2_6*b3_6*b4_6*b5_6
      coeff7 = coeff6*b1_7*b2_7*b3_7*b4_7*b5_7
      coeff8 = coeff7*b1_8*b2_8*b3_8*b4_8*b5_8
      coeff9 = coeff8*b1_9*b2_9*b3_9*b4_9*b5_9
      coeff10 = coeff9*b1_10*b2_10*b3_10*b4_10*b5_10
    endif ; @q
    if @p == 1
      numerator1 = a1_1
      numerator2 = a1_2*numerator1
      numerator3 = a1_3*numerator2
      numerator4 = a1_4*numerator3
      numerator5 = a1_5*numerator4
      numerator6 = a1_6*numerator5
      numerator7 = a1_7*numerator6
      numerator8 = a1_8*numerator7
      numerator9 = a1_9*numerator8
      numerator10 = a1_10*numerator9
    elseif @p == 2
      numerator1 = a1_1*a2_1
      numerator2 = a1_2*a2_2*numerator1
      numerator3 = a1_3*a2_3*numerator2
      numerator4 = a1_4*a2_4*numerator3
      numerator5 = a1_5*a2_5*numerator4
      numerator6 = a1_6*a2_6*numerator5
      numerator7 = a1_7*a2_7*numerator6
      numerator8 = a1_8*a2_8*numerator7
      numerator9 = a1_9*a2_9*numerator8
      numerator10 = a1_10*a2_10*numerator9
    elseif @p == 3
      numerator1 = a1_1*a2_1*a3_1
      numerator2 = a1_2*a2_2*a3_2*numerator1
      numerator3 = a1_3*a2_3*a3_3*numerator2
      numerator4 = a1_4*a2_4*a3_4*numerator3
      numerator5 = a1_5*a2_5*a3_5*numerator4
      numerator6 = a1_6*a2_6*a3_6*numerator5
      numerator7 = a1_7*a2_7*a3_7*numerator6
      numerator8 = a1_8*a2_8*a3_8*numerator7
      numerator9 = a1_9*a2_9*a3_9*numerator8
      numerator10 = a1_10*a2_10*a3_10*numerator9
    elseif @p == 4
      numerator1 = a1_1*a2_1*a3_1*a4_1
      numerator2 = a1_2*a2_2*a3_2*a4_2*numerator1
      numerator3 = a1_3*a2_3*a3_3*a4_3*numerator2
      numerator4 = a1_4*a2_4*a3_4*a4_4*numerator3
      numerator5 = a1_5*a2_5*a3_5*a4_5*numerator4
      numerator6 = a1_6*a2_6*a3_6*a4_6*numerator5
      numerator7 = a1_7*a2_7*a3_7*a4_7*numerator6
      numerator8 = a1_8*a2_8*a3_8*a4_8*numerator7
      numerator9 = a1_9*a2_9*a3_9*a4_9*numerator8
      numerator10 = a1_10*a2_10*a3_10*a4_10*numerator9
    elseif @p == 5
      numerator1 = a1_1*a2_1*a3_1*a4_1*a5_1
      numerator2 = a1_2*a2_2*a3_2*a4_2*a5_2*numerator1
      numerator3 = a1_3*a2_3*a3_3*a4_3*a5_3*numerator2
      numerator4 = a1_4*a2_4*a3_4*a4_4*a5_4*numerator3
      numerator5 = a1_5*a2_5*a3_5*a4_5*a5_5*numerator4
      numerator6 = a1_6*a2_6*a3_6*a4_6*a5_6*numerator5
      numerator7 = a1_7*a2_7*a3_7*a4_7*a5_7*numerator6
      numerator8 = a1_8*a2_8*a3_8*a4_8*a5_8*numerator7
      numerator9 = a1_9*a2_9*a3_9*a4_9*a5_9*numerator8
      numerator10 = a1_10*a2_10*a3_10*a4_10*a5_10*numerator9
    endif ; @p
    coeff1 = numerator1/coeff1
    coeff2 = numerator2/(2*coeff2)
    coeff3 = numerator3/(6*coeff3)
    coeff4 = numerator4/(24*coeff4)
    coeff5 = numerator5/(120*coeff5)
    coeff6 = numerator6/(720*coeff6)
    coeff7 = numerator7/(5040*coeff7)
    coeff8 = numerator8/(40320*coeff8)
    coeff9 = numerator9/(362880*coeff9)
    coeff10 = numerator10/(3628800*coeff10)
  endif ; @static

  ; Pixel/constant initialization section
  if @pixelformula != 0
    if @pixelformula == 1
      jc = jc * jc
    elseif  @pixelformula == 2
      jc = jc * jc * jc
    elseif  @pixelformula == 3
      zextra = jc * jc
      jc = zextra * zextra
    elseif  @pixelformula == 4
      jc = jc ^ @ppower
    elseif  @pixelformula == 5
      jc = 1/jc
    elseif  @pixelformula == 6
      jc = sqrt(jc)
    elseif  @pixelformula == 7
      jc = 1 / ( jc * jc )
    elseif  @pixelformula == 8
      jc = log(jc)
    elseif  @pixelformula == 9
      jc = exp( jc)
    elseif  @pixelformula == 10
      jc = jc^jc
    elseif  @pixelformula == 11
      jc = sin( jc )
    elseif  @pixelformula == 12
      jc = cos( jc )
    elseif  @pixelformula == 13
      jc = tan( jc )
    elseif  @pixelformula == 14
      jc = asin( jc )
    elseif  @pixelformula == 15
      jc = acos( jc )
    elseif  @pixelformula == 16
      jc = atan( jc )
    elseif  @pixelformula == 17
      jc = sinh( jc )
    elseif  @pixelformula == 18
      jc = cosh( jc )
    elseif  @pixelformula == 19
      jc = tanh( jc )
    elseif  @pixelformula == 20
      jc = asinh( jc )
    elseif  @pixelformula == 21
      jc = acosh( jc )
    elseif  @pixelformula == 22
      jc = atanh( jc )
    elseif  @pixelformula == 23
      jc = log( 1/jc )
    elseif  @pixelformula == 24
      jc = log( log( jc ))
    elseif  @pixelformula == 25
      jc = exp( -jc )
    elseif  @pixelformula == 26
      jc = exp( 1/jc )
    elseif  @pixelformula == 27
      jc = jc^(-jc)
    elseif  @pixelformula == 28
      zextra = sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 29
      zextra = cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 30
      zextra = tan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 31
      jc = cotan( jc )
    elseif  @pixelformula == 32
      jc = 1/cos( jc )
    elseif  @pixelformula == 33
      jc = 1/sin( jc )
    elseif  @pixelformula == 34
      zextra = cotan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 35
      zextra = 1/cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 36
      zextra = 1/sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 37
      zextra = jc^(jc)
      jc = jc^zextra
    elseif  @pixelformula == 38
      zextra = jc^(jc)
      jc = 1/( jc^zextra )
    elseif  @pixelformula == 39
      jc = log(-jc)
    elseif  @pixelformula == 40
      jc = 1/log( jc )
    elseif  @pixelformula == 41
      jc = jc * log( jc )
    elseif  @pixelformula == 42
      jc = sin( jc ) / jc
    elseif  @pixelformula == 43
      jc = cos( jc ) / jc
    elseif  @pixelformula == 44
      jc = sin( jc ) * cos( jc )
    elseif  @pixelformula == 45
      jc = sin( jc^2 )
    elseif  @pixelformula == 46
      jc = exp( -1/jc )
    elseif  @pixelformula == 47
      jc = jc * exp( jc )
    elseif  @pixelformula == 48
      jc = jc * exp( -jc )
    elseif  @pixelformula == 49
      jc = jc * exp( 1/jc )
    elseif  @pixelformula == 50
      jc = jc * exp( -1/jc )
    elseif  @pixelformula == 51
      jc = jc * jc * jc
    elseif  @pixelformula == 52
      jc = 1 / ( jc * jc * jc )
    elseif  @pixelformula == 53
      jc = atan( 1 / jc )
    elseif  @pixelformula == 54
      jc = acos( 1 / jc )
    elseif  @pixelformula == 55
      jc = asin( 1 / jc )
    elseif  @pixelformula == 56
      jc = tan( jc ) / jc
    elseif  @pixelformula == 57
      jc = cotan( jc ) / jc
    elseif  @pixelformula == 58
      jc = 1 / ( jc * cos( jc ))
    elseif  @pixelformula == 59
      jc = 1 / ( jc * sin( jc ))
    elseif  @pixelformula == 60
      jc = jc * sin( jc )
    elseif  @pixelformula == 61
      jc = jc * cos( jc )
    elseif  @pixelformula == 62
      jc = jc * tan( jc )
    elseif  @pixelformula == 63
      jc = jc * cotan( jc )
    elseif  @pixelformula == 64
      jc = jc/cos( jc )
    elseif  @pixelformula == 65
      jc = jc/sin( jc )
    elseif  @pixelformula == 66
      jc = sin( 1/jc )
    elseif  @pixelformula == 67
      jc = cos( 1/jc )
    elseif  @pixelformula == 68
      jc = tan( 1/jc )
    elseif  @pixelformula == 69
      jc = cotan( 1/jc )
    elseif  @pixelformula == 70
      jc = 1/cos( 1/jc )
    elseif  @pixelformula == 71
      jc = 1/sin( 1/jc )
    elseif  @pixelformula == 72
      jc = cotanh( jc )
    elseif  @pixelformula == 73
      jc = 1/cosh( jc )
    elseif  @pixelformula == 74
      jc = 1/sinh( jc )
    elseif  @pixelformula == 75
      jc = atanh( 1/jc )
    elseif  @pixelformula == 76
      jc = acosh( 1/jc )
    elseif  @pixelformula == 77
      jc = asinh( 1/jc )
    elseif @pixelformula == 78
      jc = @coeffpa * jc^@exponentpa + @coeffpb * jc^@exponentpb + \
          @coeffpc * jc^@exponentpc
    elseif  @pixelformula == 79
      zextra = sinh(#z)
      jc = zextra * zextra
    elseif  @pixelformula == 80
      zextra = cosh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 81
      zextra = tanh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 82
      zextra = cotanh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 83
      zextra = (1,0)/cosh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 84
      zextra = (1,0) / sinh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 85
      jc = sinh(1/jc)
    elseif  @pixelformula == 86
      jc = cosh(1/jc)
    elseif  @pixelformula == 87
      jc = tanh(1/jc)
    elseif  @pixelformula == 88
      jc = cotanh(1/jc)
    elseif  @pixelformula == 89
      jc = (1,0)/cosh(1/jc)
    elseif  @pixelformula == 90
      jc = (1,0)/sinh(1/jc)
    elseif  @pixelformula == 91
      jc = sin( jc ) * tan(jc)
    elseif  @pixelformula == 92
      jc = sinh(jc) * tanh(jc)
    elseif  @pixelformula == 93
      jc = sinh(jc) * cosh(jc)
    elseif  @pixelformula == 94
      ztemp = sinh(jc), zextra = cosh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 95
      ztemp = sin(jc), zextra = cos(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 96
      zextra = 1/jc
      jc = sin(zextra)*cos(zextra)
    elseif  @pixelformula == 97
      zextra = sin( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 98
      jc = sin(jc) * cos(1/jc)
    elseif  @pixelformula == 99
      jc = sin(jc) * sin(1/jc)
    elseif  @pixelformula == 100
      zextra = log(jc)
      jc = zextra*zextra
    elseif  @pixelformula == 101
      jc = sin(jc) * sin(2*jc)
    elseif @pixelformula == 102
      jc = exp(2*jc)
    elseif  @pixelformula == 103
      jc = exp(-2*jc)
    elseif  @pixelformula == 104
      zextra = 1/jc
      jc = sinh(zextra)*cosh(zextra)
    elseif  @pixelformula == 105
      zextra = sinh( 1/jc )
      jc = zextra*zextra

    elseif  @pixelformula == 106
      jc = sinh(jc) * cosh(1/jc)
    elseif  @pixelformula == 107
      jc = sinh(jc) * sinh(1/jc)
    elseif  @pixelformula == 108
      jc = sin(jc) * sinh(jc)
    elseif  @pixelformula == 109
      jc = sin(jc) * cosh(jc)
    elseif  @pixelformula == 110
      zextra = sin(jc), ztemp = sinh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 111
      jc = sin(jc)*exp(jc)
    elseif  @pixelformula == 112
      jc = cos(jc)*exp(jc)
    elseif  @pixelformula == 113
      jc = sinh(jc)*exp(jc)
    elseif  @pixelformula == 114
      jc = cosh(jc)*exp(jc)
    elseif  @pixelformula == 115
      jc = sin(jc)*log(jc)
    elseif  @pixelformula == 116
      jc = cos(jc)*log(jc)
    elseif  @pixelformula == 117
      jc = sinh(jc)*log(jc)
    else ; @pixelformula == 118
      jc = cosh(jc)*log(jc)
    endif ; @pixelformula = 1
  endif ; @pixelformula != 0

  loop:
  if @pmode != 0
    z = z + jc
  endif ; pmode

  ; Execute PF1
  if @pre1multiplier != (1,0)
    zpre1 = @pre1multiplier*z
  else
    zpre1 = z
  endif ; @pre1multiplier
  if @prefunc1 == 0
    zpre1 = (1,0)
  elseif @prefunc1 == 2
    zpre1 = 1/zpre1
  elseif @prefunc1 == 3
    zpre1 = zpre1*zpre1
  elseif @prefunc1 == 4
    zpre1 = zpre1^@pre1power
  elseif @prefunc1 == 5
    zpre1 = exp(zpre1)
  elseif @prefunc1 == 6
    zpre1 = exp(-zpre1)
  elseif @prefunc1 == 7
    zpre1 = exp(zpre1^@pre1power)
  elseif @prefunc1 == 8
    zpre1 = exp(-(zpre1^@pre1power))
  elseif @prefunc1 == 9
    zpre1 = sin(zpre1)
  elseif @prefunc1 == 10
    zpre1 = cos(zpre1)
  elseif @prefunc1 == 11
    zpre1 = sin(z^@pre1power)
  elseif @prefunc1 == 12
    zpre1 = (sin(zpre1))^@pre1power
  elseif @prefunc1 == 13
    zpre1 = log(zpre1)
  elseif @prefunc1 == 14
    zpre1 = log(log(zpre1))
  elseif @prefunc1 == 15
    zpre1 = zpre1^zpre1
  elseif @prefunc1 == 16
    zpre1 = zpre1^(-zpre1)
  elseif @prefunc1 == 17
    zpre1 = zpre1^(zpre1^@pre1power)
  elseif @prefunc1 == 18
    zpre1 = zpre1^(-(zpre1^@pre1power))
  elseif @prefunc1 == 19
    zpre1 = sinh(zpre1)
  elseif @prefunc1 == 20
    zpre1 = cosh(zpre1)
  elseif @prefunc1 == 21
    zpre1 = sinh(zpre1^@pre1power)
  elseif @prefunc1 == 22
    zpre1 = cosh(zpre1^@pre1power)
  elseif @prefunc1 == 23
    zpre1 = sinh(zpre1)^@pre1power
  elseif @prefunc1 == 24
    zpre1 = cosh(zpre1)^@pre1power
  elseif @prefunc1 == 25
    zpre1 = zpre1 + 1
  elseif @prefunc1 == 26
    zpre1 = (zpre1 + 1)^@pre1power
  elseif @prefunc1 == 27
    zpre1 = zpre1 - 1
  elseif @prefunc1 == 28
    zpre1 = (zpre1 - 1)^@pre1power
  elseif @prefunc1 == 29
    zpre1 = 1 - zpre1
  elseif @prefunc1 == 30
    zpre1 = (1 - zpre1)^@pre1power
  elseif @prefunc1 == 31
    zpre1 = (zpre1+1)*(zpre1-1)
  elseif @prefunc1 == 32
    zpre1 = ((zpre1+1)*(zpre1-1))^@pre1power
  elseif @prefunc1 == 33
    zpre1 = zpre1*zpre1+1
  elseif @prefunc1 == 34
    zpre1 = (zpre1*zpre1+1)^@pre1power
  elseif @prefunc1 == 35
    zpre1 = zpre1*zpre1-1
  elseif @prefunc1 == 36
    zpre1 = (zpre1*zpre1-1)^@pre1power
  elseif @prefunc1 == 37
    zpre1 = 1-zpre1*zpre1
  elseif @prefunc1 == 38
    zpre1 = (1-zpre1*zpre1)^@pre1power
  elseif @prefunc1 == 39
    zpre1 = zpre1^@pre1power + 1
  elseif @prefunc1 == 40
    zpre1 = zpre1^@pre1power - 1
  elseif @prefunc1 == 41
    zpre1 = 1 - zpre1^@pre1power
  elseif @prefunc1 == 42
    zpre1 = (zpre1 + 1)/(zpre1 - 1)
  elseif @prefunc1 == 43
    zpre1 = ((zpre1 + 1)/(zpre1 - 1))^@pre1power
  elseif @prefunc1 == 44
    zpre1 = (zpre1-1)/(zpre1+1)
  elseif @prefunc1 == 45
    zpre1 = ((zpre1-1)/(zpre1+1))^@pre1power
  endif ; @prefunc1

  ; Execute PF2
  if @pre2multiplier != (1,0)
    zpre2 = @pre2multiplier*z
  else
    zpre2 = z
  endif ; @pre2multiplier
  if @prefunc2 == 0
    zpre2 = (1,0)
  elseif @prefunc2 == 2
    zpre2 = 1/zpre2
  elseif @prefunc2 == 3
    zpre2 = zpre2*zpre2
  elseif @prefunc2 == 4
    zpre2 = zpre2^@pre2power
  elseif @prefunc2 == 5

    zpre2 = exp(zpre2)
  elseif @prefunc2 == 6
    zpre2 = exp(-zpre2)
  elseif @prefunc2 == 7
    zpre2 = exp(zpre2^@pre2power)
  elseif @prefunc2 == 8
    zpre2 = exp(-(zpre2^@pre2power))
  elseif @prefunc2 == 9
    zpre2 = sin(zpre2)
  elseif @prefunc2 == 10
    zpre2 = cos(zpre2)
  elseif @prefunc2 == 11
    zpre2 = sin(z^@pre2power)
  elseif @prefunc2 == 12
    zpre2 = (sin(zpre2))^@pre2power
  elseif @prefunc2 == 13
    zpre2 = log(zpre2)
  elseif @prefunc2 == 14
    zpre2 = log(log(zpre2))
  elseif @prefunc2 == 15
    zpre2 = zpre2^zpre2
  elseif @prefunc2 == 16
    zpre2 = zpre2^(-zpre2)
  elseif @prefunc2 == 17
    zpre2 = zpre2^(zpre2^@pre2power)
  elseif @prefunc2 == 18
    zpre2 = zpre2^(-(zpre2^@pre2power))
  elseif @prefunc2 == 19
    zpre2 = sinh(zpre2)
  elseif @prefunc2 == 20
    zpre2 = cosh(zpre2)
  elseif @prefunc2 == 21
    zpre2 = sinh(zpre2^@pre2power)
  elseif @prefunc2 == 22
    zpre2 = cosh(zpre2^@pre2power)
  elseif @prefunc2 == 23
    zpre2 = sinh(zpre2)^@pre2power
  elseif @prefunc2 == 24
    zpre2 = cosh(zpre2)^@pre2power
  elseif @prefunc2 == 25
    zpre2 = zpre2 + 1
  elseif @prefunc2 == 26
    zpre2 = (zpre2 + 1)^@pre2power
  elseif @prefunc2 == 27
    zpre2 = zpre2 - 1
  elseif @prefunc2 == 28
    zpre2 = (zpre2 - 1)^@pre2power
  elseif @prefunc2 == 29
    zpre2 = 1 - zpre2
  elseif @prefunc2 == 30
    zpre2 = (1 - zpre2)^@pre2power
  elseif @prefunc2 == 31
    zpre2 = (zpre2+1)*(zpre2-1)
  elseif @prefunc2 == 32
    zpre2 = ((zpre2+1)*(zpre2-1))^@pre2power
  elseif @prefunc2 == 33
    zpre2 = zpre2*zpre2+1
  elseif @prefunc2 == 34
    zpre2 = (zpre2*zpre2+1)^@pre2power
  elseif @prefunc2 == 35
    zpre2 = zpre2*zpre2-1
  elseif @prefunc2 == 36
    zpre2 = (zpre2*zpre2-1)^@pre2power
  elseif @prefunc2 == 37
    zpre2 = 1-zpre2*zpre2
  elseif @prefunc2 == 38
    zpre2 = (1-zpre2*zpre2)^@pre2power
  elseif @prefunc2 == 39
    zpre2 = zpre2^@pre2power + 1
  elseif @prefunc2 == 40
    zpre2 = zpre2^@pre2power - 1
  elseif @prefunc2 == 41
    zpre2 = 1 - zpre2^@pre2power
  elseif @prefunc2 == 42
    zpre2 = (zpre2 + 1)/(zpre2 - 1)
  elseif @prefunc2 == 43
    zpre2 = ((zpre2 + 1)/(zpre2 - 1))^@pre2power
  elseif @prefunc2 == 44
    zpre2 = (zpre2-1)/(zpre2+1)
  elseif @prefunc2 == 45
    zpre2 = ((zpre2-1)/(zpre2+1))^@pre2power
  endif ; @prefunc2

  ; Execute argument function
  if @argmultiplier != (1,0)
    zarg = @argmultiplier*z
  else
    zarg = z
  endif ; @argmultiplier
  if @argument == 1
    zarg = 1/zarg
  elseif @argument == 2
    zarg = zarg*zarg
  elseif @argument == 3
    zarg = zarg^@argpower
  elseif @argument == 4
    zarg = exp(zarg)
  elseif @argument == 5
    zarg = exp(-zarg)
  elseif @argument == 6
    zarg = exp(zarg^@argpower)
  elseif @argument == 7
    zarg = exp(-(zarg^@argpower))
  elseif @argument == 8
    zarg = sin(zarg)
  elseif @argument == 9
    zarg = cos(zarg)
  elseif @argument == 10
    zarg = sin(z^@argpower)
  elseif @argument == 11
    zarg = (sin(zarg))^@argpower
  elseif @argument == 12
    zarg = log(zarg)
  elseif @argument == 13
    zarg = log(log(zarg))
  elseif @argument == 14
    zarg = zarg^zarg
  elseif @argument == 15
    zarg = zarg^(-zarg)
  elseif @argument == 16
    zarg = zarg^(zarg^@argpower)
  elseif @argument == 17
    zarg = zarg^(-(zarg^@argpower))
  elseif @argument == 18
    zarg = sinh(zarg)
  elseif @argument == 19
    zarg = cosh(zarg)
  elseif @argument == 20
    zarg = sinh(zarg^@argpower)
  elseif @argument == 21
    zarg = cosh(zarg^@argpower)
  elseif @argument == 22
    zarg = sinh(zarg)^@argpower
  elseif @argument == 23
    zarg = cosh(zarg)^@argpower
  elseif @argument == 24
    zarg = zarg + 1
  elseif @argument == 25
    zarg = (zarg + 1)^@argpower
  elseif @argument == 26
    zarg = zarg - 1
  elseif @argument == 27
    zarg = (zarg - 1)^@argpower
  elseif @argument == 28
    zarg = 1 - zarg
  elseif @argument == 29
    zarg = (1 - zarg)^@argpower
  elseif @argument == 30
    zarg = (zarg+1)*(zarg-1)
  elseif @argument == 31
    zarg = ((zarg+1)*(zarg-1))^@argpower
  elseif @argument == 32
    zarg = zarg*zarg+1
  elseif @argument == 33
    zarg = (zarg*zarg+1)^@argpower
  elseif @argument == 34
    zarg = zarg*zarg-1
  elseif @argument == 35
    zarg = (zarg*zarg-1)^@argpower
  elseif @argument == 36
    zarg = 1-zarg*zarg
  elseif @argument == 37
    zarg = (1-zarg*zarg)^@argpower
  elseif @argument == 38
    zarg = zarg^@argpower + 1
  elseif @argument == 39
    zarg = zarg^@argpower - 1
  elseif @argument == 40
    zarg = 1 - zarg^@argpower
  elseif @argument == 41
    zarg = (zarg + 1)/(zarg - 1)
  elseif @argument == 42
    zarg = ((zarg + 1)/(zarg - 1))^@argpower
  elseif @argument == 43
    zarg = (zarg-1)/(zarg+1)
  elseif @argument == 44
    zarg = ((zarg-1)/(zarg+1))^@argpower
  endif ; @argument

  if @static ; standard 11-term Taylor expansion
    ; Execute the hypergeometric formula
    z2 = zarg*zarg, z3 = z2*zarg, z4 = z3*zarg, z5 = z4*zarg, z6 = z5*zarg
    z7 = z6*zarg, z8 = z7*zarg, z9 = z8*zarg

    zarg = coeff0 + coeff1*zarg + coeff2*z2 + coeff3*z3 + coeff4*z4 + \
        coeff5*z5 + coeff6*z6 + coeff7*z7 + coeff8*z8 + \
        coeff9*z9 + coeff10*z9*zarg
    if !@blend
        z = zpre1*zpre2*zarg
    else
        z = @weight1 * zpre1*zpre2*zarg + @weight2 * z^@blendpower
    endif ; @blend
  else ; dynamic number of terms, based on iteration count
    iter = iter + 1
    if iter > 1
      if @p == 0
        numerator1 = numerator1
      elseif @p == 1
        a1_1 = a1_1 + @ca1
        numerator1 = numerator1*a1_1
      elseif @p == 2
        a1_1 = a1_1 + @ca1, a2_1 = a2_1 + @ca2
        numerator1 = numerator1*a1_1*a2_1
      elseif @p == 3
        a1_1 = a1_1 + @ca1, a2_1 = a2_1 + @ca2, a3_1 = a3_1 + @ca3
        numerator1 = numerator1*a1_1*a2_1*a3_1
      elseif @p == 4
        a1_1 = a1_1 + @ca1, a2_1 = a2_1 + @ca2, a3_1 = a3_1 + @ca3
        a4_1 = a4_1 + @ca4
        numerator1 = numerator1*a1_1*a2_1*a3_1*a4_1
      elseif @p == 5
        a1_1 = a1_1 + @ca1, a2_1 = a2_1 + @ca2, a3_1 = a3_1 + @ca3
        a4_1 = a4_1 + @ca4, a5_1 = a5_1 + @ca5
        numerator1 = numerator1*a1_1*a2_1*a3_1*a4_1*a5_1
      endif ; @p
      if @q == 0 ; store denominator in variable coeff1
        coeff1 = coeff1
      elseif @q == 1
        b1_1 = b1_1 + @cb1
        coeff1 = coeff1*b1_1
      elseif @q == 2
        b1_1 = b1_1 + @cb1, b2_1 = b2_1 + @cb2
        coeff1 = coeff1*b1_1*b2_1
      elseif @q == 3
        b1_1 = b1_1 + @cb1, b2_1 = b2_1 + @cb2, b3_1 = b3_1 + @cb3
        coeff1 = coeff1*b1_1*b2_1*b3_1
      elseif @q == 4
        b1_1 = b1_1 + @cb1, b2_1 = b2_1 + @cb2, b3_1 = b3_1 + @cb3
        b4_1 = b4_1 + @cb4
        coeff1 = coeff1*b1_1*b2_1*b3_1*b4_1
      elseif @q == 5
        b1_1 = b1_1 + @cb1, b2_1 = b2_1 + @cb2, b3_1 = b3_1 + @cb3
        b4_1 = b4_1 + @cb4, b5_1 = b5_1 + @cb5
        coeff1 = coeff1*b1_1*b2_1*b3_1*b4_1*b5_1
      endif ; @q
      zarg = numerator1*(zarg^iter)/(iter*coeff1)
    elseif iter == 0
      zarg = (1,0) ; first series term is always constant, 1
    else ; iter == 1
      if @p == 0
        numerator1 = numerator1
      elseif @p == 1
        numerator1 = a1_1
      elseif @p == 2
        numerator1 = a1_1*a2_1
      elseif @p == 3
        numerator1 = a1_1*a2_1*a3_1
      elseif @p == 4
        numerator1 = a1_1*a2_1*a3_1*a4_1
      elseif @p == 5
        numerator1 = a1_1*a2_1*a3_1*a4_1*a5_1
      endif ; @p
      if @q == 0 ; store denominator in variable coeff1
        coeff1 = coeff1
      elseif @q == 1
        coeff1 = b1_1
      elseif @q == 2
        coeff1 = b1_1*b2_1
      elseif @q == 3
        coeff1 = b1_1*b2_1*b3_1
      elseif @q == 4
        coeff1 = b1_1*b2_1*b3_1*b4_1
      elseif @q == 5
        coeff1 = b1_1*b2_1*b3_1*b4_1*b5_1
      endif ; @q
      zarg = numerator1*zarg/coeff1
    endif ; iter
    if iter >= @skipped
      if @alternate
        if iter%2 == 0
          sign = 1.0

        else
          sign = -1.0
        endif ; sign
      endif ; @alternate
      if !@blend
        z = z + sign*zpre1*zpre2*zarg
      else
        z = @weight1 * (z + sign*zpre1*zpre2*zarg) + @weight2 * z^@blendpower
      endif ; @blend
    endif ; iter
  endif ; @static

  if @pmode != 1
    z = z + jc
  endif ; pmode

  bailout:
  |z| < @bail

  default:
  title = "zHypergeo pFq Enhanced"
  center = (0,0)
  maxiter = 100
  method = multipass
  periodicity = 0
  magn = 0.25

  heading
  	caption = "There is a newer version of this formula"
  endheading

  param p
    caption = "Numerator Constants"
    min = 0
    max = 5
    default = 2
    hint = "This is p, the number of distinct numerator parameters used as input \
          to the generalized hypergeometric function \
          pFq(a1,a2,...,ap;b1,b2,...,bq;z).  Enter 0-5"
  endparam
  param q
    caption = "Denominator Constants"
    min = 0
    max = 5
    default = 2
    hint = "This is q, the number of distinct denominator parameters used as \
          input to the generalized hypergeometric function \
          pFq(a1,a2,...,ap;b1,b2,...,bq;z).  Enter 0-5"
  endparam
  param a1
    caption = "Constant a1"
    default = (0.5,0.0)
    hint = "This is the first constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 0"
  endparam
  param a2
    caption = "Constant a2"
    default = (0.5,0.0)
    hint = "This is the second constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 1"
  endparam
  param a3
    caption = "Constant a3"
    default = (0.5,0.0)
    hint = "This is the third constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 2"
  endparam
  param a4
    caption = "Constant a4"
    default = (0.5,0.0)
    hint = "This is the fourth constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 3"
  endparam
  param a5
    caption = "Constant a5"
    default = (0.5,0.0)
    hint = "This is the fifth constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 4"
  endparam
  param b1
    caption = "Constant b1"
    default = (1.0,0.0)
    hint = "This is the first constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 0"
  endparam
  param b2
    caption = "Constant b2"
    default = (1.0,0.0)
    hint = "This is the second constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 1"
  endparam
  param b3
    caption = "Constant b3"
    default = (0.75,0.0)
    hint = "This is the third constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 2"
  endparam
  param b4
    caption = "Constant b4"
    default = (0.75,0.0)
    hint = "This is the fourth constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 3"
  endparam
  param b5
    caption = "Constant b5"
    default = (0.75,0.0)
    hint = "This is the fifth constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 4"
  endparam
  param argument
    caption = "Argument Function"
    default = 0
    enum = "z" "1/z" "z^2" "z^power" "e^z" "e^-z" "e^z^power" "e^-(z^power)" \
          "sin z" "cos z" "sin(z^power)" "(sin z)^power" "log z" "loglog z" "z^z" \
          "z^-z" "z^z^power" "z^-(z^power)" "sinh z" "cosh z" "sinh z^power" \
          "cosh z^power" "(sinh z)^power" "(cosh z)^power" "z+1" "(z+1)^power" \
          "z-1" "(z-1)^power" "1-z" "(1-z)^power" "(z+1)(z-1)" "((z+1)(z-1))^power" \
          "z^2 + 1" "(z^2 + 1)^power" "z^2 - 1" "(z^2 - 1)^power" "1-z^2" \
          "(1-z^2)^power" "z^power + 1" "z^power - 1" "1 - z^power" "(z+1)/(z-1)" \
          "((z+1)/(z-1))^power" "(z-1)/(z+1)" "((z-1)/(z+1))^power"
    hint = "This is the argument to the hypergeometric series; z can be modified \
          by this function prior to being fed to the HG"
  endparam
  param argpower
    caption = "Argument Power"
    default = (2,0)
    hint = "If param 'Argument Function' needs an exponent, this is it"
  endparam
  param argmultiplier
    caption = "Argument Multiplier"
    default = (1,0)
    hint = "z is multiplied by this value before being modified by 'Argument Function'"
  endparam
  param prefunc1
    caption = "Prefunction 1"
    default = 0
    enum = "none" "z" "1/z" "z^2" "z^power" "e^z" "e^-z" "e^z^power" "e^-(z^power)" \
          "sin z" "cos z" "sin(z^power)" "(sin z)^power" "log z" "loglog z" "z^z" \
          "z^-z" "z^z^power" "z^-(z^power)" "sinh z" "cosh z" "sinh z^power" \
          "cosh z^power" "(sinh z)^power" "(cosh z)^power" "z+1" "(z+1)^power" \
          "z-1" "(z-1)^power" "1-z" "(1-z)^power" "(z+1)(z-1)" "((z+1)(z-1))^power" \
          "z^2 + 1" "(z^2 + 1)^power" "z^2 - 1" "(z^2 - 1)^power" "1-z^2" \
          "(1-z^2)^power" "z^power + 1" "z^power - 1" "1 - z^power" "(z+1)/(z-1)" \
          "((z+1)/(z-1))^power" "(z-1)/(z+1)" "((z-1)/(z+1))^power"
    hint = "The hypergeometric function can be multiplied by this function"
  endparam
  param pre1power
    caption = "PF 1 Power"
    default = (2,0)
    hint = "If param 'Prefunction 1' needs an exponent, this is it"
  endparam
  param pre1multiplier
    caption = "PF 1 Multiplier"
    default = (1,0)
    hint = "z is multiplied by this value before being fed to 'Prefunction 1'"
  endparam
  param prefunc2
    caption = "Prefunction 2"
    default = 0
    enum = "none" "z" "1/z" "z^2" "z^power" "e^z" "e^-z" "e^z^power" "e^-(z^power)" \
          "sin z" "cos z" "sin(z^power)" "(sin z)^power" "log z" "loglog z" "z^z" \
          "z^-z" "z^z^power" "z^-(z^power)" "sinh z" "cosh z" "sinh z^power" \
          "cosh z^power" "(sinh z)^power" "(cosh z)^power" "z+1" "(z+1)^power" \
          "z-1" "(z-1)^power" "1-z" "(1-z)^power" "(z+1)(z-1)" "((z+1)(z-1))^power" \
          "z^2 + 1" "(z^2 + 1)^power" "z^2 - 1" "(z^2 - 1)^power" "1-z^2" \
          "(1-z^2)^power" "z^power + 1" "z^power - 1" "1 - z^power" "(z+1)/(z-1)" \
          "((z+1)/(z-1))^power" "(z-1)/(z+1)" "((z-1)/(z+1))^power"
    hint = "The hypergeometric function can be multiplied by this function"
  endparam
  param pre2power
    caption = "PF 2 Power"
    default = (2,0)
    hint = "If param 'Prefunction 2' needs an exponent, this is it"
  endparam
  param pre2multiplier
    caption = "PF 2 Multiplier"
    default = (1,0)
    hint = "z is multiplied by this value before being fed to 'Prefunction 2'"
  endparam
  param ca1
    caption = "a1 Increment"
    default = (1,0)
    hint = "This is the amount that constant a1 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 0"
  endparam
  param ca2
    caption = "a2 Increment"
    default = (1,0)
    hint = "This is the amount that constant a2 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 1"
  endparam
  param ca3
    caption = "a3 Increment"
    default = (1,0)
    hint = "This is the amount that constant a3 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 2"
  endparam
  param ca4
    caption = "a4 Increment"
    default = (1,0)
    hint = "This is the amount that constant a4 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 3"
  endparam
  param ca5
    caption = "a5 Increment"
    default = (1,0)
    hint = "This is the amount that constant a5 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 4"
  endparam
  param cb1
    caption = "b1 Increment"
    default = (1,0)
    hint = "This is the amount that constant b1 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 0"
  endparam
  param cb2
    caption = "b2 Increment"
    default = (1,0)
    hint = "This is the amount that constant b2 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 1"
  endparam
  param cb3
    caption = "b3 Increment"
    default = (1,0)
    hint = "This is the amount that constant b3 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 2"
  endparam
  param cb4
    caption = "b4 Increment"
    default = (1,0)
    hint = "This is the amount that constant b4 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 3"
  endparam
  param cb5
    caption = "b5 Increment"
    default = (1,0)
    hint = "This is the amount that constant b5 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 4"
  endparam
  param static
    caption = "Static Mode"
    default = TRUE
    hint = "If enabled, a static, 11-term Taylor series is used to define \
          the hypergeometric function; otherwise, the series is dynamically \
          summed based on the current iteration count"
  endparam
  param skipped
    caption = "Terms to Skip"
    default = 0
    min = 0
    hint = "In Dynamic mode only, this number of terms in the hypergeometric \
          series will be skipped"
  endparam
  param alternate
    caption = "Alternate Terms?"
    default = FALSE
    hint = "In Dynamic mode only, if enabled, the terms of the hypergeometric \
          series will alternate in sign"
  endparam
  param pixelformula
    caption = "Pixel Formula"
    enum = "p" "p^2" "p^3" "p^4" "p^power" "1/p" "sqrt(p)" "1/p^2" "log(p)" "e^p" \
          "p^p" "sin(p)" "cos(p)" \
          "tan(p)" "asin(p)" "acos(p)" "atan(p)" "sinh(p)" "cosh(p)" "tanh(p)" \
          "asinh(p)" "acosh(p)" "atanh(p)" "log(1/p)" "log(log(p))" "e^-p" \
          "e^(1/p)" "p^-p" "sin(p)^2" "cos(p)^2" "tan(p)^2" "cot(p)" "sec(p)" \
          "csc(p)" "cot(p)^2" "sec(p)^2" "csc(p)^2" "p^p^p" "1/p^p^p" "log(-p)" \
          "1/log(p)" "plog(p)" "sin(p)/p" "cos(p)/p" "sin(p)*cos(p)" "sin(p^2)" \
          "e^(-1/p)" "pe^p" "pe^-p" "pe^(1/p)" "pe^(-1/p)" "p^3" "1/p^3" \
          "acot(p)" "asec(p)" "acsc(p)" "tan(p)/p" "cot(p)/p" "sec(p)/p" \
          "csc(p)/p" "psin(p)" "pcos(p)" "ptan(p)" "pcot(p)" "psec(p)" "pcsc(p)" \
          "sin(1/p)" "cos(1/p)" "tan(1/p)" "cot(1/p)" "sec(1/p)" "csc(1/p)" \
          "cotanh(p)" "sech(p)" "cosech(p)" "acoth(p)" "asech(p)" "acosech(p)" \
          "3-term polynomial" "sinh(p)^2" "cosh(p)^2" "tanh(p)^2" "cotanh(p)^2" \
          "sech(p)^2" "cosech(p)^2" "sinh(1/p)" "cosh(1/p)" "tanh(1/p)" \
          "cotanh(1/p)" "sech(1/p)" "cosech(1/p)" "sin(p)tan(p)" "sinh(p)tanh(p)" \
          "sinh(p)cosh(p)" "sinh(p)^2*cosh(p)^2" "sin(p)^2*cos(p)^2" \
          "sin(1/p)*cos(1/p)" "sin(1/p)^2" "sin(p)cos(1/p)" "sin(p)sin(1/p)" \
          "log(p)^2" "sin(p)sin(2p)" "e^2p" "e^-2p" "sinh(1/p)cosh(1/p)" \
          "sinh(1/p)^2" "sinh(p)cosh(1/p)" "sinh(p)sinh(1/p)" "sin(p)sinh(p)" \
          "sin(p)cosh(p)" "sin(p)^2*sinh(p)^2" "sin(p)e^p" "cos(p)e^p" \
          "sinh(p)e^p" "cosh(p)e^p" "sin(p)log(p)" "cos(p)log(p)" "sinh(p)log(p)" \
          "cosh(p)log(p)"
    default = 0
    hint = "Pixel value (Mand) or seed (Julia) can be initialized \
        before iterating. For 'p^power', set parameter 'Pixel Power'; \
        for '3-term polynomial', set 'Coeff Pa', 'Exponent Pa', 'Coeff Pb', \
        'Exponent Pb', 'Coeff Pc', 'Exponent Pc'. 'p' results in normal \
        initialization"
  endparam
  param ppower
    caption = "Pixel Power"
    default = (5,0)
    hint = "This is the power used if parameter \
        'Pixel Formula' is set to 'p^power'"
  endparam
  param coeffpa
    caption = "Coeff Pa"

    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 1st term"
  endparam
  param exponentpa
    caption = "Exponent Pa"
    default = (6,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 1st term"
  endparam
  param coeffpb
    caption = "Coeff Pb"
    default = (-1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 2nd term"
  endparam
  param exponentpb
    caption = "Exponent Pb"
    default = (4,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 2nd term"
  endparam
  param coeffpc
    caption = "Coeff Pc"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 3rd term"
  endparam
  param exponentpc
    caption = "Exponent Pc"
    default = (2,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 3rd term"
  endparam
  param pmode
    caption = "Pixel Mode"
    default = 0
    enum = "Post-add" "Pre-add" "Both"
    hint = "'Post-add' -- formula is executed, then pixel/constant is added to result; \
        'Pre-add' -- pixel is added to z, then formula executed; 'Both' -- pixel added, \
        formula executed, then pixel added again to result"
  endparam
  param blend
    caption = "Blend Z^Power"
    default = FALSE
    hint = "If true, then the hypergeometric function is blended with a normal \
            z^powerMandelbrot/Julia, z = c1*hypergeo(z) + c2*z^power.  Set the \
            weight coefficients c1 & c2 with params 'Hypergeo Weight' and 'Z^Power \
            Weight'.  The exponent is set with param 'Blend Power'"
  endparam
  param weight1
    caption = "Hypergeo Weight"
    default = -0.1
    hint = "If 'Blend Z^Power' is enabled (TRUE), then this coefficient sets the \
            relative proportion of the hypergeometric function that is blended \
            with z^power each iteration to obtain the final z"
  endparam
  param weight2
    caption = "Z^Power Weight"
    default = 1.0
    hint = "If 'Blend Z^Power' is enabled (TRUE), then this coefficient sets the \
            relative proportion of the z^power function that is blended \
            with the hypergeometric each iteration to obtain the final z"
  endparam
  param blendpower
    caption = "Blend Power"
    default = (2,0)
    hint = "If 'Blend Z^Power' is enabled (TRUE), then this parameter sets the \
          exponent for the z^power function (i.e., this is the power)"
  endparam
  param jconstant
    caption = "Seed/Perturbation"
    default = (0,0)
    hint = "This is the seed constant for Julia-type fractals, or the initial \
          perturbation for Mandelbrot-types"
  endparam
  param bail
    caption = "Bailout Value"
    default = 64.0
    hint = "Value needed to 'escape' to infinity"
  endparam
  param mandy
    caption = "Mandelbrot flag"
    default = TRUE
    hint = "Works in combination with the Julia flag for switching"
  endparam
  param julia
    caption = "Julia flag"
    default = FALSE
    hint = "Works in combination with the Mandelbrot flag for switching"
  endparam

  switch:
  type = "jam-hypergeometricPFQ"
  jconstant = #pixel
  bail = bail
  p = p
  q = q
  a1 = a1

  a2 = a2
  a3 = a3
  a4 = a4
  a5 = a5
  b1 = b1
  b2 = b2
  b3 = b3
  b4 = b4
  b5 = b5
  argument = argument
  argpower = argpower
  argmultiplier = argmultiplier
  prefunc1 = prefunc1
  pre1power = pre1power
  pre1multiplier = pre1multiplier
  prefunc2 = prefunc2
  pre2power = pre2power
  pre2multiplier = pre2multiplier
  ca1 = ca1
  ca2 = ca2
  ca3 = ca3
  ca4 = ca4
  ca5 = ca5
  cb1 = cb1
  cb2 = cb2
  cb3 = cb3
  cb4 = cb4
  cb5 = cb5
  static = static
  skipped = skipped
  alternate = alternate
  pixelformula = pixelformula
  ppower = ppower
  coeffpa = coeffpa
  exponentpa = exponentpa
  coeffpb = coeffpb
  exponentpb = exponentpb
  coeffpc = coeffpc
  exponentpc = exponentpc
  blend = blend
  weight1 = weight1
  weight2 = weight2
  blendpower = blendpower
  pmode = pmode
  mandy = julia
  julia = mandy
}

jam-hypergeometricPFQ-explorer { ; jam 020424
  ; Fake Mandelbrot/Julia based on the generalized hypergeometric function pFq,
  ; pFq(a1,a2,...,ap;b1,b2,...,bq;z) = 1 + (a1*a2*...*ap/(b1*b2*...*bq*1!))z +
  ; (a1*[a1+1]*a2*[a2+2]*...*ap*[ap+1]/(b1*[b1+1]*b2*[b2+1]*...*bq*[bq+1]*2!))z^2
  ; + ...
  ; The function is implemented as an 11-term series expansion about z=0,
  ; or as a dynamic expansion using an indefinite number of terms based on
  ; the current iteration count.
  ; z argument may be modified before passage to the hypergeometric function,
  ; and the HG function may also be multiplied by 1 or 2 other functions.

  ; This formula is not really meant for iterating fractals, but for
  ; identifying useful or interesting input constants for the
  ; generalized hypergeometric fractal jam-hypergeometricPFQ ('pFq Enhanced').
  ; After finding constants here, use that formula instead, i.e., after identifying
  ; constants of interest, switch to the other formula
  ; for a faster iterating, Mandelbrot/Julia formula pair.

  ; Please disregard the initially all black screen should it occur.  This
  ; view results from the 'Switch Constant' not yet being properly intialized.
  ; Just turn on UF's switch feature, move the cursor around normally,
  ; and click when the preview window shows something interesting.  The
  ; constants selected by the switch can then be read off from the formula
  ; parameter 'Switch Constant', and correspond to whichever hypergeometric
  ; constants are currently selected by param 'Switch Variables'.

  ; If these formulas are directly used for iterating fractals, there will
  ; be some performance hit due to the overhead associated with the
  ; 'Switch Variables' logic, and ordinary switching between Mandelbrot/Julia
  ; types will not be possible.

  ; Please contact me (maddry@sri.org) if you have questions/comments about
  ; these formulas.  Thanks, enjoy, & happy fractaling!

  ; In a bit more detail:
  ; This is a fake Mandelbrot formula to facilitate finding interesting
  ; a & b constants for the hypergeometric function pFq, as defined above.
  ; The function is implemented as an 11-term series expansion about z=0
  ; (static mode enabled, the default), or as a continuous summation
  ; based on iteration count.

  ; By selecting the appropriate pair of 'Switch Variables', UF's switching feature
  ; can be used to search for interesting combinations of the a & b constants.
  ; Use the Explorer this way: set the 'Switch Variables' to the pair of
  ; HG constants you wish to vary, & set the others manually if desired.  Then
  ; enter switch mode, move the cursor to vary the selected constants, then click
  ; upon finding something interesting.  After the switch, the selected
  ; constants can be read off from UF param 'Switch Constant'; the real part
  ; corresponds to the first of the 'Switch Variables', the imag part to the
  ; second of the 'Switch Variables'.  You can then set these manually and change
  ; the 'Switch Variables' setting to continue searching for other HG constants.
  ; Disregard any initially blank screen, which results from the 'Switch Constant'
  ; not having been set yet; just turn on UF's switch feature and move around
  ; the screen normally.  Either two numerator constants, two denominator
  ; constants, or one numerator and one denominator constant may be searched at a
  ; time.

  init:
  if @mandy
    z = @jconstant, jc = #pixel
  else ; Julia
    z = #pixel, jc = @jconstant
  endif

  complex zextra = complex ztemp = (0,0) ; temp/spare scratch variables
  complex zarg = complex zpre1 = complex zpre2 = (0,0)

  ; declare vars for powers of z
  complex z2 = complex z3 = complex z4 = complex z5 = complex z6 = (0,0)
  complex z7 = complex z8 = complex z9 = (0,0)

  ; compute coefficients for series
  ; start with the numerator and denominator input parameters (the a's & b's)
  complex a1_1 = @a1, complex a2_1 = @a2, complex a3_1 = @a3, complex a4_1 = @a4
  complex b1_1 = @b1, complex b2_1 = @b2, complex b3_1 = @b3, complex b4_1 = @b4
  complex a5_1 = @a5, complex b5_1 = @b5

  if @switchvars == 0 ; a1--a2
    a1_1 = real(@switchconst), a2_1 = imag(@switchconst)
  elseif @switchvars == 1 ; a1--b1
    a1_1 = real(@switchconst), b1_1 = imag(@switchconst)
  elseif @switchvars == 2 ; b1--b2
    b1_1 = real(@switchconst), b2_1 = imag(@switchconst)
  endif ; @switchvars

  ; initialize all the other variables, to eliminate annoying warning messages
  complex a1_2 = complex a1_3 = complex a1_4 = complex a1_5 = (0,0)
  complex a1_6 = complex a1_7 = complex a1_8 = complex a1_9 = complex a1_10 = (0,0)
  complex a2_2 = complex a2_3 = complex a2_4 = complex a2_5 = (0,0)
  complex a2_6 = complex a2_7 = complex a2_8 = complex a2_9 = complex a2_10 = (0,0)
  complex a3_2 = complex a3_3 = complex a3_4 = complex a3_5 = (0,0)
  complex a3_6 = complex a3_7 = complex a3_8 = complex a3_9 = complex a3_10 = (0,0)
  complex a4_2 = complex a4_3 = complex a4_4 = complex a4_5 = (0,0)
  complex a4_6 = complex a4_7 = complex a4_8 = complex a4_9 = complex a4_10 = (0,0)
  complex a5_2 = complex a5_3 = complex a5_4 = complex a5_5 = (0,0)
  complex a5_6 = complex a5_7 = complex a5_8 = complex a5_9 = complex a5_10 = (0,0)
  complex b1_2 = complex b1_3 = complex b1_4 = complex b1_5 = (0,0)
  complex b1_6 = complex b1_7 = complex b1_8 = complex b1_9 = complex b1_10 = (0,0)
  complex b2_2 = complex b2_3 = complex b2_4 = complex b2_5 = (0,0)
  complex b2_6 = complex b2_7 = complex b2_8 = complex b2_9 = complex b2_10 = (0,0)
  complex b3_2 = complex b3_3 = complex b3_4 = complex b3_5 = (0,0)
  complex b3_6 = complex b3_7 = complex b3_8 = complex b3_9 = complex b3_10 = (0,0)
  complex b4_2 = complex b4_3 = complex b4_4 = complex b4_5 = (0,0)
  complex b4_6 = complex b4_7 = complex b4_8 = complex b4_9 = complex b4_10 = (0,0)
  complex b5_2 = complex b5_3 = complex b5_4 = complex b5_5 = (0,0)
  complex b5_6 = complex b5_7 = complex b5_8 = complex b5_9 = complex b5_10 = (0,0)
  complex coeff0 = complex coeff1 = (1,0)
  complex coeff2 = complex coeff3 = (1,0)
  complex coeff4 = complex coeff5 = (1,0)
  complex coeff6 = complex coeff7 = (1,0)
  complex coeff8 = complex coeff9 = (1,0)
  complex coeff10 = (1,0)
  complex numerator1 = complex numerator2 = complex numerator3 = (1,0)
  complex numerator4 = complex numerator5 = complex numerator6 = (1,0)
  complex numerator7 = complex numerator8 = complex numerator9 = (1,0)
  complex numerator10 = (1,0)
  int iter = -1, float sign = 1.0

  if @static ; using 11-term Taylor series expansion
    ; now define the coefficient numerator constants
    if @p == 0 ; nothing more to do to the numerator
      coeff0 = coeff0 ; but we have to do something to avoid a UF error
    else ; p must be at least 1
      a1_2 =  a1_1+@ca1, a1_3 = a1_2+@ca1
      a1_4 = a1_3+@ca1, a1_5 = a1_4+@ca1, a1_6 = a1_5+@ca1
      a1_7 = a1_6+@ca1, a1_8 = a1_7+@ca1, a1_9 = a1_8+@ca1
      a1_10 = a1_9+@ca1
      if @p > 1 ; p must be at least 2
        a2_2 =  a2_1+@ca2, a2_3 = a2_2+@ca2
        a2_4 = a2_3+@ca2, a2_5 = a2_4+@ca2, a2_6 = a2_5+@ca2
        a2_7 = a2_6+@ca2, a2_8 = a2_7+@ca2, a2_9 = a2_8+@ca2
        a2_10 = a2_9+@ca2
      endif ; @p
      if @p > 2 ; p must be at least 3
        a3_2 =  a3_1+@ca3, a3_3 = a3_2+@ca3
        a3_4 = a3_3+@ca3, a3_5 = a3_4+@ca3, a3_6 = a3_5+@ca3
        a3_7 = a3_6+@ca3, a3_8 = a3_7+@ca3, a3_9 = a3_8+@ca3
        a3_10 = a3_9+@ca3
      endif ; @p
      if @p > 3 ; p must be at least 4
        a4_2 =  a4_1+@ca4, a4_3 = a4_2+@ca4
        a4_4 = a4_3+@ca4, a4_5 = a4_4+@ca4, a4_6 = a4_5+@ca4
        a4_7 = a4_6+@ca4, a4_8 = a4_7+@ca4, a4_9 = a4_8+@ca4
        a4_10 = a4_9+@ca4
      endif ; @p
      if @p > 4 ; p must be at least 5
        a5_2 =  a5_1+@ca5, a5_3 = a5_2+@ca5
        a5_4 = a5_3+@ca5, a5_5 = a5_4+@ca5, a5_6 = a5_5+@ca5
        a5_7 = a5_6+@ca5, a5_8 = a5_7+@ca5, a5_9 = a5_8+@ca5
        a5_10 = a5_9+@ca5
      endif ; @p
    endif ; @p
    ; define the coefficient denominator constants
    if @q == 0 ; nothing more to do to the denominator
      coeff0 = coeff0 ; but we have to do something to avoid a UF error
    else ; q must be at least 1
      b1_2 =  b1_1+@cb1, b1_3 = b1_2+@cb1
      b1_4 = b1_3+@cb1, b1_5 = b1_4+@cb1, b1_6 = b1_5+@cb1
      b1_7 = b1_6+@cb1, b1_8 = b1_7+@cb1, b1_9 = b1_8+@cb1
      b1_10 = b1_9+@cb1
      if @q > 1 ; q must be at least 2
        b2_2 =  b2_1+@cb2, b2_3 = b2_2+@cb2
        b2_4 = b2_3+@cb2, b2_5 = b2_4+@cb2, b2_6 = b2_5+@cb2
        b2_7 = b2_6+@cb2, b2_8 = b2_7+@cb2, b2_9 = b2_8+@cb2
        b2_10 = b2_9+@cb2
      endif ; @q
      if @q > 2 ; q must be at least 3
        b3_2 =  b3_1+@cb3, b3_3 = b3_2+@cb3
        b3_4 = b3_3+@cb3, b3_5 = b3_4+@cb3, b3_6 = b3_5+@cb3
        b3_7 = b3_6+@cb3, b3_8 = b3_7+@cb3, b3_9 = b3_8+@cb3
        b3_10 = b3_9+@cb3
      endif ; @q
      if @q > 3 ; q must be at least 4
        b4_2 =  b4_1+@cb4, b4_3 = b4_2+@cb4
        b4_4 = b4_3+@cb4, b4_5 = b4_4+@cb4, b4_6 = b4_5+@cb4
        b4_7 = b4_6+@cb4, b4_8 = b4_7+@cb4, b4_9 = b4_8+@cb4
        b4_10 = b4_9+@cb4
      endif ; @q
      if @q > 4 ; q must be at least 5
        b5_2 =  b5_1+@cb5, b5_3 = b5_2+@cb5
        b5_4 = b5_3+@cb5, b5_5 = b5_4+@cb5, b5_6 = b5_5+@cb5
        b5_7 = b5_6+@cb5, b5_8 = b5_7+@cb5, b5_9 = b5_8+@cb5
        b5_10 = b5_9+@cb5
      endif ; @q
    endif ; @q
    ; now put them all together, in the process converting the factorials to their
    ; reciprocals.  We are doing it the long way, to minimize the number of divisions
    if @q == 1
      coeff1 = coeff0*b1_1
      coeff2 = coeff1*b1_2
      coeff3 = coeff2*b1_3
      coeff4 = coeff3*b1_4
      coeff5 = coeff4*b1_5
      coeff6 = coeff5*b1_6
      coeff7 = coeff6*b1_7
      coeff8 = coeff7*b1_8
      coeff9 = coeff8*b1_9
      coeff10 = coeff9*b1_10
    elseif @q == 2
      coeff1 = coeff0*b1_1*b2_1
      coeff2 = coeff1*b1_2*b2_2
      coeff3 = coeff2*b1_3*b2_3
      coeff4 = coeff3*b1_4*b2_4
      coeff5 = coeff4*b1_5*b2_5
      coeff6 = coeff5*b1_6*b2_6
      coeff7 = coeff6*b1_7*b2_7
      coeff8 = coeff7*b1_8*b2_8
      coeff9 = coeff8*b1_9*b2_9
      coeff10 = coeff9*b1_10*b2_10
    elseif @q == 3
      coeff1 = coeff0*b1_1*b2_1*b3_1
      coeff2 = coeff1*b1_2*b2_2*b3_2
      coeff3 = coeff2*b1_3*b2_3*b3_3
      coeff4 = coeff3*b1_4*b2_4*b3_4
      coeff5 = coeff4*b1_5*b2_5*b3_5
      coeff6 = coeff5*b1_6*b2_6*b3_6
      coeff7 = coeff6*b1_7*b2_7*b3_7
      coeff8 = coeff7*b1_8*b2_8*b3_8
      coeff9 = coeff8*b1_9*b2_9*b3_9
      coeff10 = coeff9*b1_10*b2_10*b3_10
    elseif @q == 4
      coeff1 = coeff0*b1_1*b2_1*b3_1*b4_1
      coeff2 = coeff1*b1_2*b2_2*b3_2*b4_2
      coeff3 = coeff2*b1_3*b2_3*b3_3*b4_3
      coeff4 = coeff3*b1_4*b2_4*b3_4*b4_4
      coeff5 = coeff4*b1_5*b2_5*b3_5*b4_5
      coeff6 = coeff5*b1_6*b2_6*b3_6*b4_6
      coeff7 = coeff6*b1_7*b2_7*b3_7*b4_7
      coeff8 = coeff7*b1_8*b2_8*b3_8*b4_8
      coeff9 = coeff8*b1_9*b2_9*b3_9*b4_9
      coeff10 = coeff9*b1_10*b2_10*b3_10*b4_10
    elseif @q == 5
      coeff1 = coeff0*b1_1*b2_1*b3_1*b4_1*b5_1
      coeff2 = coeff1*b1_2*b2_2*b3_2*b4_2*b5_2
      coeff3 = coeff2*b1_3*b2_3*b3_3*b4_3*b5_3
      coeff4 = coeff3*b1_4*b2_4*b3_4*b4_4*b5_4
      coeff5 = coeff4*b1_5*b2_5*b3_5*b4_5*b5_5
      coeff6 = coeff5*b1_6*b2_6*b3_6*b4_6*b5_6
      coeff7 = coeff6*b1_7*b2_7*b3_7*b4_7*b5_7
      coeff8 = coeff7*b1_8*b2_8*b3_8*b4_8*b5_8
      coeff9 = coeff8*b1_9*b2_9*b3_9*b4_9*b5_9
      coeff10 = coeff9*b1_10*b2_10*b3_10*b4_10*b5_10
    endif ; @q
    if @p == 1
      numerator1 = a1_1
      numerator2 = a1_2*numerator1
      numerator3 = a1_3*numerator2
      numerator4 = a1_4*numerator3
      numerator5 = a1_5*numerator4
      numerator6 = a1_6*numerator5
      numerator7 = a1_7*numerator6
      numerator8 = a1_8*numerator7
      numerator9 = a1_9*numerator8
      numerator10 = a1_10*numerator9
    elseif @p == 2
      numerator1 = a1_1*a2_1
      numerator2 = a1_2*a2_2*numerator1
      numerator3 = a1_3*a2_3*numerator2
      numerator4 = a1_4*a2_4*numerator3
      numerator5 = a1_5*a2_5*numerator4
      numerator6 = a1_6*a2_6*numerator5
      numerator7 = a1_7*a2_7*numerator6
      numerator8 = a1_8*a2_8*numerator7
      numerator9 = a1_9*a2_9*numerator8
      numerator10 = a1_10*a2_10*numerator9
    elseif @p == 3
      numerator1 = a1_1*a2_1*a3_1
      numerator2 = a1_2*a2_2*a3_2*numerator1
      numerator3 = a1_3*a2_3*a3_3*numerator2
      numerator4 = a1_4*a2_4*a3_4*numerator3
      numerator5 = a1_5*a2_5*a3_5*numerator4
      numerator6 = a1_6*a2_6*a3_6*numerator5
      numerator7 = a1_7*a2_7*a3_7*numerator6
      numerator8 = a1_8*a2_8*a3_8*numerator7
      numerator9 = a1_9*a2_9*a3_9*numerator8
      numerator10 = a1_10*a2_10*a3_10*numerator9
    elseif @p == 4
      numerator1 = a1_1*a2_1*a3_1*a4_1
      numerator2 = a1_2*a2_2*a3_2*a4_2*numerator1
      numerator3 = a1_3*a2_3*a3_3*a4_3*numerator2
      numerator4 = a1_4*a2_4*a3_4*a4_4*numerator3
      numerator5 = a1_5*a2_5*a3_5*a4_5*numerator4
      numerator6 = a1_6*a2_6*a3_6*a4_6*numerator5
      numerator7 = a1_7*a2_7*a3_7*a4_7*numerator6
      numerator8 = a1_8*a2_8*a3_8*a4_8*numerator7
      numerator9 = a1_9*a2_9*a3_9*a4_9*numerator8
      numerator10 = a1_10*a2_10*a3_10*a4_10*numerator9
    elseif @p == 5
      numerator1 = a1_1*a2_1*a3_1*a4_1*a5_1
      numerator2 = a1_2*a2_2*a3_2*a4_2*a5_2*numerator1
      numerator3 = a1_3*a2_3*a3_3*a4_3*a5_3*numerator2
      numerator4 = a1_4*a2_4*a3_4*a4_4*a5_4*numerator3
      numerator5 = a1_5*a2_5*a3_5*a4_5*a5_5*numerator4
      numerator6 = a1_6*a2_6*a3_6*a4_6*a5_6*numerator5
      numerator7 = a1_7*a2_7*a3_7*a4_7*a5_7*numerator6
      numerator8 = a1_8*a2_8*a3_8*a4_8*a5_8*numerator7
      numerator9 = a1_9*a2_9*a3_9*a4_9*a5_9*numerator8
      numerator10 = a1_10*a2_10*a3_10*a4_10*a5_10*numerator9
    endif ; @p
    coeff1 = numerator1/coeff1
    coeff2 = numerator2/(2*coeff2)
    coeff3 = numerator3/(6*coeff3)
    coeff4 = numerator4/(24*coeff4)
    coeff5 = numerator5/(120*coeff5)
    coeff6 = numerator6/(720*coeff6)
    coeff7 = numerator7/(5040*coeff7)
    coeff8 = numerator8/(40320*coeff8)
    coeff9 = numerator9/(362880*coeff9)
    coeff10 = numerator10/(3628800*coeff10)
  endif ; @static

  ; Pixel/constant initialization section
  if @pixelformula != 0
    if @pixelformula == 1
      jc = jc * jc
    elseif  @pixelformula == 2
      jc = jc * jc * jc
    elseif  @pixelformula == 3
      zextra = jc * jc
      jc = zextra * zextra
    elseif  @pixelformula == 4
      jc = jc ^ @ppower
    elseif  @pixelformula == 5
      jc = 1/jc
    elseif  @pixelformula == 6
      jc = sqrt(jc)
    elseif  @pixelformula == 7
      jc = 1 / ( jc * jc )
    elseif  @pixelformula == 8
      jc = log(jc)
    elseif  @pixelformula == 9
      jc = exp( jc)
    elseif  @pixelformula == 10
      jc = jc^jc
    elseif  @pixelformula == 11
      jc = sin( jc )
    elseif  @pixelformula == 12
      jc = cos( jc )
    elseif  @pixelformula == 13
      jc = tan( jc )
    elseif  @pixelformula == 14
      jc = asin( jc )
    elseif  @pixelformula == 15
      jc = acos( jc )
    elseif  @pixelformula == 16
      jc = atan( jc )
    elseif  @pixelformula == 17
      jc = sinh( jc )
    elseif  @pixelformula == 18
      jc = cosh( jc )
    elseif  @pixelformula == 19
      jc = tanh( jc )
    elseif  @pixelformula == 20
      jc = asinh( jc )
    elseif  @pixelformula == 21
      jc = acosh( jc )
    elseif  @pixelformula == 22
      jc = atanh( jc )
    elseif  @pixelformula == 23
      jc = log( 1/jc )
    elseif  @pixelformula == 24
      jc = log( log( jc ))
    elseif  @pixelformula == 25
      jc = exp( -jc )
    elseif  @pixelformula == 26
      jc = exp( 1/jc )
    elseif  @pixelformula == 27
      jc = jc^(-jc)

    elseif  @pixelformula == 28
      zextra = sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 29
      zextra = cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 30
      zextra = tan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 31
      jc = cotan( jc )
    elseif  @pixelformula == 32
      jc = 1/cos( jc )
    elseif  @pixelformula == 33
      jc = 1/sin( jc )
    elseif  @pixelformula == 34
      zextra = cotan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 35
      zextra = 1/cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 36
      zextra = 1/sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 37
      zextra = jc^(jc)
      jc = jc^zextra
    elseif  @pixelformula == 38
      zextra = jc^(jc)
      jc = 1/( jc^zextra )
    elseif  @pixelformula == 39
      jc = log(-jc)
    elseif  @pixelformula == 40
      jc = 1/log( jc )
    elseif  @pixelformula == 41
      jc = jc * log( jc )
    elseif  @pixelformula == 42
      jc = sin( jc ) / jc
    elseif  @pixelformula == 43
      jc = cos( jc ) / jc
    elseif  @pixelformula == 44
      jc = sin( jc ) * cos( jc )
    elseif  @pixelformula == 45
      jc = sin( jc^2 )
    elseif  @pixelformula == 46
      jc = exp( -1/jc )
    elseif  @pixelformula == 47
      jc = jc * exp( jc )
    elseif  @pixelformula == 48
      jc = jc * exp( -jc )
    elseif  @pixelformula == 49
      jc = jc * exp( 1/jc )
    elseif  @pixelformula == 50
      jc = jc * exp( -1/jc )
    elseif  @pixelformula == 51
      jc = jc * jc * jc
    elseif  @pixelformula == 52
      jc = 1 / ( jc * jc * jc )
    elseif  @pixelformula == 53
      jc = atan( 1 / jc )
    elseif  @pixelformula == 54
      jc = acos( 1 / jc )
    elseif  @pixelformula == 55
      jc = asin( 1 / jc )
    elseif  @pixelformula == 56
      jc = tan( jc ) / jc
    elseif  @pixelformula == 57
      jc = cotan( jc ) / jc
    elseif  @pixelformula == 58
      jc = 1 / ( jc * cos( jc ))
    elseif  @pixelformula == 59
      jc = 1 / ( jc * sin( jc ))
    elseif  @pixelformula == 60
      jc = jc * sin( jc )
    elseif  @pixelformula == 61
      jc = jc * cos( jc )
    elseif  @pixelformula == 62
      jc = jc * tan( jc )
    elseif  @pixelformula == 63
      jc = jc * cotan( jc )
    elseif  @pixelformula == 64
      jc = jc/cos( jc )
    elseif  @pixelformula == 65
      jc = jc/sin( jc )
    elseif  @pixelformula == 66
      jc = sin( 1/jc )
    elseif  @pixelformula == 67
      jc = cos( 1/jc )
    elseif  @pixelformula == 68
      jc = tan( 1/jc )
    elseif  @pixelformula == 69
      jc = cotan( 1/jc )
    elseif  @pixelformula == 70
      jc = 1/cos( 1/jc )
    elseif  @pixelformula == 71
      jc = 1/sin( 1/jc )
    elseif  @pixelformula == 72
      jc = cotanh( jc )
    elseif  @pixelformula == 73
      jc = 1/cosh( jc )
    elseif  @pixelformula == 74
      jc = 1/sinh( jc )
    elseif  @pixelformula == 75
      jc = atanh( 1/jc )
    elseif  @pixelformula == 76
      jc = acosh( 1/jc )
    elseif  @pixelformula == 77
      jc = asinh( 1/jc )
    elseif @pixelformula == 78
      jc = @coeffpa * jc^@exponentpa + @coeffpb * jc^@exponentpb + \
          @coeffpc * jc^@exponentpc
    elseif  @pixelformula == 79
      zextra = sinh(#z)
      jc = zextra * zextra
    elseif  @pixelformula == 80
      zextra = cosh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 81
      zextra = tanh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 82
      zextra = cotanh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 83
      zextra = (1,0)/cosh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 84
      zextra = (1,0) / sinh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 85
      jc = sinh(1/jc)
    elseif  @pixelformula == 86
      jc = cosh(1/jc)
    elseif  @pixelformula == 87
      jc = tanh(1/jc)
    elseif  @pixelformula == 88
      jc = cotanh(1/jc)
    elseif  @pixelformula == 89
      jc = (1,0)/cosh(1/jc)
    elseif  @pixelformula == 90
      jc = (1,0)/sinh(1/jc)
    elseif  @pixelformula == 91
      jc = sin( jc ) * tan(jc)
    elseif  @pixelformula == 92
      jc = sinh(jc) * tanh(jc)
    elseif  @pixelformula == 93
      jc = sinh(jc) * cosh(jc)
    elseif  @pixelformula == 94
      ztemp = sinh(jc), zextra = cosh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 95
      ztemp = sin(jc), zextra = cos(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 96
      zextra = 1/jc
      jc = sin(zextra)*cos(zextra)
    elseif  @pixelformula == 97
      zextra = sin( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 98
      jc = sin(jc) * cos(1/jc)
    elseif  @pixelformula == 99
      jc = sin(jc) * sin(1/jc)
    elseif  @pixelformula == 100
      zextra = log(jc)
      jc = zextra*zextra
    elseif  @pixelformula == 101
      jc = sin(jc) * sin(2*jc)
    elseif @pixelformula == 102
      jc = exp(2*jc)
    elseif  @pixelformula == 103
      jc = exp(-2*jc)
    elseif  @pixelformula == 104
      zextra = 1/jc
      jc = sinh(zextra)*cosh(zextra)
    elseif  @pixelformula == 105
      zextra = sinh( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 106
      jc = sinh(jc) * cosh(1/jc)
    elseif  @pixelformula == 107
      jc = sinh(jc) * sinh(1/jc)
    elseif  @pixelformula == 108
      jc = sin(jc) * sinh(jc)
    elseif  @pixelformula == 109
      jc = sin(jc) * cosh(jc)
    elseif  @pixelformula == 110
      zextra = sin(jc), ztemp = sinh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 111
      jc = sin(jc)*exp(jc)
    elseif  @pixelformula == 112
      jc = cos(jc)*exp(jc)
    elseif  @pixelformula == 113
      jc = sinh(jc)*exp(jc)
    elseif  @pixelformula == 114
      jc = cosh(jc)*exp(jc)
    elseif  @pixelformula == 115
      jc = sin(jc)*log(jc)
    elseif  @pixelformula == 116
      jc = cos(jc)*log(jc)
    elseif  @pixelformula == 117
      jc = sinh(jc)*log(jc)
    else ; @pixelformula == 118
      jc = cosh(jc)*log(jc)
    endif ; @pixelformula = 1
  endif ; @pixelformula != 0

  loop:
  if @pmode != 0
    z = z + jc
  endif ; pmode

  ; Execute PF1
  if @pre1multiplier != (1,0)
    zpre1 = @pre1multiplier*z
  else
    zpre1 = z
  endif ; @pre1multiplier
  if @prefunc1 == 0
    zpre1 = (1,0)
  elseif @prefunc1 == 2
    zpre1 = 1/zpre1
  elseif @prefunc1 == 3
    zpre1 = zpre1*zpre1
  elseif @prefunc1 == 4
    zpre1 = zpre1^@pre1power
  elseif @prefunc1 == 5
    zpre1 = exp(zpre1)
  elseif @prefunc1 == 6
    zpre1 = exp(-zpre1)
  elseif @prefunc1 == 7
    zpre1 = exp(zpre1^@pre1power)
  elseif @prefunc1 == 8
    zpre1 = exp(-(zpre1^@pre1power))
  elseif @prefunc1 == 9
    zpre1 = sin(zpre1)
  elseif @prefunc1 == 10
    zpre1 = cos(zpre1)
  elseif @prefunc1 == 11
    zpre1 = sin(z^@pre1power)
  elseif @prefunc1 == 12
    zpre1 = (sin(zpre1))^@pre1power
  elseif @prefunc1 == 13
    zpre1 = log(zpre1)
  elseif @prefunc1 == 14
    zpre1 = log(log(zpre1))
  elseif @prefunc1 == 15
    zpre1 = zpre1^zpre1
  elseif @prefunc1 == 16
    zpre1 = zpre1^(-zpre1)
  elseif @prefunc1 == 17
    zpre1 = zpre1^(zpre1^@pre1power)
  elseif @prefunc1 == 18
    zpre1 = zpre1^(-(zpre1^@pre1power))
  elseif @prefunc1 == 19
    zpre1 = sinh(zpre1)
  elseif @prefunc1 == 20
    zpre1 = cosh(zpre1)
  elseif @prefunc1 == 21
    zpre1 = sinh(zpre1^@pre1power)
  elseif @prefunc1 == 22
    zpre1 = cosh(zpre1^@pre1power)
  elseif @prefunc1 == 23
    zpre1 = sinh(zpre1)^@pre1power
  elseif @prefunc1 == 24
    zpre1 = cosh(zpre1)^@pre1power
  elseif @prefunc1 == 25
    zpre1 = zpre1 + 1
  elseif @prefunc1 == 26
    zpre1 = (zpre1 + 1)^@pre1power
  elseif @prefunc1 == 27
    zpre1 = zpre1 - 1
  elseif @prefunc1 == 28
    zpre1 = (zpre1 - 1)^@pre1power
  elseif @prefunc1 == 29
    zpre1 = 1 - zpre1
  elseif @prefunc1 == 30
    zpre1 = (1 - zpre1)^@pre1power
  elseif @prefunc1 == 31
    zpre1 = (zpre1+1)*(zpre1-1)
  elseif @prefunc1 == 32
    zpre1 = ((zpre1+1)*(zpre1-1))^@pre1power
  elseif @prefunc1 == 33
    zpre1 = zpre1*zpre1+1
  elseif @prefunc1 == 34
    zpre1 = (zpre1*zpre1+1)^@pre1power
  elseif @prefunc1 == 35
    zpre1 = zpre1*zpre1-1
  elseif @prefunc1 == 36
    zpre1 = (zpre1*zpre1-1)^@pre1power
  elseif @prefunc1 == 37
    zpre1 = 1-zpre1*zpre1
  elseif @prefunc1 == 38
    zpre1 = (1-zpre1*zpre1)^@pre1power
  elseif @prefunc1 == 39
    zpre1 = zpre1^@pre1power + 1
  elseif @prefunc1 == 40
    zpre1 = zpre1^@pre1power - 1
  elseif @prefunc1 == 41
    zpre1 = 1 - zpre1^@pre1power
  elseif @prefunc1 == 42
    zpre1 = (zpre1 + 1)/(zpre1 - 1)
  elseif @prefunc1 == 43
    zpre1 = ((zpre1 + 1)/(zpre1 - 1))^@pre1power
  elseif @prefunc1 == 44
    zpre1 = (zpre1-1)/(zpre1+1)
  elseif @prefunc1 == 45
    zpre1 = ((zpre1-1)/(zpre1+1))^@pre1power
  endif ; @prefunc1

  ; Execute PF2
  if @pre2multiplier != (1,0)
    zpre2 = @pre2multiplier*z
  else
    zpre2 = z
  endif ; @pre2multiplier
  if @prefunc2 == 0
    zpre2 = (1,0)
  elseif @prefunc2 == 2
    zpre2 = 1/zpre2
  elseif @prefunc2 == 3
    zpre2 = zpre2*zpre2
  elseif @prefunc2 == 4
    zpre2 = zpre2^@pre2power
  elseif @prefunc2 == 5
    zpre2 = exp(zpre2)
  elseif @prefunc2 == 6
    zpre2 = exp(-zpre2)
  elseif @prefunc2 == 7
    zpre2 = exp(zpre2^@pre2power)
  elseif @prefunc2 == 8
    zpre2 = exp(-(zpre2^@pre2power))
  elseif @prefunc2 == 9
    zpre2 = sin(zpre2)
  elseif @prefunc2 == 10
    zpre2 = cos(zpre2)
  elseif @prefunc2 == 11
    zpre2 = sin(z^@pre2power)
  elseif @prefunc2 == 12
    zpre2 = (sin(zpre2))^@pre2power
  elseif @prefunc2 == 13
    zpre2 = log(zpre2)
  elseif @prefunc2 == 14
    zpre2 = log(log(zpre2))
  elseif @prefunc2 == 15
    zpre2 = zpre2^zpre2
  elseif @prefunc2 == 16
    zpre2 = zpre2^(-zpre2)
  elseif @prefunc2 == 17
    zpre2 = zpre2^(zpre2^@pre2power)
  elseif @prefunc2 == 18
    zpre2 = zpre2^(-(zpre2^@pre2power))
  elseif @prefunc2 == 19
    zpre2 = sinh(zpre2)
  elseif @prefunc2 == 20
    zpre2 = cosh(zpre2)
  elseif @prefunc2 == 21
    zpre2 = sinh(zpre2^@pre2power)
  elseif @prefunc2 == 22
    zpre2 = cosh(zpre2^@pre2power)
  elseif @prefunc2 == 23
    zpre2 = sinh(zpre2)^@pre2power
  elseif @prefunc2 == 24
    zpre2 = cosh(zpre2)^@pre2power
  elseif @prefunc2 == 25
    zpre2 = zpre2 + 1
  elseif @prefunc2 == 26
    zpre2 = (zpre2 + 1)^@pre2power
  elseif @prefunc2 == 27
    zpre2 = zpre2 - 1
  elseif @prefunc2 == 28
    zpre2 = (zpre2 - 1)^@pre2power
  elseif @prefunc2 == 29
    zpre2 = 1 - zpre2
  elseif @prefunc2 == 30
    zpre2 = (1 - zpre2)^@pre2power
  elseif @prefunc2 == 31
    zpre2 = (zpre2+1)*(zpre2-1)
  elseif @prefunc2 == 32
    zpre2 = ((zpre2+1)*(zpre2-1))^@pre2power
  elseif @prefunc2 == 33
    zpre2 = zpre2*zpre2+1
  elseif @prefunc2 == 34
    zpre2 = (zpre2*zpre2+1)^@pre2power
  elseif @prefunc2 == 35
    zpre2 = zpre2*zpre2-1
  elseif @prefunc2 == 36
    zpre2 = (zpre2*zpre2-1)^@pre2power
  elseif @prefunc2 == 37
    zpre2 = 1-zpre2*zpre2
  elseif @prefunc2 == 38
    zpre2 = (1-zpre2*zpre2)^@pre2power
  elseif @prefunc2 == 39
    zpre2 = zpre2^@pre2power + 1
  elseif @prefunc2 == 40
    zpre2 = zpre2^@pre2power - 1
  elseif @prefunc2 == 41
    zpre2 = 1 - zpre2^@pre2power
  elseif @prefunc2 == 42
    zpre2 = (zpre2 + 1)/(zpre2 - 1)
  elseif @prefunc2 == 43
    zpre2 = ((zpre2 + 1)/(zpre2 - 1))^@pre2power
  elseif @prefunc2 == 44
    zpre2 = (zpre2-1)/(zpre2+1)
  elseif @prefunc2 == 45
    zpre2 = ((zpre2-1)/(zpre2+1))^@pre2power
  endif ; @prefunc2

  ; Execute argument function
  if @argmultiplier != (1,0)
    zarg = @argmultiplier*z
  else
    zarg = z
  endif ; @argmultiplier
  if @argument == 1
    zarg = 1/zarg
  elseif @argument == 2
    zarg = zarg*zarg
  elseif @argument == 3
    zarg = zarg^@argpower
  elseif @argument == 4
    zarg = exp(zarg)
  elseif @argument == 5
    zarg = exp(-zarg)
  elseif @argument == 6
    zarg = exp(zarg^@argpower)
  elseif @argument == 7
    zarg = exp(-(zarg^@argpower))
  elseif @argument == 8
    zarg = sin(zarg)
  elseif @argument == 9
    zarg = cos(zarg)
  elseif @argument == 10
    zarg = sin(z^@argpower)
  elseif @argument == 11
    zarg = (sin(zarg))^@argpower
  elseif @argument == 12
    zarg = log(zarg)
  elseif @argument == 13
    zarg = log(log(zarg))
  elseif @argument == 14
    zarg = zarg^zarg
  elseif @argument == 15
    zarg = zarg^(-zarg)
  elseif @argument == 16
    zarg = zarg^(zarg^@argpower)
  elseif @argument == 17
    zarg = zarg^(-(zarg^@argpower))
  elseif @argument == 18
    zarg = sinh(zarg)
  elseif @argument == 19
    zarg = cosh(zarg)
  elseif @argument == 20
    zarg = sinh(zarg^@argpower)
  elseif @argument == 21
    zarg = cosh(zarg^@argpower)
  elseif @argument == 22
    zarg = sinh(zarg)^@argpower
  elseif @argument == 23
    zarg = cosh(zarg)^@argpower
  elseif @argument == 24
    zarg = zarg + 1
  elseif @argument == 25
    zarg = (zarg + 1)^@argpower
  elseif @argument == 26
    zarg = zarg - 1
  elseif @argument == 27
    zarg = (zarg - 1)^@argpower
  elseif @argument == 28
    zarg = 1 - zarg
  elseif @argument == 29
    zarg = (1 - zarg)^@argpower
  elseif @argument == 30
    zarg = (zarg+1)*(zarg-1)
  elseif @argument == 31
    zarg = ((zarg+1)*(zarg-1))^@argpower
  elseif @argument == 32
    zarg = zarg*zarg+1
  elseif @argument == 33
    zarg = (zarg*zarg+1)^@argpower
  elseif @argument == 34
    zarg = zarg*zarg-1
  elseif @argument == 35
    zarg = (zarg*zarg-1)^@argpower
  elseif @argument == 36
    zarg = 1-zarg*zarg
  elseif @argument == 37
    zarg = (1-zarg*zarg)^@argpower
  elseif @argument == 38
    zarg = zarg^@argpower + 1
  elseif @argument == 39
    zarg = zarg^@argpower - 1
  elseif @argument == 40
    zarg = 1 - zarg^@argpower
  elseif @argument == 41
    zarg = (zarg + 1)/(zarg - 1)
  elseif @argument == 42
    zarg = ((zarg + 1)/(zarg - 1))^@argpower
  elseif @argument == 43
    zarg = (zarg-1)/(zarg+1)
  elseif @argument == 44
    zarg = ((zarg-1)/(zarg+1))^@argpower
  endif ; @argument

  if @static ; standard 11-term Taylor expansion
    ; Execute the hypergeometric formula
    z2 = zarg*zarg, z3 = z2*zarg, z4 = z3*zarg, z5 = z4*zarg, z6 = z5*zarg
    z7 = z6*zarg, z8 = z7*zarg, z9 = z8*zarg

    z = coeff0 + coeff1*zarg + coeff2*z2 + coeff3*z3 + coeff4*z4 + \
        coeff5*z5 + coeff6*z6 + coeff7*z7 + coeff8*z8 + \
        coeff9*z9 + coeff10*z9*zarg
    z = zpre1*zpre2*z
  else ; dynamic number of terms, based on iteration count
    iter = iter + 1
    if iter > 1
      if @p == 0
        numerator1 = numerator1
      elseif @p == 1
        a1_1 = a1_1 + @ca1
        numerator1 = numerator1*a1_1
      elseif @p == 2
        a1_1 = a1_1 + @ca1, a2_1 = a2_1 + @ca2
        numerator1 = numerator1*a1_1*a2_1
      elseif @p == 3
        a1_1 = a1_1 + @ca1, a2_1 = a2_1 + @ca2, a3_1 = a3_1 + @ca3
        numerator1 = numerator1*a1_1*a2_1*a3_1
      elseif @p == 4
        a1_1 = a1_1 + @ca1, a2_1 = a2_1 + @ca2, a3_1 = a3_1 + @ca3
        a4_1 = a4_1 + @ca4
        numerator1 = numerator1*a1_1*a2_1*a3_1*a4_1
      elseif @p == 5
        a1_1 = a1_1 + @ca1, a2_1 = a2_1 + @ca2, a3_1 = a3_1 + @ca3
        a4_1 = a4_1 + @ca4, a5_1 = a5_1 + @ca5
        numerator1 = numerator1*a1_1*a2_1*a3_1*a4_1*a5_1
      endif ; @p
      if @q == 0 ; store denominator in variable coeff1
        coeff1 = coeff1
      elseif @q == 1
        b1_1 = b1_1 + @cb1
        coeff1 = coeff1*b1_1
      elseif @q == 2
        b1_1 = b1_1 + @cb1, b2_1 = b2_1 + @cb2
        coeff1 = coeff1*b1_1*b2_1
      elseif @q == 3
        b1_1 = b1_1 + @cb1, b2_1 = b2_1 + @cb2, b3_1 = b3_1 + @cb3
        coeff1 = coeff1*b1_1*b2_1*b3_1
      elseif @q == 4
        b1_1 = b1_1 + @cb1, b2_1 = b2_1 + @cb2, b3_1 = b3_1 + @cb3
        b4_1 = b4_1 + @cb4
        coeff1 = coeff1*b1_1*b2_1*b3_1*b4_1
      elseif @q == 5
        b1_1 = b1_1 + @cb1, b2_1 = b2_1 + @cb2, b3_1 = b3_1 + @cb3
        b4_1 = b4_1 + @cb4, b5_1 = b5_1 + @cb5
        coeff1 = coeff1*b1_1*b2_1*b3_1*b4_1*b5_1
      endif ; @q
      zarg = numerator1*(zarg^iter)/(iter*coeff1)
    elseif iter == 0
      zarg = (1,0) ; first series term is always constant, 1
    else ; iter == 1
      if @p == 0
        numerator1 = numerator1
      elseif @p == 1
        numerator1 = a1_1
      elseif @p == 2
        numerator1 = a1_1*a2_1
      elseif @p == 3
        numerator1 = a1_1*a2_1*a3_1
      elseif @p == 4
        numerator1 = a1_1*a2_1*a3_1*a4_1
      elseif @p == 5
        numerator1 = a1_1*a2_1*a3_1*a4_1*a5_1
      endif ; @p
      if @q == 0 ; store denominator in variable coeff1
        coeff1 = coeff1
      elseif @q == 1
        coeff1 = b1_1
      elseif @q == 2
        coeff1 = b1_1*b2_1
      elseif @q == 3
        coeff1 = b1_1*b2_1*b3_1
      elseif @q == 4
        coeff1 = b1_1*b2_1*b3_1*b4_1
      elseif @q == 5
        coeff1 = b1_1*b2_1*b3_1*b4_1*b5_1
      endif ; @q
      zarg = numerator1*zarg/coeff1
    endif ; iter
    if iter >= @skipped
      if @alternate
        if iter%2 == 0
          sign = 1.0
        else
          sign = -1.0
        endif ; sign
      endif ; @alternate
      z = z + sign*zpre1*zpre2*zarg
    endif ; iter
  endif ; @static

  if @pmode != 1
    z = z + jc
  endif ; pmode

  bailout:
  |z| < @bail

  default:
  title = "zHypergeometric pFq Explorer"
  center = (0,0)
  maxiter = 100
  method = multipass
  periodicity = 0
  magn = 0.25

  heading
  	caption = "There is a newer version of this formula"
  endheading

  param p
    caption = "Numerator Constants"
    min = 0
    max = 5
    default = 2
    hint = "This is p, the number of distinct numerator parameters used as input \
          to the generalized hypergeometric function \
          pFq(a1,a2,...,ap;b1,b2,...,bq;z).  Enter 0-5"
  endparam
  param q
    caption = "Denominator Constants"
    min = 0
    max = 5
    default = 2
    hint = "This is q, the number of distinct denominator parameters used as \
          input to the generalized hypergeometric function \
          pFq(a1,a2,...,ap;b1,b2,...,bq;z).  Enter 0-5"
  endparam
  param switchvars
    caption = "Switch Variables"
    enum = "a1 a2" "a1 b1" "b1 b2"
    default = 0
    hint = "These are the 2 hypergeometric function constants that will be \
            varied by cursor movement during a switch; the others should be \
            entered manually below, if desired, using the appropriate params"
  endparam
  param switchconst
    caption = "Switch Constant"
    default = (0.5,0.5)
    hint = "This is a dummy variable used to set the HG function constants \
          during a switch, and should not be set manually. After the switch, \
          the two 'Switch Variables' can be read from the real/imag parts of \
          this parameter"
  endparam
  param a1
    caption = "Constant a1"
    default = (0.5,0.0)
    hint = "This is the first constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 0"
  endparam
  param a2
    caption = "Constant a2"
    default = (0.5,0.0)
    hint = "This is the second constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 1"
  endparam
  param a3
    caption = "Constant a3"
    default = (0.5,0.0)
    hint = "This is the third constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 2"
  endparam
  param a4
    caption = "Constant a4"
    default = (0.5,0.0)
    hint = "This is the fourth constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 3"
  endparam
  param a5
    caption = "Constant a5"
    default = (0.5,0.0)
    hint = "This is the fifth constant used to define the numerator of the \
          hypergeometric function, if 'Numerator Constants' > 4"
  endparam
  param b1
    caption = "Constant b1"
    default = (1.0,0.0)
    hint = "This is the first constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 0"
  endparam
  param b2
    caption = "Constant b2"
    default = (1.0,0.0)
    hint = "This is the second constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 1"
  endparam
  param b3
    caption = "Constant b3"
    default = (0.75,0.0)
    hint = "This is the third constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 2"
  endparam
  param b4
    caption = "Constant b4"
    default = (0.75,0.0)
    hint = "This is the fourth constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 3"
  endparam
  param b5
    caption = "Constant b5"
    default = (0.75,0.0)
    hint = "This is the fifth constant used to define the denominator of the \
          hypergeometric function, if 'Denominator Constants' > 4"
  endparam
  param argument
    caption = "Argument Function"
    default = 0
    enum = "z" "1/z" "z^2" "z^power" "e^z" "e^-z" "e^z^power" "e^-(z^power)" \
          "sin z" "cos z" "sin(z^power)" "(sin z)^power" "log z" "loglog z" "z^z" \
          "z^-z" "z^z^power" "z^-(z^power)" "sinh z" "cosh z" "sinh z^power" \
          "cosh z^power" "(sinh z)^power" "(cosh z)^power" "z+1" "(z+1)^power" \
          "z-1" "(z-1)^power" "1-z" "(1-z)^power" "(z+1)(z-1)" "((z+1)(z-1))^power" \
          "z^2 + 1" "(z^2 + 1)^power" "z^2 - 1" "(z^2 - 1)^power" "1-z^2" \
          "(1-z^2)^power" "z^power + 1" "z^power - 1" "1 - z^power" "(z+1)/(z-1)" \
          "((z+1)/(z-1))^power" "(z-1)/(z+1)" "((z-1)/(z+1))^power"
    hint = "This is the argument to the hypergeometric series; z can be modified \
          by this function prior to being fed to the HG"
  endparam
  param argpower
    caption = "Argument Power"
    default = (2,0)
    hint = "If param 'Argument Function' needs an exponent, this is it"
  endparam
  param argmultiplier
    caption = "Argument Multiplier"
    default = (1,0)
    hint = "z is multiplied by this value before being modified by 'Argument Function'"
  endparam
  param prefunc1
    caption = "Prefunction 1"
    default = 0
    enum = "none" "z" "1/z" "z^2" "z^power" "e^z" "e^-z" "e^z^power" "e^-(z^power)" \
          "sin z" "cos z" "sin(z^power)" "(sin z)^power" "log z" "loglog z" "z^z" \
          "z^-z" "z^z^power" "z^-(z^power)" "sinh z" "cosh z" "sinh z^power" \
          "cosh z^power" "(sinh z)^power" "(cosh z)^power" "z+1" "(z+1)^power" \
          "z-1" "(z-1)^power" "1-z" "(1-z)^power" "(z+1)(z-1)" "((z+1)(z-1))^power" \
          "z^2 + 1" "(z^2 + 1)^power" "z^2 - 1" "(z^2 - 1)^power" "1-z^2" \
          "(1-z^2)^power" "z^power + 1" "z^power - 1" "1 - z^power" "(z+1)/(z-1)" \
          "((z+1)/(z-1))^power" "(z-1)/(z+1)" "((z-1)/(z+1))^power"
    hint = "The hypergeometric function can be multiplied by this function"
  endparam
  param pre1power
    caption = "PF 1 Power"
    default = (2,0)
    hint = "If param 'Prefunction 1' needs an exponent, this is it"
  endparam
  param pre1multiplier
    caption = "PF 1 Multiplier"
    default = (1,0)
    hint = "z is multiplied by this value before being fed to 'Prefunction 1'"
  endparam
  param prefunc2
    caption = "Prefunction 2"
    default = 0
    enum = "none" "z" "1/z" "z^2" "z^power" "e^z" "e^-z" "e^z^power" "e^-(z^power)" \
          "sin z" "cos z" "sin(z^power)" "(sin z)^power" "log z" "loglog z" "z^z" \
          "z^-z" "z^z^power" "z^-(z^power)" "sinh z" "cosh z" "sinh z^power" \
          "cosh z^power" "(sinh z)^power" "(cosh z)^power" "z+1" "(z+1)^power" \
          "z-1" "(z-1)^power" "1-z" "(1-z)^power" "(z+1)(z-1)" "((z+1)(z-1))^power" \
          "z^2 + 1" "(z^2 + 1)^power" "z^2 - 1" "(z^2 - 1)^power" "1-z^2" \
          "(1-z^2)^power" "z^power + 1" "z^power - 1" "1 - z^power" "(z+1)/(z-1)" \
          "((z+1)/(z-1))^power" "(z-1)/(z+1)" "((z-1)/(z+1))^power"
    hint = "The hypergeometric function can be multiplied by this function"
  endparam
  param pre2power
    caption = "PF 2 Power"
    default = (2,0)
    hint = "If param 'Prefunction 2' needs an exponent, this is it"
  endparam
  param pre2multiplier
    caption = "PF 2 Multiplier"
    default = (1,0)
    hint = "z is multiplied by this value before being fed to 'Prefunction 2'"
  endparam
  param ca1
    caption = "a1 Increment"
    default = (1,0)
    hint = "This is the amount that constant a1 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 0"
  endparam
  param ca2
    caption = "a2 Increment"
    default = (1,0)
    hint = "This is the amount that constant a2 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 1"
  endparam
  param ca3
    caption = "a3 Increment"
    default = (1,0)
    hint = "This is the amount that constant a3 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 2"
  endparam
  param ca4
    caption = "a4 Increment"
    default = (1,0)
    hint = "This is the amount that constant a4 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Numerator Constants' > 3"
  endparam
  param ca5
    caption = "a5 Increment"
    default = (1,0)
    hint = "This is the amount that constant a5 is increased in each \
            successive term of the series expansion of the hypergeometric \

            function, if 'Numerator Constants' > 4"
  endparam
  param cb1
    caption = "b1 Increment"
    default = (1,0)
    hint = "This is the amount that constant b1 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 0"
  endparam
  param cb2
    caption = "b2 Increment"
    default = (1,0)
    hint = "This is the amount that constant b2 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 1"
  endparam
  param cb3
    caption = "b3 Increment"
    default = (1,0)
    hint = "This is the amount that constant b3 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 2"
  endparam
  param cb4
    caption = "b4 Increment"
    default = (1,0)
    hint = "This is the amount that constant b4 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 3"
  endparam
  param cb5
    caption = "b5 Increment"
    default = (1,0)
    hint = "This is the amount that constant b5 is increased in each \
            successive term of the series expansion of the hypergeometric \
            function, if 'Denominator Constants' > 4"
  endparam
  param static
    caption = "Static Mode"
    default = TRUE
    hint = "If enabled, a static, 11-term Taylor series is used to define \
          the hypergeometric function; otherwise, the series is dynamically \
          summed based on the current iteration count"
  endparam
  param skipped
    caption = "Terms to Skip"
    default = 0
    min = 0
    hint = "In Dynamic mode only, this number of terms in the hypergeometric \
          series will be skipped"
  endparam
  param alternate
    caption = "Alternate Terms?"
    default = FALSE
    hint = "In Dynamic mode only, if enabled, the terms of the hypergeometric \
          series will alternate in sign"
  endparam
  param pixelformula
    caption = "Pixel Formula"
    enum = "p" "p^2" "p^3" "p^4" "p^power" "1/p" "sqrt(p)" "1/p^2" "log(p)" "e^p" \
          "p^p" "sin(p)" "cos(p)" \
          "tan(p)" "asin(p)" "acos(p)" "atan(p)" "sinh(p)" "cosh(p)" "tanh(p)" \
          "asinh(p)" "acosh(p)" "atanh(p)" "log(1/p)" "log(log(p))" "e^-p" \
          "e^(1/p)" "p^-p" "sin(p)^2" "cos(p)^2" "tan(p)^2" "cot(p)" "sec(p)" \
          "csc(p)" "cot(p)^2" "sec(p)^2" "csc(p)^2" "p^p^p" "1/p^p^p" "log(-p)" \
          "1/log(p)" "plog(p)" "sin(p)/p" "cos(p)/p" "sin(p)*cos(p)" "sin(p^2)" \
          "e^(-1/p)" "pe^p" "pe^-p" "pe^(1/p)" "pe^(-1/p)" "p^3" "1/p^3" \
          "acot(p)" "asec(p)" "acsc(p)" "tan(p)/p" "cot(p)/p" "sec(p)/p" \
          "csc(p)/p" "psin(p)" "pcos(p)" "ptan(p)" "pcot(p)" "psec(p)" "pcsc(p)" \
          "sin(1/p)" "cos(1/p)" "tan(1/p)" "cot(1/p)" "sec(1/p)" "csc(1/p)" \
          "cotanh(p)" "sech(p)" "cosech(p)" "acoth(p)" "asech(p)" "acosech(p)" \
          "3-term polynomial" "sinh(p)^2" "cosh(p)^2" "tanh(p)^2" "cotanh(p)^2" \
          "sech(p)^2" "cosech(p)^2" "sinh(1/p)" "cosh(1/p)" "tanh(1/p)" \
          "cotanh(1/p)" "sech(1/p)" "cosech(1/p)" "sin(p)tan(p)" "sinh(p)tanh(p)" \
          "sinh(p)cosh(p)" "sinh(p)^2*cosh(p)^2" "sin(p)^2*cos(p)^2" \
          "sin(1/p)*cos(1/p)" "sin(1/p)^2" "sin(p)cos(1/p)" "sin(p)sin(1/p)" \
          "log(p)^2" "sin(p)sin(2p)" "e^2p" "e^-2p" "sinh(1/p)cosh(1/p)" \
          "sinh(1/p)^2" "sinh(p)cosh(1/p)" "sinh(p)sinh(1/p)" "sin(p)sinh(p)" \
          "sin(p)cosh(p)" "sin(p)^2*sinh(p)^2" "sin(p)e^p" "cos(p)e^p" \
          "sinh(p)e^p" "cosh(p)e^p" "sin(p)log(p)" "cos(p)log(p)" "sinh(p)log(p)" \
          "cosh(p)log(p)"
    default = 0
    hint = "Pixel value (Mand) or seed (Julia) can be initialized \
        before iterating. For 'p^power', set parameter 'Pixel Power'; \
        for '3-term polynomial', set 'Coeff Pa', 'Exponent Pa', 'Coeff Pb', \
        'Exponent Pb', 'Coeff Pc', 'Exponent Pc'. 'p' results in normal \
        initialization"
  endparam
  param ppower
    caption = "Pixel Power"
    default = (5,0)
    hint = "This is the power used if parameter \
        'Pixel Formula' is set to 'p^power'"
  endparam
  param coeffpa
    caption = "Coeff Pa"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 1st term"
  endparam
  param exponentpa
    caption = "Exponent Pa"
    default = (6,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 1st term"
  endparam
  param coeffpb
    caption = "Coeff Pb"
    default = (-1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 2nd term"
  endparam
  param exponentpb
    caption = "Exponent Pb"
    default = (4,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 2nd term"
  endparam
  param coeffpc
    caption = "Coeff Pc"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 3rd term"
  endparam
  param exponentpc
    caption = "Exponent Pc"
    default = (2,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 3rd term"
  endparam
  param pmode
    caption = "Pixel Mode"
    default = 0
    enum = "Post-add" "Pre-add" "Both"
    hint = "'Post-add' -- formula is executed, then pixel/constant is added to result; \
        'Pre-add' -- pixel is added to z, then formula executed; 'Both' -- pixel added, \
        formula executed, then pixel added again to result"
  endparam
  param jconstant
    caption = "Seed/Perturbation"
    default = (0,0)
    hint = "This is the seed constant for Julia-type fractals, or the initial \
          perturbation for Mandelbrot-types"
  endparam
  param bail
    caption = "Bailout Value"
    default = 64.0
    hint = "Value needed to 'escape' to infinity"
  endparam
  param mandy
    caption = "Mandelbrot flag"
    default = TRUE
    hint = "Plot type. Enabled = Mandelbrot, disabled = Julia"
  endparam

  switch:
  type = "jam-hypergeometricPFQ-explorer"
  jconstant = jconstant
  bail = bail
  switchconst = #pixel
  switchvars = switchvars
  p = p
  q = q
  a1 = a1
  a2 = a2
  a3 = a3
  a4 = a4
  a5 = a5
  b1 = b1
  b2 = b2
  b3 = b3
  b4 = b4
  b5 = b5
  argument = argument
  argpower = argpower
  argmultiplier = argmultiplier
  prefunc1 = prefunc1
  pre1power = pre1power
  pre1multiplier = pre1multiplier
  prefunc2 = prefunc2
  pre2power = pre2power
  pre2multiplier = pre2multiplier
  ca1 = ca1
  ca2 = ca2
  ca3 = ca3
  ca4 = ca4
  ca5 = ca5
  cb1 = cb1
  cb2 = cb2
  cb3 = cb3
  cb4 = cb4
  cb5 = cb5
  static = static
  skipped = skipped
  alternate = alternate
  pixelformula = pixelformula
  ppower = ppower
  coeffpa = coeffpa
  exponentpa = exponentpa
  coeffpb = coeffpb
  exponentpb = exponentpb
  coeffpc = coeffpc
  exponentpc = exponentpc
  pmode = pmode
  mandy = mandy
}

jam-3stageGen { ; jam 020430
  ; 2 or 3 different Mandelbrot/Julia style formulas are executed
  ; and combined in a user-specified manner, either each iteration
  ; or every N iterations.  Each formula may depend on the current z
  ; or any of the previous 5 z's.  The primary formula, Formula F,
  ; is executed every iteration, while the other 2 formulas (G & H)
  ; may execute each iteration, or only intermittently every N iters.
  ; To use just 2 formulas, set 'Formula H' to 'none'.

  ; Questions/comments to Joe Maddry (maddry@sri.org).  Thanks!

  init:
  if @mandy
    z = @jconstant, jc = #pixel
  else
    z = #pixel, jc = @jconstant
  endif

  int iterations = 0
  complex zextra = complex ztemp = (0,0) ; temp/spare scratch variable
  complex zold = complex zold2 = complex zold3 = complex zold4 = complex zold5 = (0,0)
  complex ztemp1 = complex ztemp2 = complex ztemp3 = (0,0)

  ; Pixel/constant initialization section
  if @pixelformula != 0
    if @pixelformula == 1
      jc = jc * jc
    elseif  @pixelformula == 2
      jc = jc * jc * jc
    elseif  @pixelformula == 3
      zextra = jc * jc
      jc = zextra * zextra
    elseif  @pixelformula == 4
      jc = jc ^ @ppower
    elseif  @pixelformula == 5
      jc = 1/jc
    elseif  @pixelformula == 6
      jc = sqrt(jc)
    elseif  @pixelformula == 7
      jc = 1 / ( jc * jc )
    elseif  @pixelformula == 8
      jc = log(jc)
    elseif  @pixelformula == 9
      jc = exp( jc)
    elseif  @pixelformula == 10
      jc = jc^jc
    elseif  @pixelformula == 11
      jc = sin( jc )
    elseif  @pixelformula == 12
      jc = cos( jc )
    elseif  @pixelformula == 13
      jc = tan( jc )
    elseif  @pixelformula == 14
      jc = asin( jc )
    elseif  @pixelformula == 15
      jc = acos( jc )
    elseif  @pixelformula == 16
      jc = atan( jc )
    elseif  @pixelformula == 17
      jc = sinh( jc )
    elseif  @pixelformula == 18
      jc = cosh( jc )
    elseif  @pixelformula == 19
      jc = tanh( jc )
    elseif  @pixelformula == 20
      jc = asinh( jc )
    elseif  @pixelformula == 21
      jc = acosh( jc )
    elseif  @pixelformula == 22
      jc = atanh( jc )
    elseif  @pixelformula == 23
      jc = log( 1/jc )
    elseif  @pixelformula == 24
      jc = log( log( jc ))
    elseif  @pixelformula == 25
      jc = exp( -jc )
    elseif  @pixelformula == 26
      jc = exp( 1/jc )
    elseif  @pixelformula == 27
      jc = jc^(-jc)
    elseif  @pixelformula == 28
      zextra = sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 29
      zextra = cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 30
      zextra = tan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 31
      jc = cotan( jc )
    elseif  @pixelformula == 32
      jc = 1/cos( jc )
    elseif  @pixelformula == 33
      jc = 1/sin( jc )
    elseif  @pixelformula == 34
      zextra = cotan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 35
      zextra = 1/cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 36
      zextra = 1/sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 37
      zextra = jc^(jc)
      jc = jc^zextra
    elseif  @pixelformula == 38
      zextra = jc^(jc)
      jc = 1/( jc^zextra )
    elseif  @pixelformula == 39
      jc = log(-jc)
    elseif  @pixelformula == 40
      jc = 1/log( jc )
    elseif  @pixelformula == 41
      jc = jc * log( jc )
    elseif  @pixelformula == 42
      jc = sin( jc ) / jc
    elseif  @pixelformula == 43
      jc = cos( jc ) / jc
    elseif  @pixelformula == 44
      jc = sin( jc ) * cos( jc )
    elseif  @pixelformula == 45
      jc = sin( jc^2 )
    elseif  @pixelformula == 46
      jc = exp( -1/jc )
    elseif  @pixelformula == 47
      jc = jc * exp( jc )
    elseif  @pixelformula == 48
      jc = jc * exp( -jc )
    elseif  @pixelformula == 49
      jc = jc * exp( 1/jc )
    elseif  @pixelformula == 50
      jc = jc * exp( -1/jc )
    elseif  @pixelformula == 51
      jc = jc * jc * jc
    elseif  @pixelformula == 52
      jc = 1 / ( jc * jc * jc )
    elseif  @pixelformula == 53
      jc = atan( 1 / jc )
    elseif  @pixelformula == 54
      jc = acos( 1 / jc )
    elseif  @pixelformula == 55
      jc = asin( 1 / jc )
    elseif  @pixelformula == 56
      jc = tan( jc ) / jc
    elseif  @pixelformula == 57
      jc = cotan( jc ) / jc
    elseif  @pixelformula == 58
      jc = 1 / ( jc * cos( jc ))
    elseif  @pixelformula == 59
      jc = 1 / ( jc * sin( jc ))
    elseif  @pixelformula == 60
      jc = jc * sin( jc )
    elseif  @pixelformula == 61
      jc = jc * cos( jc )
    elseif  @pixelformula == 62
      jc = jc * tan( jc )
    elseif  @pixelformula == 63
      jc = jc * cotan( jc )
    elseif  @pixelformula == 64
      jc = jc/cos( jc )
    elseif  @pixelformula == 65
      jc = jc/sin( jc )
    elseif  @pixelformula == 66
      jc = sin( 1/jc )
    elseif  @pixelformula == 67
      jc = cos( 1/jc )
    elseif  @pixelformula == 68
      jc = tan( 1/jc )
    elseif  @pixelformula == 69
      jc = cotan( 1/jc )
    elseif  @pixelformula == 70
      jc = 1/cos( 1/jc )
    elseif  @pixelformula == 71
      jc = 1/sin( 1/jc )
    elseif  @pixelformula == 72
      jc = cotanh( jc )
    elseif  @pixelformula == 73
      jc = 1/cosh( jc )
    elseif  @pixelformula == 74
      jc = 1/sinh( jc )
    elseif  @pixelformula == 75
      jc = atanh( 1/jc )
    elseif  @pixelformula == 76
      jc = acosh( 1/jc )
    elseif  @pixelformula == 77
      jc = asinh( 1/jc )
    elseif @pixelformula == 78
      jc = @coeffpa * jc^@exponentpa + @coeffpb * jc^@exponentpb + \
          @coeffpc * jc^@exponentpc
    elseif  @pixelformula == 79
      zextra = sinh(#z)
      jc = zextra * zextra
    elseif  @pixelformula == 80
      zextra = cosh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 81
      zextra = tanh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 82
      zextra = cotanh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 83
      zextra = (1,0)/cosh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 84
      zextra = (1,0) / sinh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 85
      jc = sinh(1/jc)
    elseif  @pixelformula == 86
      jc = cosh(1/jc)
    elseif  @pixelformula == 87
      jc = tanh(1/jc)
    elseif  @pixelformula == 88
      jc = cotanh(1/jc)
    elseif  @pixelformula == 89
      jc = (1,0)/cosh(1/jc)
    elseif  @pixelformula == 90
      jc = (1,0)/sinh(1/jc)
    elseif  @pixelformula == 91
      jc = sin( jc ) * tan(jc)
    elseif  @pixelformula == 92
      jc = sinh(jc) * tanh(jc)
    elseif  @pixelformula == 93
      jc = sinh(jc) * cosh(jc)
    elseif  @pixelformula == 94
      ztemp = sinh(jc), zextra = cosh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 95
      ztemp = sin(jc), zextra = cos(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 96
      zextra = 1/jc
      jc = sin(zextra)*cos(zextra)
    elseif  @pixelformula == 97
      zextra = sin( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 98
      jc = sin(jc) * cos(1/jc)
    elseif  @pixelformula == 99
      jc = sin(jc) * sin(1/jc)
    elseif  @pixelformula == 100
      zextra = log(jc)
      jc = zextra*zextra
    elseif  @pixelformula == 101
      jc = sin(jc) * sin(2*jc)
    elseif @pixelformula == 102
      jc = exp(2*jc)
    elseif  @pixelformula == 103
      jc = exp(-2*jc)
    elseif  @pixelformula == 104
      zextra = 1/jc
      jc = sinh(zextra)*cosh(zextra)
    elseif  @pixelformula == 105
      zextra = sinh( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 106
      jc = sinh(jc) * cosh(1/jc)
    elseif  @pixelformula == 107
      jc = sinh(jc) * sinh(1/jc)
    elseif  @pixelformula == 108
      jc = sin(jc) * sinh(jc)
    elseif  @pixelformula == 109
      jc = sin(jc) * cosh(jc)
    elseif  @pixelformula == 110
      zextra = sin(jc), ztemp = sinh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 111
      jc = sin(jc)*exp(jc)
    elseif  @pixelformula == 112
      jc = cos(jc)*exp(jc)
    elseif  @pixelformula == 113
      jc = sinh(jc)*exp(jc)
    elseif  @pixelformula == 114
      jc = cosh(jc)*exp(jc)
    elseif  @pixelformula == 115
      jc = sin(jc)*log(jc)
    elseif  @pixelformula == 116
      jc = cos(jc)*log(jc)
    elseif  @pixelformula == 117
      jc = sinh(jc)*log(jc)
    else ; @pixelformula == 118
      jc = cosh(jc)*log(jc)
    endif ; @pixelformula = 1
  endif ; @pixelformula != 0

  loop:
  iterations = iterations + 1

  if @fgen == 0
    ztemp1 = z
  elseif @fgen == 1
    ztemp1 = zold
  elseif @fgen == 2
    ztemp1 = zold2
  elseif @fgen == 3
    ztemp1 = zold3

  elseif @fgen == 4
    ztemp1 = zold4
  elseif @fgen == 5
    ztemp1 = zold5
  endif ; @fgen
  if @ggen == 0
    ztemp2 = z
  elseif @ggen == 1
    ztemp2 = zold
  elseif @ggen == 2
    ztemp2 = zold2
  elseif @ggen == 3
    ztemp2 = zold3
  elseif @ggen == 4
    ztemp2 = zold4
  elseif @ggen == 5
    ztemp2 = zold5
  endif ; @ggen
  if @hgen == 0
    ztemp3 = z
  elseif @hgen == 1
    ztemp3 = zold
  elseif @hgen == 2
    ztemp3 = zold2
  elseif @hgen == 3
    ztemp3 = zold3
  elseif @hgen == 4
    ztemp3 = zold4
  elseif @hgen == 5
    ztemp3 = zold5
  endif ; @hgen

  zold5 = zold4
  zold4 = zold3
  zold3 = zold2
  zold2 = zold
  zold = z

  if @pmode != 0
    ztemp1 = ztemp1 + jc
  endif ; pmode

  if @formula1 == 0
    ztemp1 = ztemp1 * ztemp1
  elseif  @formula1 == 1
    ztemp1 = ztemp1 * ztemp1 * ztemp1
  elseif  @formula1 == 2
    ztemp1extra = ztemp1 * ztemp1
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 3
    ztemp1 = ztemp1 ^ @power1
  elseif  @formula1 == 4
    ztemp1 = 1/ztemp1
  elseif  @formula1 == 5
    ztemp1 = sqrt(ztemp1)
  elseif  @formula1 == 6
    ztemp1 = 1 / ( ztemp1 * ztemp1 )
  elseif  @formula1 == 7
    ztemp1 = log(ztemp1)
  elseif  @formula1 == 8
    ztemp1 = exp( ztemp1)
  elseif  @formula1 == 9
    ztemp1 = ztemp1^ztemp1
  elseif  @formula1 == 10
    ztemp1 = sin( ztemp1 )
  elseif  @formula1 == 11
    ztemp1 = cos( ztemp1 )
  elseif  @formula1 == 12
    ztemp1 = tan( ztemp1 )
  elseif  @formula1 == 13
    ztemp1 = asin( ztemp1 )
  elseif  @formula1 == 14
    ztemp1 = acos( ztemp1 )
  elseif  @formula1 == 15
    ztemp1 = atan( ztemp1 )
  elseif  @formula1 == 16
    ztemp1 = sinh( ztemp1 )
  elseif  @formula1 == 17
    ztemp1 = cosh( ztemp1 )
  elseif  @formula1 == 18
    ztemp1 = tanh( ztemp1 )
  elseif  @formula1 == 19
    ztemp1 = asinh( ztemp1 )
  elseif @formula1 == 20
    ztemp1 = acosh( ztemp1 )
  elseif  @formula1 == 21
    ztemp1 = atanh( ztemp1 )
  elseif  @formula1 == 22
    ztemp1 = log( 1/ztemp1 )
  elseif  @formula1 == 23
    ztemp1 = log( log( ztemp1 ))
  elseif  @formula1 == 24
    ztemp1 = exp( -ztemp1 )
  elseif  @formula1 == 25
    ztemp1 = exp( 1/ztemp1 )
  elseif  @formula1 == 26
    ztemp1 = ztemp1^(-ztemp1)
  elseif  @formula1 == 27
    ztemp1extra = sin( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 28
    ztemp1extra = cos( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 29
    ztemp1extra = tan( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 30
    ztemp1 = cotan( ztemp1 )
  elseif  @formula1 == 31
    ztemp1 = 1/cos( ztemp1 )
  elseif  @formula1 == 32
    ztemp1 = 1/sin( ztemp1 )
  elseif  @formula1 == 33
    ztemp1extra = cotan( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 34
    ztemp1extra = 1/cos( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 35
    ztemp1extra = 1/sin( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 36
    ztemp1extra = ztemp1^(ztemp1)
    ztemp1 = ztemp1^ztemp1extra
  elseif  @formula1 == 37
    ztemp1extra = ztemp1^(ztemp1)
    ztemp1 = 1/( ztemp1^ztemp1extra )
  elseif  @formula1 == 38
    ztemp1 = log(-ztemp1)
  elseif  @formula1 == 39
    ztemp1 = 1/log( ztemp1 )
  elseif  @formula1 == 40
    ztemp1 = ztemp1 * log( ztemp1 )
  elseif  @formula1 == 41
    ztemp1 = sin( ztemp1 ) / ztemp1
  elseif  @formula1 == 42
    ztemp1 = cos( ztemp1 ) / ztemp1
  elseif  @formula1 == 43
    ztemp1 = sin( ztemp1 ) * cos( ztemp1 )
  elseif  @formula1 == 44
    ztemp1 = sin( ztemp1^2 )
  elseif  @formula1 == 45
    ztemp1 = exp( -1/ztemp1 )
  elseif  @formula1 == 46
    ztemp1 = ztemp1 * exp( ztemp1 )
  elseif  @formula1 == 47
    ztemp1 = ztemp1 * exp( -ztemp1 )
  elseif  @formula1 == 48
    ztemp1 = ztemp1 * exp( 1/ztemp1 )
  elseif  @formula1 == 49
    ztemp1 = ztemp1 * exp( -1/ztemp1 )
  elseif  @formula1 == 50
    ztemp1 = ztemp1 * ztemp1 * ztemp1
  elseif  @formula1 == 51
    ztemp1 = 1 / ( ztemp1 * ztemp1 * ztemp1 )
  elseif  @formula1 == 52
    ztemp1 = atan( 1 / ztemp1 )
  elseif  @formula1 == 53
    ztemp1 = acos( 1 / ztemp1 )
  elseif  @formula1 == 54
    ztemp1 = asin( 1 / ztemp1 )
  elseif  @formula1 == 55
    ztemp1 = tan( ztemp1 ) / ztemp1
  elseif  @formula1 == 56
    ztemp1 = cotan( ztemp1 ) / ztemp1
  elseif  @formula1 == 57
    ztemp1 = 1 / ( ztemp1 * cos( ztemp1 ))
  elseif  @formula1 == 58
    ztemp1 = 1 / ( ztemp1 * sin( ztemp1 ))
  elseif  @formula1 == 59
    ztemp1 = ztemp1 * sin( ztemp1 )
  elseif  @formula1 == 60
    ztemp1 = ztemp1 * cos( ztemp1 )
  elseif  @formula1 == 61
    ztemp1 = ztemp1 * tan( ztemp1 )
  elseif  @formula1 == 62
    ztemp1 = ztemp1 * cotan( ztemp1 )
  elseif  @formula1 == 63
    ztemp1 = ztemp1/cos( ztemp1 )
  elseif  @formula1 == 64
    ztemp1 = ztemp1/sin( ztemp1 )
  elseif  @formula1 == 65
    ztemp1 = sin( 1/ztemp1 )
  elseif  @formula1 == 66
    ztemp1 = cos( 1/ztemp1 )
  elseif  @formula1 == 67
    ztemp1 = tan( 1/ztemp1 )
  elseif  @formula1 == 68
    ztemp1 = cotan( 1/ztemp1 )
  elseif  @formula1 == 69
    ztemp1 = 1/cos( 1/ztemp1 )
  elseif  @formula1 == 70
    ztemp1 = 1/sin( 1/ztemp1 )
  elseif  @formula1 == 71
    ztemp1 = cotanh( ztemp1 )
  elseif  @formula1 == 72
    ztemp1 = 1/cosh( ztemp1 )
  elseif  @formula1 == 73
    ztemp1 = 1/sinh( ztemp1 )
  elseif  @formula1 == 74
    ztemp1 = atanh( 1/ztemp1 )
  elseif  @formula1 == 75
    ztemp1 = acosh( 1/ztemp1 )
  elseif  @formula1 == 76
    ztemp1 = asinh( 1/ztemp1 )
  elseif @formula1 == 77
    ztemp1 = @coeff1a * ztemp1^@exponent1a + @coeff1b * ztemp1^@exponent1b + \
          @coeff1c * ztemp1^@exponent1c
  elseif  @formula1 == 78
    ztemp1extra = sinh(ztemp1)
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 79
    ztemp1extra = cosh( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 80
    ztemp1extra = tanh(ztemp1)
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 81
    ztemp1extra = cotanh( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 82
    ztemp1extra = (1,0)/cosh(ztemp1)
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 83
    ztemp1extra = (1,0) / sinh( ztemp1 )
    ztemp1 = ztemp1extra * ztemp1extra
  elseif  @formula1 == 84
    ztemp1 = sinh(1/ztemp1)
  elseif  @formula1 == 85
    ztemp1 = cosh(1/ztemp1)
  elseif  @formula1 == 86
    ztemp1 = tanh(1/ztemp1)
  elseif  @formula1 == 87
    ztemp1 = cotanh(1/ztemp1)
  elseif  @formula1 == 88
    ztemp1 = (1,0)/cosh(1/ztemp1)
  elseif  @formula1 == 89
    ztemp1 = (1,0)/sinh(1/ztemp1)
  elseif  @formula1 == 90
    ztemp1 = sin( ztemp1 ) * tan(ztemp1)
  elseif  @formula1 == 91
    ztemp1 = sinh(ztemp1) * tanh(ztemp1)
  elseif  @formula1 == 92
    ztemp1 = sinh(ztemp1) * cosh(ztemp1)
  elseif  @formula1 == 93
    ztemp1temp = sinh(ztemp1), ztemp1extra = cosh(ztemp1)
    ztemp1 = ztemp1temp*ztemp1temp*ztemp1extra*ztemp1extra
  elseif  @formula1 == 94
    ztemp1temp = sin(ztemp1), ztemp1extra = cos(ztemp1)
    ztemp1 = ztemp1temp*ztemp1temp*ztemp1extra*ztemp1extra
  elseif  @formula1 == 95
    ztemp1extra = 1/ztemp1
    ztemp1 = sin(ztemp1extra)*cos(ztemp1extra)
  elseif  @formula1 == 96
    ztemp1extra = sin( 1/ztemp1 )
    ztemp1 = ztemp1extra*ztemp1extra
  elseif  @formula1 == 97
    ztemp1 = sin(ztemp1) * cos(1/ztemp1)
  elseif  @formula1 == 98
    ztemp1 = sin(ztemp1) * sin(1/ztemp1)
  elseif  @formula1 == 99
    ztemp1extra = log(ztemp1)
    ztemp1 = ztemp1extra*ztemp1extra
  elseif  @formula1 == 100
    ztemp1 = sin(ztemp1) * sin(2*ztemp1)
  elseif @formula1 == 101
    ztemp1 = exp(2*ztemp1)
  elseif  @formula1 == 102
    ztemp1 = exp(-2*ztemp1)
  elseif  @formula1 == 103
    ztemp1extra = 1/ztemp1
    ztemp1 = sinh(ztemp1extra)*cosh(ztemp1extra)
  elseif  @formula1 == 104
    ztemp1extra = sinh( 1/ztemp1 )
    ztemp1 = ztemp1extra*ztemp1extra
  elseif  @formula1 == 105
    ztemp1 = sinh(ztemp1) * cosh(1/ztemp1)
  elseif  @formula1 == 106
    ztemp1 = sinh(ztemp1) * sinh(1/ztemp1)
  elseif  @formula1 == 107
    ztemp1 = sin(ztemp1) * sinh(ztemp1)
  elseif  @formula1 == 108
    ztemp1 = sin(ztemp1) * cosh(ztemp1)
  elseif  @formula1 == 109
    ztemp1extra = sin(ztemp1), ztemp1temp = sinh(ztemp1)
    ztemp1 = ztemp1temp*ztemp1temp*ztemp1extra*ztemp1extra
  elseif  @formula1 == 110
    ztemp1 = sin(ztemp1)*exp(ztemp1)
  elseif  @formula1 == 111
    ztemp1 = cos(ztemp1)*exp(ztemp1)
  elseif  @formula1 == 112
    ztemp1 = sinh(ztemp1)*exp(ztemp1)
  elseif  @formula1 == 113
    ztemp1 = cosh(ztemp1)*exp(ztemp1)
  elseif  @formula1 == 114
    ztemp1 = sin(ztemp1)*log(ztemp1)
  elseif  @formula1 == 115
    ztemp1 = cos(ztemp1)*log(ztemp1)
  elseif  @formula1 == 116
    ztemp1 = sinh(ztemp1)*log(ztemp1)
  elseif @formula1 == 117
    ztemp1 = cosh(ztemp1)*log(ztemp1)
  elseif @formula1 == 118
    ztemp1 = exp(ztemp1*ztemp1)
  elseif @formula1 == 119
    ztemp1 = exp(-(ztemp1*ztemp1))
  elseif @formula1 == 120
    ztemp1 = exp(1/(ztemp1*ztemp1))
  elseif @formula1 == 121
    ztemp1 = exp(-1/(ztemp1*ztemp1))
  else
    ztemp1 = ztemp1
  endif ; @formula1

  if iterations % @frequency == 0 ; execute formulas G & H and combine

    if @pmode != 0
      ztemp2 = ztemp2 + jc
      ztemp3 = ztemp3 + jc
    endif ; pmode

    if @formula2 == 0
      ztemp2 = ztemp2 * ztemp2
    elseif  @formula2 == 1
      ztemp2 = ztemp2 * ztemp2 * ztemp2
    elseif  @formula2 == 2
      zextra = ztemp2 * ztemp2
      ztemp2 = zextra * zextra
    elseif  @formula2 == 3
      ztemp2 = ztemp2 ^ @power2
    elseif  @formula2 == 4
      ztemp2 = 1/ztemp2
    elseif  @formula2 == 5
      ztemp2 = sqrt(ztemp2)
    elseif  @formula2 == 6
      ztemp2 = 1 / ( ztemp2 * ztemp2 )
    elseif  @formula2 == 7
      ztemp2 = log(ztemp2)
    elseif  @formula2 == 8
      ztemp2 = exp( ztemp2)
    elseif  @formula2 == 9
      ztemp2 = ztemp2^ztemp2
    elseif  @formula2 == 10
      ztemp2 = sin( ztemp2 )
    elseif  @formula2 == 11
      ztemp2 = cos( ztemp2 )
    elseif  @formula2 == 12
      ztemp2 = tan( ztemp2 )
    elseif  @formula2 == 13
      ztemp2 = asin( ztemp2 )
    elseif  @formula2 == 14
      ztemp2 = acos( ztemp2 )
    elseif  @formula2 == 15
      ztemp2 = atan( ztemp2 )
    elseif  @formula2 == 16
      ztemp2 = sinh( ztemp2 )
    elseif  @formula2 == 17
      ztemp2 = cosh( ztemp2 )
    elseif  @formula2 == 18
      ztemp2 = tanh( ztemp2 )
    elseif  @formula2 == 19
      ztemp2 = asinh( ztemp2 )
    elseif @formula2 == 20
      ztemp2 = acosh( ztemp2 )
    elseif  @formula2 == 21
      ztemp2 = atanh( ztemp2 )
    elseif  @formula2 == 22
      ztemp2 = log( 1/ztemp2 )
    elseif  @formula2 == 23
      ztemp2 = log( log( ztemp2 ))
    elseif  @formula2 == 24
      ztemp2 = exp( -ztemp2 )
    elseif  @formula2 == 25
      ztemp2 = exp( 1/ztemp2 )
    elseif  @formula2 == 26
      ztemp2 = ztemp2^(-ztemp2)
    elseif  @formula2 == 27
      zextra = sin( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 28
      zextra = cos( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 29
      zextra = tan( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 30
      ztemp2 = cotan( ztemp2 )
    elseif  @formula2 == 31
      ztemp2 = 1/cos( ztemp2 )
    elseif  @formula2 == 32
      ztemp2 = 1/sin( ztemp2 )
    elseif  @formula2 == 33
      zextra = cotan( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 34
      zextra = 1/cos( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 35
      zextra = 1/sin( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 36
      zextra = ztemp2^(ztemp2)
      ztemp2 = ztemp2^zextra
    elseif  @formula2 == 37
      zextra = ztemp2^(ztemp2)
      ztemp2 = 1/( ztemp2^zextra )
    elseif  @formula2 == 38
      ztemp2 = log(-ztemp2)
    elseif  @formula2 == 39
      ztemp2 = 1/log( ztemp2 )
    elseif  @formula2 == 40
      ztemp2 = ztemp2 * log( ztemp2 )
    elseif  @formula2 == 41
      ztemp2 = sin( ztemp2 ) / ztemp2
    elseif  @formula2 == 42
      ztemp2 = cos( ztemp2 ) / ztemp2
    elseif  @formula2 == 43
      ztemp2 = sin( ztemp2 ) * cos( ztemp2 )
    elseif  @formula2 == 44
      ztemp2 = sin( ztemp2^2 )
    elseif  @formula2 == 45
      ztemp2 = exp( -1/ztemp2 )
    elseif  @formula2 == 46
      ztemp2 = ztemp2 * exp( ztemp2 )
    elseif  @formula2 == 47
      ztemp2 = ztemp2 * exp( -ztemp2 )
    elseif  @formula2 == 48
      ztemp2 = ztemp2 * exp( 1/ztemp2 )
    elseif  @formula2 == 49
      ztemp2 = ztemp2 * exp( -1/ztemp2 )
    elseif  @formula2 == 50
      ztemp2 = ztemp2 * ztemp2 * ztemp2
    elseif  @formula2 == 51
      ztemp2 = 1 / ( ztemp2 * ztemp2 * ztemp2 )
    elseif  @formula2 == 52
      ztemp2 = atan( 1 / ztemp2 )
    elseif  @formula2 == 53
      ztemp2 = acos( 1 / ztemp2 )
    elseif  @formula2 == 54
      ztemp2 = asin( 1 / ztemp2 )
    elseif  @formula2 == 55
      ztemp2 = tan( ztemp2 ) / ztemp2
    elseif  @formula2 == 56
      ztemp2 = cotan( ztemp2 ) / ztemp2
    elseif  @formula2 == 57
      ztemp2 = 1 / ( ztemp2 * cos( ztemp2 ))
    elseif  @formula2 == 58
      ztemp2 = 1 / ( ztemp2 * sin( ztemp2 ))
    elseif  @formula2 == 59
      ztemp2 = ztemp2 * sin( ztemp2 )
    elseif  @formula2 == 60
      ztemp2 = ztemp2 * cos( ztemp2 )
    elseif  @formula2 == 61
      ztemp2 = ztemp2 * tan( ztemp2 )
    elseif  @formula2 == 62
      ztemp2 = ztemp2 * cotan( ztemp2 )
    elseif  @formula2 == 63
      ztemp2 = ztemp2/cos( ztemp2 )
    elseif  @formula2 == 64
      ztemp2 = ztemp2/sin( ztemp2 )
    elseif  @formula2 == 65
      ztemp2 = sin( 1/ztemp2 )
    elseif  @formula2 == 66
      ztemp2 = cos( 1/ztemp2 )
    elseif  @formula2 == 67
      ztemp2 = tan( 1/ztemp2 )
    elseif  @formula2 == 68
      ztemp2 = cotan( 1/ztemp2 )
    elseif  @formula2 == 69
      ztemp2 = 1/cos( 1/ztemp2 )
    elseif  @formula2 == 70

      ztemp2 = 1/sin( 1/ztemp2 )
    elseif  @formula2 == 71
      ztemp2 = cotanh( ztemp2 )
    elseif  @formula2 == 72
      ztemp2 = 1/cosh( ztemp2 )
    elseif  @formula2 == 73
      ztemp2 = 1/sinh( ztemp2 )
    elseif  @formula2 == 74
      ztemp2 = atanh( 1/ztemp2 )
    elseif  @formula2 == 75
      ztemp2 = acosh( 1/ztemp2 )
    elseif  @formula2 == 76
      ztemp2 = asinh( 1/ztemp2 )
    elseif @formula2 == 77
      ztemp2 = @coeff2a * ztemp2^@exponent2a + @coeff2b * ztemp2^@exponent2b + \
            @coeff2c * ztemp2^@exponent2c
    elseif  @formula2 == 78
      zextra = sinh(ztemp2)
      ztemp2 = zextra * zextra
    elseif  @formula2 == 79
      zextra = cosh( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 80
      zextra = tanh(ztemp2)
      ztemp2 = zextra * zextra
    elseif  @formula2 == 81
      zextra = cotanh( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 82
      zextra = (1,0)/cosh(ztemp2)
      ztemp2 = zextra * zextra
    elseif  @formula2 == 83
      zextra = (1,0) / sinh( ztemp2 )
      ztemp2 = zextra * zextra
    elseif  @formula2 == 84
      ztemp2 = sinh(1/ztemp2)
    elseif  @formula2 == 85
      ztemp2 = cosh(1/ztemp2)
    elseif  @formula2 == 86
      ztemp2 = tanh(1/ztemp2)
    elseif  @formula2 == 87
      ztemp2 = cotanh(1/ztemp2)
    elseif  @formula2 == 88
      ztemp2 = (1,0)/cosh(1/ztemp2)
    elseif  @formula2 == 89
      ztemp2 = (1,0)/sinh(1/ztemp2)
    elseif  @formula2 == 90
      ztemp2 = sin( ztemp2 ) * tan(ztemp2)
    elseif  @formula2 == 91
      ztemp2 = sinh(ztemp2) * tanh(ztemp2)
    elseif  @formula2 == 92
      ztemp2 = sinh(ztemp2) * cosh(ztemp2)
    elseif  @formula2 == 93
      ztemp = sinh(ztemp2), zextra = cosh(ztemp2)
      ztemp2 = ztemp*ztemp*zextra*zextra
    elseif  @formula2 == 94
      ztemp = sin(ztemp2), zextra = cos(ztemp2)
      ztemp2 = ztemp*ztemp*zextra*zextra
    elseif  @formula2 == 95
      zextra = 1/ztemp2
      ztemp2 = sin(zextra)*cos(zextra)
    elseif  @formula2 == 96
      zextra = sin( 1/ztemp2 )
      ztemp2 = zextra*zextra
    elseif  @formula2 == 97
      ztemp2 = sin(ztemp2) * cos(1/ztemp2)
    elseif  @formula2 == 98
      ztemp2 = sin(ztemp2) * sin(1/ztemp2)
    elseif  @formula2 == 99
      zextra = log(ztemp2)
      ztemp2 = zextra*zextra
    elseif  @formula2 == 100
      ztemp2 = sin(ztemp2) * sin(2*ztemp2)
    elseif @formula2 == 101
      ztemp2 = exp(2*ztemp2)
    elseif  @formula2 == 102
      ztemp2 = exp(-2*ztemp2)
    elseif  @formula2 == 103
      zextra = 1/ztemp2
      ztemp2 = sinh(zextra)*cosh(zextra)
    elseif  @formula2 == 104
      zextra = sinh( 1/ztemp2 )
      ztemp2 = zextra*zextra
    elseif  @formula2 == 105
      ztemp2 = sinh(ztemp2) * cosh(1/ztemp2)
    elseif  @formula2 == 106
      ztemp2 = sinh(ztemp2) * sinh(1/ztemp2)
    elseif  @formula2 == 107
      ztemp2 = sin(ztemp2) * sinh(ztemp2)
    elseif  @formula2 == 108
      ztemp2 = sin(ztemp2) * cosh(ztemp2)
    elseif  @formula2 == 109
      zextra = sin(ztemp2), ztemp = sinh(ztemp2)
      ztemp2 = ztemp*ztemp*zextra*zextra
    elseif  @formula2 == 110
      ztemp2 = sin(ztemp2)*exp(ztemp2)
    elseif  @formula2 == 111
      ztemp2 = cos(ztemp2)*exp(ztemp2)
    elseif  @formula2 == 112
      ztemp2 = sinh(ztemp2)*exp(ztemp2)
    elseif  @formula2 == 113
      ztemp2 = cosh(ztemp2)*exp(ztemp2)
    elseif  @formula2 == 114
      ztemp2 = sin(ztemp2)*log(ztemp2)
    elseif  @formula2 == 115
      ztemp2 = cos(ztemp2)*log(ztemp2)
    elseif  @formula2 == 116
      ztemp2 = sinh(ztemp2)*log(ztemp2)
    elseif @formula2 == 117
      ztemp2 = cosh(ztemp2)*log(ztemp2)
    elseif @formula2 == 118
      ztemp2 = exp(ztemp2*ztemp2)
    elseif @formula2 == 119
      ztemp2 = exp(-(ztemp2*ztemp2))
    elseif @formula2 == 120
      ztemp2 = exp(1/(ztemp2*ztemp2))
    elseif @formula2 == 121
      ztemp2 = exp(-1/(ztemp2*ztemp2))
    else
      ztemp2 = ztemp2
    endif ; @formula2

    if @formula3 == 0
      ztemp3 = ztemp3 * ztemp3
    elseif  @formula3 == 1
      ztemp3 = ztemp3 * ztemp3 * ztemp3
    elseif  @formula3 == 2
      zextra = ztemp3 * ztemp3
      ztemp3 = zextra * zextra
    elseif  @formula3 == 3
      ztemp3 = ztemp3 ^ @power3
    elseif  @formula3 == 4
      ztemp3 = 1/ztemp3
    elseif  @formula3 == 5
      ztemp3 = sqrt(ztemp3)
    elseif  @formula3 == 6
      ztemp3 = 1 / ( ztemp3 * ztemp3 )
    elseif  @formula3 == 7
      ztemp3 = log(ztemp3)
    elseif  @formula3 == 8
      ztemp3 = exp( ztemp3)
    elseif  @formula3 == 9
      ztemp3 = ztemp3^ztemp3
    elseif  @formula3 == 10
      ztemp3 = sin( ztemp3 )
    elseif  @formula3 == 11
      ztemp3 = cos( ztemp3 )
    elseif  @formula3 == 12
      ztemp3 = tan( ztemp3 )
    elseif  @formula3 == 13
      ztemp3 = asin( ztemp3 )
    elseif  @formula3 == 14
      ztemp3 = acos( ztemp3 )
    elseif  @formula3 == 15
      ztemp3 = atan( ztemp3 )
    elseif  @formula3 == 16
      ztemp3 = sinh( ztemp3 )
    elseif  @formula3 == 17
      ztemp3 = cosh( ztemp3 )
    elseif  @formula3 == 18
      ztemp3 = tanh( ztemp3 )
    elseif  @formula3 == 19
      ztemp3 = asinh( ztemp3 )
    elseif @formula3 == 20
      ztemp3 = acosh( ztemp3 )
    elseif  @formula3 == 21
      ztemp3 = atanh( ztemp3 )
    elseif  @formula3 == 22
      ztemp3 = log( 1/ztemp3 )
    elseif  @formula3 == 23
      ztemp3 = log( log( ztemp3 ))
    elseif  @formula3 == 24
      ztemp3 = exp( -ztemp3 )
    elseif  @formula3 == 25
      ztemp3 = exp( 1/ztemp3 )
    elseif  @formula3 == 26
      ztemp3 = ztemp3^(-ztemp3)
    elseif  @formula3 == 27
      zextra = sin( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 28
      zextra = cos( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 29
      zextra = tan( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 30
      ztemp3 = cotan( ztemp3 )
    elseif  @formula3 == 31
      ztemp3 = 1/cos( ztemp3 )
    elseif  @formula3 == 32
      ztemp3 = 1/sin( ztemp3 )
    elseif  @formula3 == 33
      zextra = cotan( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 34
      zextra = 1/cos( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 35
      zextra = 1/sin( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 36
      zextra = ztemp3^(ztemp3)
      ztemp3 = ztemp3^zextra
    elseif  @formula3 == 37
      zextra = ztemp3^(ztemp3)
      ztemp3 = 1/( ztemp3^zextra )
    elseif  @formula3 == 38
      ztemp3 = log(-ztemp3)
    elseif  @formula3 == 39
      ztemp3 = 1/log( ztemp3 )
    elseif  @formula3 == 40
      ztemp3 = ztemp3 * log( ztemp3 )
    elseif  @formula3 == 41
      ztemp3 = sin( ztemp3 ) / ztemp3
    elseif  @formula3 == 42
      ztemp3 = cos( ztemp3 ) / ztemp3
    elseif  @formula3 == 43
      ztemp3 = sin( ztemp3 ) * cos( ztemp3 )
    elseif  @formula3 == 44
      ztemp3 = sin( ztemp3^2 )
    elseif  @formula3 == 45
      ztemp3 = exp( -1/ztemp3 )
    elseif  @formula3 == 46
      ztemp3 = ztemp3 * exp( ztemp3 )
    elseif  @formula3 == 47
      ztemp3 = ztemp3 * exp( -ztemp3 )
    elseif  @formula3 == 48
      ztemp3 = ztemp3 * exp( 1/ztemp3 )
    elseif  @formula3 == 49
      ztemp3 = ztemp3 * exp( -1/ztemp3 )
    elseif  @formula3 == 50
      ztemp3 = ztemp3 * ztemp3 * ztemp3
    elseif  @formula3 == 51
      ztemp3 = 1 / ( ztemp3 * ztemp3 * ztemp3 )
    elseif  @formula3 == 52
      ztemp3 = atan( 1 / ztemp3 )
    elseif  @formula3 == 53
      ztemp3 = acos( 1 / ztemp3 )
    elseif  @formula3 == 54
      ztemp3 = asin( 1 / ztemp3 )
    elseif  @formula3 == 55
      ztemp3 = tan( ztemp3 ) / ztemp3
    elseif  @formula3 == 56
      ztemp3 = cotan( ztemp3 ) / ztemp3
    elseif  @formula3 == 57
      ztemp3 = 1 / ( ztemp3 * cos( ztemp3 ))
    elseif  @formula3 == 58
      ztemp3 = 1 / ( ztemp3 * sin( ztemp3 ))
    elseif  @formula3 == 59
      ztemp3 = ztemp3 * sin( ztemp3 )
    elseif  @formula3 == 60
      ztemp3 = ztemp3 * cos( ztemp3 )
    elseif  @formula3 == 61
      ztemp3 = ztemp3 * tan( ztemp3 )
    elseif  @formula3 == 62
      ztemp3 = ztemp3 * cotan( ztemp3 )
    elseif  @formula3 == 63
      ztemp3 = ztemp3/cos( ztemp3 )
    elseif  @formula3 == 64
      ztemp3 = ztemp3/sin( ztemp3 )
    elseif  @formula3 == 65
      ztemp3 = sin( 1/ztemp3 )
    elseif  @formula3 == 66
      ztemp3 = cos( 1/ztemp3 )
    elseif  @formula3 == 67
      ztemp3 = tan( 1/ztemp3 )
    elseif  @formula3 == 68
      ztemp3 = cotan( 1/ztemp3 )
    elseif  @formula3 == 69
      ztemp3 = 1/cos( 1/ztemp3 )
    elseif  @formula3 == 70
      ztemp3 = 1/sin( 1/ztemp3 )
    elseif  @formula3 == 71
      ztemp3 = cotanh( ztemp3 )
    elseif  @formula3 == 72
      ztemp3 = 1/cosh( ztemp3 )
    elseif  @formula3 == 73
      ztemp3 = 1/sinh( ztemp3 )
    elseif  @formula3 == 74
      ztemp3 = atanh( 1/ztemp3 )
    elseif  @formula3 == 75
      ztemp3 = acosh( 1/ztemp3 )
    elseif  @formula3 == 76
      ztemp3 = asinh( 1/ztemp3 )
    elseif @formula3 == 77
      ztemp3 = @coeff3a * ztemp3^@exponent3a + @coeff3b * ztemp3^@exponent3b + \
            @coeff3c * ztemp3^@exponent3c
    elseif  @formula3 == 78
      zextra = sinh(ztemp3)
      ztemp3 = zextra * zextra
    elseif  @formula3 == 79
      zextra = cosh( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 80
      zextra = tanh(ztemp3)
      ztemp3 = zextra * zextra
    elseif  @formula3 == 81
      zextra = cotanh( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 82
      zextra = (1,0)/cosh(ztemp3)
      ztemp3 = zextra * zextra
    elseif  @formula3 == 83
      zextra = (1,0) / sinh( ztemp3 )
      ztemp3 = zextra * zextra
    elseif  @formula3 == 84
      ztemp3 = sinh(1/ztemp3)
    elseif  @formula3 == 85
      ztemp3 = cosh(1/ztemp3)
    elseif  @formula3 == 86
      ztemp3 = tanh(1/ztemp3)
    elseif  @formula3 == 87
      ztemp3 = cotanh(1/ztemp3)
    elseif  @formula3 == 88
      ztemp3 = (1,0)/cosh(1/ztemp3)
    elseif  @formula3 == 89
      ztemp3 = (1,0)/sinh(1/ztemp3)
    elseif  @formula3 == 90
      ztemp3 = sin( ztemp3 ) * tan(ztemp3)
    elseif  @formula3 == 91
      ztemp3 = sinh(ztemp3) * tanh(ztemp3)
    elseif  @formula3 == 92
      ztemp3 = sinh(ztemp3) * cosh(ztemp3)
    elseif  @formula3 == 93
      ztemp = sinh(ztemp3), zextra = cosh(ztemp3)
      ztemp3 = ztemp*ztemp*zextra*zextra
    elseif  @formula3 == 94
      ztemp = sin(ztemp3), zextra = cos(ztemp3)
      ztemp3 = ztemp*ztemp*zextra*zextra
    elseif  @formula3 == 95
      zextra = 1/ztemp3
      ztemp3 = sin(zextra)*cos(zextra)
    elseif  @formula3 == 96
      zextra = sin( 1/ztemp3 )
      ztemp3 = zextra*zextra
    elseif  @formula3 == 97
      ztemp3 = sin(ztemp3) * cos(1/ztemp3)
    elseif  @formula3 == 98
      ztemp3 = sin(ztemp3) * sin(1/ztemp3)
    elseif  @formula3 == 99
      zextra = log(ztemp3)
      ztemp3 = zextra*zextra
    elseif  @formula3 == 100
      ztemp3 = sin(ztemp3) * sin(2*ztemp3)
    elseif @formula3 == 101
      ztemp3 = exp(2*ztemp3)
    elseif  @formula3 == 102
      ztemp3 = exp(-2*ztemp3)
    elseif  @formula3 == 103
      zextra = 1/ztemp3
      ztemp3 = sinh(zextra)*cosh(zextra)
    elseif  @formula3 == 104
      zextra = sinh( 1/ztemp3 )
      ztemp3 = zextra*zextra
    elseif  @formula3 == 105
      ztemp3 = sinh(ztemp3) * cosh(1/ztemp3)
    elseif  @formula3 == 106
      ztemp3 = sinh(ztemp3) * sinh(1/ztemp3)
    elseif  @formula3 == 107
      ztemp3 = sin(ztemp3) * sinh(ztemp3)
    elseif  @formula3 == 108
      ztemp3 = sin(ztemp3) * cosh(ztemp3)
    elseif  @formula3 == 109
      zextra = sin(ztemp3), ztemp = sinh(ztemp3)
      ztemp3 = ztemp*ztemp*zextra*zextra
    elseif  @formula3 == 110
      ztemp3 = sin(ztemp3)*exp(ztemp3)
    elseif  @formula3 == 111
      ztemp3 = cos(ztemp3)*exp(ztemp3)
    elseif  @formula3 == 112
      ztemp3 = sinh(ztemp3)*exp(ztemp3)
    elseif  @formula3 == 113
      ztemp3 = cosh(ztemp3)*exp(ztemp3)
    elseif  @formula3 == 114
      ztemp3 = sin(ztemp3)*log(ztemp3)
    elseif  @formula3 == 115
      ztemp3 = cos(ztemp3)*log(ztemp3)
    elseif  @formula3 == 116
      ztemp3 = sinh(ztemp3)*log(ztemp3)
    elseif @formula3 == 117
      ztemp3 = cosh(ztemp3)*log(ztemp3)
    elseif @formula3 == 118
      ztemp3 = exp(ztemp3*ztemp3)
    elseif @formula3 == 119
      ztemp3 = exp(-(ztemp3*ztemp3))
    elseif @formula3 == 120
      ztemp3 = exp(1/(ztemp3*ztemp3))
    elseif @formula3 == 121
      ztemp3 = exp(-1/(ztemp3*ztemp3))
    elseif @formula3 == 122
      ztemp3 = ztemp3
    else
      if ((@combo == 0) || (@combo == 3) || (@combo == 4) || (@combo == 5) || \
          (@combo == 10) || (@combo == 11) || (@combo == 12))
        ztemp3 = (0,0)
      else
        ztemp3 = (1,0)
      endif ; @combo
    endif ; @formula3

    if @blend
      ztemp1 = @weight1*ztemp1, ztemp2 = @weight2*ztemp2
      ztemp3 = @weight3*ztemp3
    endif ; @blend

    if @combo == 0
      z = ztemp1 + ztemp2 + ztemp3
    elseif @combo == 1
      z = ztemp1 * ztemp2 * ztemp3
    elseif @combo == 2
      z = (ztemp1 + ztemp2) * ztemp3
    elseif @combo == 3
      z = (ztemp1 * ztemp2) + ztemp3
    elseif @combo == 4
      z = ztemp1 + ztemp2 - ztemp3
    elseif @combo == 5
      z = ztemp1 - ztemp2 - ztemp3
    elseif @combo == 6
      z = (ztemp1 - ztemp2) * ztemp3
    elseif @combo == 7
      z = (ztemp1 + ztemp2) / ztemp3
    elseif @combo == 8
      z = (ztemp1 - ztemp2) / ztemp3
    elseif @combo == 9
      z = ztemp1 * ztemp2 / ztemp3
    elseif @combo == 10
      z = (ztemp1 * ztemp2) - ztemp3
    elseif @combo == 11
      z = (ztemp1 / ztemp2) + ztemp3
    elseif @combo == 12
      z = (ztemp1 / ztemp2) - ztemp3
    endif ; @combo
  else
    z = ztemp1
  endif ; iterations

  if @pmode != 1
    z = z + jc
  endif ; pmode

  if @biomorph
  	if @biomorphtype == "real + imag"
	  	bail = (abs(real(z)) < @biomorphtest) || (abs(imag(z)) < @biomorphtest)
  	elseif @biomorphtype == "real + imag + cabs"
	  	bail = (abs(real(z)) < @biomorphtest) || (abs(imag(z)) < @biomorphtest) || (cabs(z) < sqr(@biomorphtest))
  	elseif @biomorphtype == "real"
	  	bail = abs(real(z)) < @biomorphtest
  	elseif @biomorphtype == "imag"
	  	bail = abs(imag(z)) < @biomorphtest
  	elseif @biomorphtype == "cabs"
	  	bail = cabs(z) < sqr(@biomorphtest)
	endif ; @biomorphtype
  else
		bail = |z| < @bail
  endif ; @biomorph

  bailout:
  	bail

  default:
  title = "oz3 Stage General"
  center = (0,0)
  maxiter = 100
  method = multipass
  periodicity = 0

  param frequency
    caption = "Cycle Length"
    default = 1
    min = 1
    hint = "This is the frequency that Formulas G and H are executed (Formula \
          F is executed every iteration). If 'Cycle length' = 1, then Formulas \
          G and H are also both executed every iter, else every N iters"
  endparam
  param combo
    caption = "Func Combo"
    enum = "f+g+h" "f*g*h" "(f+g)*h" "(f*g)+h" \
          "f+g-h" "f-g-h" "(f-g)*h" "(f+g)/h" "(f-g)/h" "f*g/h" \
          "(f*g)-h" "(f/g)+h" "(f/g)-h"
    default = 0
    min = 0
    hint = "Selects how the functions will be combined"
  endparam
  param formula1
    caption = "Formula F"
    enum = "z^2" "z^3" "z^4" "z^power" "1/z" "sqrt(z)" "1/z^2" "log(z)" "e^z" "z^z" \
          "sin(z)" "cos(z)" \
          "tan(z)" "asin(z)" "acos(z)" "atan(z)" "sinh(z)" "cosh(z)" "tanh(z)" \
          "asinh(z)" "acosh(z)" "atanh(z)" "log(1/z)" "log(log(z))" "e^-z" \
          "e^(1/z)" "z^-z" "sin(z)^2" "cos(z)^2" "tan(z)^2" "cot(z)" "sec(z)" \
          "csc(z)" "cot(z)^2" "sec(z)^2" "csc(z)^2" "z^z^z" "1/z^z^z" "log(-z)" \
          "1/log(z)" "zlog(z)" "sin(z)/z" "cos(z)/z" "sin(z)*cos(z)" "sin(z^2)" \
          "e^(-1/z)" "ze^z" "ze^-z" "ze^(1/z)" "ze^(-1/z)" "z^3" "1/z^3" \
          "acot(z)" "asec(z)" "acsc(z)" "tan(z)/z" "cot(z)/z" "sec(z)/z" \
          "csc(z)/z" "zsin(z)" "zcos(z)" "ztan(z)" "zcot(z)" "zsec(z)" "zcsc(z)" \
          "sin(1/z)" "cos(1/z)" "tan(1/z)" "cot(1/z)" "sec(1/z)" "csc(1/z)" \
          "cotanh(z)" "sech(z)" "cosech(z)" "acoth(z)" "asech(z)" "acosech(z)" \
          "3-term polynomial" "sinh(z)^2" "cosh(z)^2" "tanh(z)^2" "cotanh(z)^2" \
          "sech(z)^2" "cosech(z)^2" "sinh(1/z)" "cosh(1/z)" "tanh(1/z)" \
          "cotanh(1/z)" "sech(1/z)" "cosech(1/z)" "sin(z)tan(z)" "sinh(z)tanh(z)" \
          "sinh(z)cosh(z)" "sinh(z)^2*cosh(z)^2" "sin(z)^2*cos(z)^2" \
          "sin(1/z)*cos(1/z)" "sin(1/z)^2" "sin(z)cos(1/z)" "sin(z)sin(1/z)" \
          "log(z)^2" "sin(z)sin(2z)" "e^2z" "e^-2z" "sinh(1/z)cosh(1/z)" \
          "sinh(1/z)^2" "sinh(z)cosh(1/z)" "sinh(z)sinh(1/z)" "sin(z)sinh(z)" \
          "sin(z)cosh(z)" "sin(z)^2*sinh(z)^2" "sin(z)e^z" "cos(z)e^z" \
          "sinh(z)e^z" "cosh(z)e^z" "sin(z)log(z)" "cos(z)log(z)" "sinh(z)log(z)" \
          "cosh(z)log(z)" "e^(z^2)" "e^(-(z^2))" "e^(1/z^2)" "e^(-1/z^2)" "z"
    default = 0
    hint = "Default formula, executed each iteration. For 'z^power', set \
          parameter 'Power F'. For '3-term polynomial' set 6 params 'Coefficient' \
          & 'Exponent' FA, FB, and FC. Operates on z selected by 'F Generation'"
  endparam
  param fgen
    caption = "F Generation"
    default = 0

    enum = "Current z" "Previous z" "2nd Previous z" "3rd Previous z" \
          "4th Previous z" "5th Previous z"
    hint = "This is the z that gets iterated by Formula F (the default \
          formula) every iteration"
  endparam
  param power1
    caption = "Power F"
    default = (5,0)
    hint = "This is the power used for the first formula series if parameter \
        'Formula F' is set to 'z^power'"
  endparam
  param formula2
    caption = "Formula G"
    enum = "z^2" "z^3" "z^4" "z^power" "1/z" "sqrt(z)" "1/z^2" "log(z)" "e^z" "z^z" \
          "sin(z)" "cos(z)" \
          "tan(z)" "asin(z)" "acos(z)" "atan(z)" "sinh(z)" "cosh(z)" "tanh(z)" \
          "asinh(z)" "acosh(z)" "atanh(z)" "log(1/z)" "log(log(z))" "e^-z" \
          "e^(1/z)" "z^-z" "sin(z)^2" "cos(z)^2" "tan(z)^2" "cot(z)" "sec(z)" \
          "csc(z)" "cot(z)^2" "sec(z)^2" "csc(z)^2" "z^z^z" "1/z^z^z" "log(-z)" \
          "1/log(z)" "zlog(z)" "sin(z)/z" "cos(z)/z" "sin(z)*cos(z)" "sin(z^2)" \
          "e^(-1/z)" "ze^z" "ze^-z" "ze^(1/z)" "ze^(-1/z)" "z^3" "1/z^3" \
          "acot(z)" "asec(z)" "acsc(z)" "tan(z)/z" "cot(z)/z" "sec(z)/z" \
          "csc(z)/z" "zsin(z)" "zcos(z)" "ztan(z)" "zcot(z)" "zsec(z)" "zcsc(z)" \
          "sin(1/z)" "cos(1/z)" "tan(1/z)" "cot(1/z)" "sec(1/z)" "csc(1/z)" \
          "cotanh(z)" "sech(z)" "cosech(z)" "acoth(z)" "asech(z)" "acosech(z)" \
          "3-term polynomial" "sinh(z)^2" "cosh(z)^2" "tanh(z)^2" "cotanh(z)^2" \
          "sech(z)^2" "cosech(z)^2" "sinh(1/z)" "cosh(1/z)" "tanh(1/z)" \
          "cotanh(1/z)" "sech(1/z)" "cosech(1/z)" "sin(z)tan(z)" "sinh(z)tanh(z)" \
          "sinh(z)cosh(z)" "sinh(z)^2*cosh(z)^2" "sin(z)^2*cos(z)^2" \
          "sin(1/z)*cos(1/z)" "sin(1/z)^2" "sin(z)cos(1/z)" "sin(z)sin(1/z)" \
          "log(z)^2" "sin(z)sin(2z)" "e^2z" "e^-2z" "sinh(1/z)cosh(1/z)" \
          "sinh(1/z)^2" "sinh(z)cosh(1/z)" "sinh(z)sinh(1/z)" "sin(z)sinh(z)" \
          "sin(z)cosh(z)" "sin(z)^2*sinh(z)^2" "sin(z)e^z" "cos(z)e^z" \
          "sinh(z)e^z" "cosh(z)e^z" "sin(z)log(z)" "cos(z)log(z)" "sinh(z)log(z)" \
          "cosh(z)log(z)" "e^(z^2)" "e^(-(z^2))" "e^(1/z^2)" "e^(-1/z^2)" "z"
    default = 1
    hint = "Formula G, executed every N iterations, where N is set \
          by param 'Cycle Length'. For 'z^power', set param 'Power G'. For \
          '3-term polynomial' set 6 params 'Coefficient' & 'Exponent' GA, GB, \
          and GC. Operates on z selected by 'G Generation'"
  endparam
  param ggen
    caption = "G Generation"
    default = 1
    enum = "Current z" "Previous z" "2nd Previous z" "3rd Previous z" \
          "4th Previous z" "5th Previous z"
    hint = "This is the z that gets iterated by Formula G either \
          every iteration (if 'Cycle Length' = 1), or every N iters \
          (where N = 'Cycle Length')"
  endparam
  param power2
    caption = "Power G"
    default = (6,0)
    hint = "This is the power used for the second formula series if parameter \
        'Formula G' is set to 'z^power'"
  endparam
  param formula3
    caption = "Formula H"
    enum = "z^2" "z^3" "z^4" "z^power" "1/z" "sqrt(z)" "1/z^2" "log(z)" "e^z" "z^z" \
          "sin(z)" "cos(z)" \
          "tan(z)" "asin(z)" "acos(z)" "atan(z)" "sinh(z)" "cosh(z)" "tanh(z)" \
          "asinh(z)" "acosh(z)" "atanh(z)" "log(1/z)" "log(log(z))" "e^-z" \
          "e^(1/z)" "z^-z" "sin(z)^2" "cos(z)^2" "tan(z)^2" "cot(z)" "sec(z)" \
          "csc(z)" "cot(z)^2" "sec(z)^2" "csc(z)^2" "z^z^z" "1/z^z^z" "log(-z)" \
          "1/log(z)" "zlog(z)" "sin(z)/z" "cos(z)/z" "sin(z)*cos(z)" "sin(z^2)" \
          "e^(-1/z)" "ze^z" "ze^-z" "ze^(1/z)" "ze^(-1/z)" "z^3" "1/z^3" \
          "acot(z)" "asec(z)" "acsc(z)" "tan(z)/z" "cot(z)/z" "sec(z)/z" \
          "csc(z)/z" "zsin(z)" "zcos(z)" "ztan(z)" "zcot(z)" "zsec(z)" "zcsc(z)" \
          "sin(1/z)" "cos(1/z)" "tan(1/z)" "cot(1/z)" "sec(1/z)" "csc(1/z)" \
          "cotanh(z)" "sech(z)" "cosech(z)" "acoth(z)" "asech(z)" "acosech(z)" \
          "3-term polynomial" "sinh(z)^2" "cosh(z)^2" "tanh(z)^2" "cotanh(z)^2" \
          "sech(z)^2" "cosech(z)^2" "sinh(1/z)" "cosh(1/z)" "tanh(1/z)" \
          "cotanh(1/z)" "sech(1/z)" "cosech(1/z)" "sin(z)tan(z)" "sinh(z)tanh(z)" \
          "sinh(z)cosh(z)" "sinh(z)^2*cosh(z)^2" "sin(z)^2*cos(z)^2" \
          "sin(1/z)*cos(1/z)" "sin(1/z)^2" "sin(z)cos(1/z)" "sin(z)sin(1/z)" \
          "log(z)^2" "sin(z)sin(2z)" "e^2z" "e^-2z" "sinh(1/z)cosh(1/z)" \
          "sinh(1/z)^2" "sinh(z)cosh(1/z)" "sinh(z)sinh(1/z)" "sin(z)sinh(z)" \
          "sin(z)cosh(z)" "sin(z)^2*sinh(z)^2" "sin(z)e^z" "cos(z)e^z" \
          "sinh(z)e^z" "cosh(z)e^z" "sin(z)log(z)" "cos(z)log(z)" "sinh(z)log(z)" \
          "cosh(z)log(z)" "e^(z^2)" "e^(-(z^2))" "e^(1/z^2)" "e^(-1/z^2)" "z" "none"
    default = 2
    hint = "Formula H, executed every N iterations, where N is set \
          by param 'Cycle Length'. For 'z^power', set param 'Power H'. For \
          '3-term polynomial' set 6 params 'Coefficient' & 'Exponent' HA, HB, \
          and HC. Operates on z selected by 'H Generation'"
  endparam
  param hgen
    caption = "H Generation"
    default = 2
    enum = "Current z" "Previous z" "2nd Previous z" "3rd Previous z" \
          "4th Previous z" "5th Previous z"
    hint = "This is the z that gets iterated by Formula H either \
          every iteration (if 'Cycle Length' = 1), or every N iters \
          (where N = 'Cycle Length')"
  endparam
  param power3
    caption = "Power H"
    default = (6,0)
    hint = "This is the power used for the third formula series if parameter \
        'Formula H' is set to 'z^power'"
  endparam
  param blend
    caption = "Blend Functions?"
    default = FALSE
    hint = "If enabled, then the three functions F, G, and H can be individually \
          weighted, rather than being blended equally"
  endparam
  param weight1
    caption = "Weight F"
    default = 1.0
    hint = "If 'Blend Functions' is enabled, then this is the amount of function \
          F that is blended with the others to yield the final z value"
    visible = @blend == TRUE
  endparam
  param weight2
    caption = "Weight G"
    default = 1.0
    hint = "If 'Blend Functions' is enabled, then this is the amount of function \
          G that is blended with the others to yield the final z value"
    visible = @blend == TRUE
  endparam
  param weight3
    caption = "Weight H"
    default = 1.0
    hint = "If 'Blend Functions' is enabled, then this is the amount of function \
          H that is blended with the others to yield the final z value"
    visible = @blend == TRUE
  endparam
  param coeff1a
    caption = "Coefficient FA"
    default = (1,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the coefficient \
          of the 1st term"
  endparam
  param exponent1a
    caption = "Exponent FA"
    default = (6,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the exponent \
          of the 1st term"
  endparam
  param coeff1b
    caption = "Coefficient FB"
    default = (-1,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the coefficient \
          of the 2nd term"
  endparam
  param exponent1b
    caption = "Exponent FB"
    default = (4,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the exponent \
          of the 2nd term"
  endparam
  param coeff1c
    caption = "Coefficient FC"
    default = (1,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the coefficient \
          of the 3rd term"
  endparam
  param exponent1c
    caption = "Exponent FC"
    default = (2,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the exponent \
          of the 3rd term"
  endparam
  param coeff2a
    caption = "Coefficient GA"
    default = (1,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the coefficient \
          of the 1st term"
  endparam
  param exponent2a
    caption = "Exponent GA"
    default = (6,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the exponent \
          of the 1st term"
  endparam
  param coeff2b
    caption = "Coefficient GB"
    default = (-1,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the coefficient \
          of the 2nd term"
  endparam
  param exponent2b
    caption = "Exponent GB"
    default = (4,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the exponent \
          of the 2nd term"
  endparam
  param coeff2c
    caption = "Coefficient GC"
    default = (1,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the coefficient \
          of the 3rd term"
  endparam
  param exponent2c
    caption = "Exponent GC"
    default = (2,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the exponent \
          of the 3rd term"
  endparam
  param coeff3a
    caption = "Coefficient HA"
    default = (1,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the coefficient \
          of the 1st term"
  endparam
  param exponent3a
    caption = "Exponent HA"
    default = (6,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the exponent \
          of the 1st term"
  endparam
  param coeff3b
    caption = "Coefficient HB"
    default = (-1,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the coefficient \
          of the 2nd term"
  endparam
  param exponent3b
    caption = "Exponent HB"
    default = (4,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the exponent \
          of the 2nd term"
  endparam
  param coeff3c
    caption = "Coefficient HC"
    default = (1,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the coefficient \
          of the 3rd term"
  endparam
  param exponent3c
    caption = "Exponent HC"
    default = (2,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the exponent \
          of the 3rd term"
  endparam
  param pixelformula
    caption = "Pixel Formula"
    enum = "p" "p^2" "p^3" "p^4" "p^power" "1/p" "sqrt(p)" "1/p^2" "log(p)" "e^p" "p^p" \
          "sin(p)" "cos(p)" \
          "tan(p)" "asin(p)" "acos(p)" "atan(p)" "sinh(p)" "cosh(p)" "tanh(p)" \
          "asinh(p)" "acosh(p)" "atanh(p)" "log(1/p)" "log(log(p))" "e^-p" \
          "e^(1/p)" "p^-p" "sin(p)^2" "cos(p)^2" "tan(p)^2" "cot(p)" "sec(p)" \
          "csc(p)" "cot(p)^2" "sec(p)^2" "csc(p)^2" "p^p^p" "1/p^p^p" "log(-p)" \
          "1/log(p)" "plog(p)" "sin(p)/p" "cos(p)/p" "sin(p)*cos(p)" "sin(p^2)" \
          "e^(-1/p)" "pe^p" "pe^-p" "pe^(1/p)" "pe^(-1/p)" "p^3" "1/p^3" \
          "acot(p)" "asec(p)" "acsc(p)" "tan(p)/p" "cot(p)/p" "sec(p)/p" \
          "csc(p)/p" "psin(p)" "pcos(p)" "ptan(p)" "pcot(p)" "psec(p)" "pcsc(p)" \
          "sin(1/p)" "cos(1/p)" "tan(1/p)" "cot(1/p)" "sec(1/p)" "csc(1/p)" \
          "cotanh(p)" "sech(p)" "cosech(p)" "acoth(p)" "asech(p)" "acosech(p)" \
          "3-term polynomial" "sinh(p)^2" "cosh(p)^2" "tanh(p)^2" "cotanh(p)^2" \
          "sech(p)^2" "cosech(p)^2" "sinh(1/p)" "cosh(1/p)" "tanh(1/p)" \
          "cotanh(1/p)" "sech(1/p)" "cosech(1/p)" "sin(p)tan(p)" "sinh(p)tanh(p)" \
          "sinh(p)cosh(p)" "sinh(p)^2*cosh(p)^2" "sin(p)^2*cos(p)^2" \
          "sin(1/p)*cos(1/p)" "sin(1/p)^2" "sin(p)cos(1/p)" "sin(p)sin(1/p)" \
          "log(p)^2" "sin(p)sin(2p)" "e^2p" "e^-2p" "sinh(1/p)cosh(1/p)" \
          "sinh(1/p)^2" "sinh(p)cosh(1/p)" "sinh(p)sinh(1/p)" "sin(p)sinh(p)" \
          "sin(p)cosh(p)" "sin(p)^2*sinh(p)^2" "sin(p)e^p" "cos(p)e^p" \
          "sinh(p)e^p" "cosh(p)e^p" "sin(p)log(p)" "cos(p)log(p)" "sinh(p)log(p)" \
          "cosh(p)log(p)"
    default = 0
    hint = "Pixel value (Mand) or seed (Julia) can be initialized \
        before iterating. For 'p^power', set parameter 'Pixel Power'; \
        for '3-term polynomial', set 'Coeff Pa', 'Exponent Pa', 'Coeff Pb', \
        'Exponent Pb', 'Coeff Pc', 'Exponent Pc'. 'p' results in normal \
        initialization"
  endparam
  param ppower
    caption = "Pixel Power"
    default = (5,0)
    hint = "This is the power used if parameter \
        'Pixel Formula' is set to 'p^power'"
  endparam
  param coeffpa
    caption = "Coeff Pa"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 1st term"
  endparam
  param exponentpa
    caption = "Exponent Pa"
    default = (6,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 1st term"
  endparam
  param coeffpb
    caption = "Coeff Pb"
    default = (-1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 2nd term"
  endparam
  param exponentpb
    caption = "Exponent Pb"
    default = (4,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 2nd term"
  endparam
  param coeffpc
    caption = "Coeff Pc"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 3rd term"
  endparam
  param exponentpc
    caption = "Exponent Pc"
    default = (2,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 3rd term"
  endparam
  param pmode
    caption = "Pixel Mode"
    default = 0
    enum = "Post-add" "Pre-add" "Both"
    hint = "'Post-add' -- formula is executed, then pixel/constant is added to result; \
        'Pre-add' -- pixel is added to z, then formula executed; 'Both' -- pixel added, \
        formula executed, then pixel added again to result"
  endparam
  param jconstant
    caption = "Seed/Perturbation"
    default = (0,0)
    hint = "This is the seed constant for Julia-type fractals, or the initial \
          perturbation for Mandelbrot-types"
  endparam
  param bail
    caption = "Bailout Value"
    default = 64.0
    hint = "Value needed to 'escape' to infinity"
    visible = !@biomorph
  endparam
  param biomorph
  	caption = "Biomorph Bailout?"
  	default = FALSE
  	hint = "Enabling this setting changes the bailout condition to match \
  		Pickover's 'biomorph' definition.  For coloring, consider using \
  		'Biomorph' in the public folder 'jam2.ucl'."
  endparam  		
  param biomorphtest
    caption = "Biomorph Bailout Test"
    default = 10.0
    hint = "The bailout value for the 'Biomorph' test."
    visible = @biomorph
  endparam
param biomorphtype
	caption = "Biomorph Type"
	enum = "real" "imag" "real + imag" "real + imag + cabs" "cabs"
	default = 3
	hint = "This determines the bailout condition for the Biomorph."
	visible = @biomorph
endparam
  param mandy
    caption = "Mandelbrot flag"
    default = TRUE
    hint = "Works in combination with the Julia flag for switching"
  endparam
  param julia
    caption = "Julia flag"
    default = FALSE
    hint = "Works in combination with the Mandelbrot flag for switching"
  endparam


  switch:
  type = "jam-3stageGen"
  jconstant = #pixel
  bail = bail
  biomorph = biomorph
  biomorphtest = biomorphtest
  biomorphtype = biomorphtype
  frequency = frequency
  combo = combo
  formula1 = formula1
  formula2 = formula2
  formula3 = formula3
  fgen = fgen
  ggen = ggen
  hgen = hgen
  power1 = power1
  power2 = power2
  power3 = power3
  blend = blend
  weight1 = weight1
  weight2 = weight2
  weight3 = weight3
  coeff1a = coeff1a
  exponent1a = exponent1a
  coeff1b = coeff1b
  exponent1b = exponent1b
  coeff1c = coeff1c
  exponent1c = exponent1c
  coeff2a = coeff2a
  exponent2a = exponent2a
  coeff2b = coeff2b
  exponent2b = exponent2b
  coeff2c = coeff2c
  exponent2c = exponent2c
  coeff3a = coeff3a
  exponent3a = exponent3a
  coeff3b = coeff3b
  exponent3b = exponent3b
  coeff3c = coeff3c
  exponent3c = exponent3c
  pixelformula = pixelformula
  ppower = ppower
  coeffpa = coeffpa
  exponentpa = exponentpa
  coeffpb = coeffpb
  exponentpb = exponentpb
  coeffpc = coeffpc
  exponentpc = exponentpc
  pmode = pmode
  mandy = julia
  julia = mandy
}

jam-LHODE { ; jam 030319
  ; Mandelbrot/Julia based on some general solutions to
  ; linear homogeneous ordinary differential equations.
  ;
  ; The specific functions implemented, and the equations for which they are
  ; solutions, are:
  ; y = e^(z/2) * cos((sqrt(3)/2)z); y'''(z) + y(z) = 0
  ; y = e^(z/2) * sin((sqrt(3)/2)z); y'''(z) + y(z) = 0
  ; y = e^(-z/2) * cos((sqrt(3)/2)z); y'''(z) - y(z) = 0
  ; y = e^(-z/2) * sin((sqrt(3)/2)z); y'''(z) - y(z) = 0
  ; y = c1*e^-z + c2*e^(z/2) * cos((sqrt(3)/2)z) + c3*e^(z/2) * sin((sqrt(3)/2)z);
  ;     y'''(z) - y(z) = 0
  ; y = c1*e^z + c2*e^(-z/2) * cos((sqrt(3)/2)z) + c3*e^(-z/2) * sin((sqrt(3)/2)z);
  ;     y'''(z) + y(z) = 0
  ;
  ; Similar linearly independent solutions of the following LHODEs
  ; are also included:  y'''' + y = 0, y''''' + y = 0, and
  ; y''''' - y = 0.
  ;
  ; Each of these functions can be used alone, or blended with the standard
  ; Mandelbrot power function, z(n+1) = z(n)^power.

  ; Contact Joe Maddry (maddry@sri.org) with comments/questions.  Enjoy!

  global:
; float excoeff = 0.0, float trigcoeff = 0.0
  if @solution < 6
    excoeff = 1/2
    trigcoeff = excoeff*sqrt(3)
    if @solution > 2
      excoeff = -excoeff
    endif ; solution
  elseif @solution < 10
    excoeff = 1/sqrt(2)
    trigcoeff = excoeff
    if @solution > 7
      excoeff = -excoeff
    endif ; solution
  elseif @solution < 12
    excoeff = cos(#pi/5)
    trigcoeff = sin(#pi/5)
  elseif @solution < 14
    excoeff = cos(3*#pi/5)
    trigcoeff = sin(3*#pi/5)
  elseif @solution < 16
    excoeff = cos(2*#pi/5)
    trigcoeff = sin(2*#pi/5)
  elseif @solution < 18
    excoeff = cos(4*#pi/5)
    trigcoeff = sin(4*#pi/5)
  elseif @solution < 20
    excoeff = cos(#pi/6)
    trigcoeff = sin(#pi/6)
  elseif @solution < 22
    excoeff = cos(5*#pi/6)
    trigcoeff = sin(5*#pi/6)
  elseif @solution < 24
    excoeff = cos(#pi/7)
    trigcoeff = sin(#pi/7)
  elseif @solution < 26
    excoeff = cos(3*#pi/7)
    trigcoeff = sin(3*#pi/7)
  elseif @solution < 28
    excoeff = cos(5*#pi/7)
    trigcoeff = sin(5*#pi/7)
  elseif @solution < 30
    excoeff = cos(2*#pi/7)
    trigcoeff = sin(2*#pi/7)
  elseif @solution < 32
    excoeff = cos(4*#pi/7)
    trigcoeff = sin(4*#pi/7)
  else ; @solution < 34
    excoeff = cos(6*#pi/7)
    trigcoeff = sin(6*#pi/7)
  endif ; solution

  init:
  if @mandy
    z = @jconstant, jc = #pixel
  else ; Julia
    z = #pixel, jc = @jconstant
  endif

  complex zextra = complex ztemp = (0,0) ; temp/spare scratch variables

  ; Pixel/constant initialization section
  if @pixelformula != 0
    if @pixelformula == 1
      jc = jc * jc
    elseif  @pixelformula == 2
      jc = jc * jc * jc
    elseif  @pixelformula == 3
      zextra = jc * jc
      jc = zextra * zextra
    elseif  @pixelformula == 4
      jc = jc ^ @ppower
    elseif  @pixelformula == 5
      jc = 1/jc
    elseif  @pixelformula == 6
      jc = sqrt(jc)
    elseif  @pixelformula == 7
      jc = 1 / ( jc * jc )
    elseif  @pixelformula == 8
      jc = log(jc)
    elseif  @pixelformula == 9
      jc = exp( jc)
    elseif  @pixelformula == 10
      jc = jc^jc
    elseif  @pixelformula == 11
      jc = sin( jc )
    elseif  @pixelformula == 12
      jc = cos( jc )
    elseif  @pixelformula == 13
      jc = tan( jc )
    elseif  @pixelformula == 14
      jc = asin( jc )
    elseif  @pixelformula == 15
      jc = acos( jc )
    elseif  @pixelformula == 16
      jc = atan( jc )
    elseif  @pixelformula == 17
      jc = sinh( jc )
    elseif  @pixelformula == 18
      jc = cosh( jc )
    elseif  @pixelformula == 19
      jc = tanh( jc )
    elseif  @pixelformula == 20
      jc = asinh( jc )
    elseif  @pixelformula == 21
      jc = acosh( jc )
    elseif  @pixelformula == 22
      jc = atanh( jc )
    elseif  @pixelformula == 23
      jc = log( 1/jc )
    elseif  @pixelformula == 24
      jc = log( log( jc ))
    elseif  @pixelformula == 25
      jc = exp( -jc )
    elseif  @pixelformula == 26
      jc = exp( 1/jc )
    elseif  @pixelformula == 27
      jc = jc^(-jc)
    elseif  @pixelformula == 28
      zextra = sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 29
      zextra = cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 30
      zextra = tan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 31
      jc = cotan( jc )
    elseif  @pixelformula == 32
      jc = 1/cos( jc )
    elseif  @pixelformula == 33
      jc = 1/sin( jc )
    elseif  @pixelformula == 34
      zextra = cotan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 35
      zextra = 1/cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 36
      zextra = 1/sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 37
      zextra = jc^(jc)
      jc = jc^zextra
    elseif  @pixelformula == 38
      zextra = jc^(jc)
      jc = 1/( jc^zextra )
    elseif  @pixelformula == 39
      jc = log(-jc)
    elseif  @pixelformula == 40
      jc = 1/log( jc )
    elseif  @pixelformula == 41
      jc = jc * log( jc )
    elseif  @pixelformula == 42
      jc = sin( jc ) / jc
    elseif  @pixelformula == 43
      jc = cos( jc ) / jc
    elseif  @pixelformula == 44
      jc = sin( jc ) * cos( jc )
    elseif  @pixelformula == 45
      jc = sin( jc^2 )
    elseif  @pixelformula == 46
      jc = exp( -1/jc )
    elseif  @pixelformula == 47
      jc = jc * exp( jc )
    elseif  @pixelformula == 48
      jc = jc * exp( -jc )
    elseif  @pixelformula == 49
      jc = jc * exp( 1/jc )
    elseif  @pixelformula == 50
      jc = jc * exp( -1/jc )
    elseif  @pixelformula == 51
      jc = jc * jc * jc
    elseif  @pixelformula == 52
      jc = 1 / ( jc * jc * jc )
    elseif  @pixelformula == 53
      jc = atan( 1 / jc )
    elseif  @pixelformula == 54
      jc = acos( 1 / jc )
    elseif  @pixelformula == 55
      jc = asin( 1 / jc )
    elseif  @pixelformula == 56
      jc = tan( jc ) / jc
    elseif  @pixelformula == 57
      jc = cotan( jc ) / jc

    elseif  @pixelformula == 58
      jc = 1 / ( jc * cos( jc ))
    elseif  @pixelformula == 59
      jc = 1 / ( jc * sin( jc ))
    elseif  @pixelformula == 60
      jc = jc * sin( jc )
    elseif  @pixelformula == 61
      jc = jc * cos( jc )
    elseif  @pixelformula == 62
      jc = jc * tan( jc )
    elseif  @pixelformula == 63
      jc = jc * cotan( jc )
    elseif  @pixelformula == 64
      jc = jc/cos( jc )
    elseif  @pixelformula == 65
      jc = jc/sin( jc )
    elseif  @pixelformula == 66
      jc = sin( 1/jc )
    elseif  @pixelformula == 67
      jc = cos( 1/jc )
    elseif  @pixelformula == 68
      jc = tan( 1/jc )
    elseif  @pixelformula == 69
      jc = cotan( 1/jc )
    elseif  @pixelformula == 70
      jc = 1/cos( 1/jc )
    elseif  @pixelformula == 71
      jc = 1/sin( 1/jc )
    elseif  @pixelformula == 72
      jc = cotanh( jc )
    elseif  @pixelformula == 73
      jc = 1/cosh( jc )
    elseif  @pixelformula == 74
      jc = 1/sinh( jc )
    elseif  @pixelformula == 75
      jc = atanh( 1/jc )
    elseif  @pixelformula == 76
      jc = acosh( 1/jc )
    elseif  @pixelformula == 77
      jc = asinh( 1/jc )
    elseif @pixelformula == 78
      jc = @coeffpa * jc^@exponentpa + @coeffpb * jc^@exponentpb + \
          @coeffpc * jc^@exponentpc
    elseif  @pixelformula == 79
      zextra = sinh(#z)
      jc = zextra * zextra
    elseif  @pixelformula == 80
      zextra = cosh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 81
      zextra = tanh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 82
      zextra = cotanh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 83
      zextra = (1,0)/cosh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 84
      zextra = (1,0) / sinh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 85
      jc = sinh(1/jc)
    elseif  @pixelformula == 86
      jc = cosh(1/jc)
    elseif  @pixelformula == 87
      jc = tanh(1/jc)
    elseif  @pixelformula == 88
      jc = cotanh(1/jc)
    elseif  @pixelformula == 89
      jc = (1,0)/cosh(1/jc)
    elseif  @pixelformula == 90
      jc = (1,0)/sinh(1/jc)
    elseif  @pixelformula == 91
      jc = sin( jc ) * tan(jc)
    elseif  @pixelformula == 92
      jc = sinh(jc) * tanh(jc)
    elseif  @pixelformula == 93
      jc = sinh(jc) * cosh(jc)
    elseif  @pixelformula == 94
      ztemp = sinh(jc), zextra = cosh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 95
      ztemp = sin(jc), zextra = cos(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 96
      zextra = 1/jc
      jc = sin(zextra)*cos(zextra)
    elseif  @pixelformula == 97
      zextra = sin( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 98
      jc = sin(jc) * cos(1/jc)
    elseif  @pixelformula == 99
      jc = sin(jc) * sin(1/jc)
    elseif  @pixelformula == 100
      zextra = log(jc)
      jc = zextra*zextra
    elseif  @pixelformula == 101
      jc = sin(jc) * sin(2*jc)
    elseif @pixelformula == 102
      jc = exp(2*jc)
    elseif  @pixelformula == 103
      jc = exp(-2*jc)
    elseif  @pixelformula == 104
      zextra = 1/jc
      jc = sinh(zextra)*cosh(zextra)
    elseif  @pixelformula == 105
      zextra = sinh( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 106
      jc = sinh(jc) * cosh(1/jc)
    elseif  @pixelformula == 107
      jc = sinh(jc) * sinh(1/jc)
    elseif  @pixelformula == 108
      jc = sin(jc) * sinh(jc)
    elseif  @pixelformula == 109
      jc = sin(jc) * cosh(jc)
    elseif  @pixelformula == 110
      zextra = sin(jc), ztemp = sinh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 111
      jc = sin(jc)*exp(jc)
    elseif  @pixelformula == 112
      jc = cos(jc)*exp(jc)
    elseif  @pixelformula == 113
      jc = sinh(jc)*exp(jc)
    elseif  @pixelformula == 114
      jc = cosh(jc)*exp(jc)
    elseif  @pixelformula == 115
      jc = sin(jc)*log(jc)
    elseif  @pixelformula == 116
      jc = cos(jc)*log(jc)
    elseif  @pixelformula == 117
      jc = sinh(jc)*log(jc)
    else ; @pixelformula == 118
      jc = cosh(jc)*log(jc)
    endif ; @pixelformula = 1
  endif ; @pixelformula != 0

  loop:
  if @pmode != 0
    z = z + jc
  endif ; pmode

  ztemp = z ; save old value for possible blending

  if @solution == 4 ; linear combination of Order-3 solutions
  ; z(n+1) = c1*e^-z + c2*e^(z/2) * cos((sqrt(3)/2)z) + c3*e^(z/2) * sin((sqrt(3)/2)z)
    z = @c1*exp(-z) + (exp(excoeff*z)) * (@c2*(cos(trigcoeff*z)) + @c3*(sin(trigcoeff*z)))
  elseif @solution == 5 ; linear combination #2
    z = @c1*exp(z) + (exp(-excoeff*z)) * (@c2*(cos(trigcoeff*z)) + @c3*(sin(trigcoeff*z)))
  elseif ( @solution % 2 == 0 )
    z = (exp(excoeff*z)) * (cos(trigcoeff*z))
  else;  @solution % 2 == 1
    z = (exp(excoeff*z)) * (sin(trigcoeff*z))
  endif ; solution

  if @blend
    z = (@weight1 * z) + (@weight2 * (ztemp^@power))
  endif ; blend

  if @pmode != 1
    z = z + jc
  endif ; pmode

  bailout:
  |z| < @bail

  default:
  title = "zLHODE Solutions"
  center = (0,0)
  maxiter = 100
  method = multipass
  periodicity = 0
  magn = 0.5

  heading
  	caption = "There will soon be a newer version of this formula"
  endheading

  param solution
    caption = "Solution to Iterate"
    enum = "e^(a3*z) * cos(b3*z)" "e^(a3*z) * sin(b3*z)" \
        "e^(-a3*z) * cos(b3*z)" "e^(-a3*z) * sin(b3*z)" \
        "c1*e^(-z)+c2*e^(a3*z)*cos(b3*z)+c3*e^(a3*z)*sin(b3*z)" \
        "c1*e^(z)+c2*e^(-a3*z)*cos(b3*z)+c3*e^(-a3*z)*sin(b3*z)" \
        "e^(a4*z) * cos(b4*z)" "e^(a4*z) * sin(b4*z)" \
        "e^(-a4*z) * cos(b4*z)" "e^(-a4*z) * sin(b4*z)" \
        "e^(a5A*z) * cos(b5A*z)" "e^(a5A*z) * sin(b5A*z)" \
        "e^(a5B*z) * cos(b5B*z)" "e^(a5B*z) * sin(b5B*z)" \
        "e^(a5C*z) * cos(b5C*z)" "e^(a5C*z) * sin(b5C*z)" \
        "e^(a5D*z) * cos(b5D*z)" "e^(a5D*z) * sin(b5D*z)" \
        "e^(a6A*z) * cos(b6A*z)" "e^(a6A*z) * sin(b6A*z)" \
        "e^(a6B*z) * cos(b6B*z)" "e^(a6B*z) * sin(b6B*z)" \
        "e^(a7A*z) * cos(b7A*z)" "e^(a7A*z) * sin(b7A*z)" \
        "e^(a7B*z) * cos(b7B*z)" "e^(a7B*z) * sin(b7B*z)" \
        "e^(a7C*z) * cos(b7C*z)" "e^(a7C*z) * sin(b7C*z)" \
        "e^(a7D*z) * cos(b7D*z)" "e^(a7D*z) * sin(b7D*z)" \
        "e^(a7E*z) * cos(b7E*z)" "e^(a7E*z) * sin(b7E*z)" \
        "e^(a7F*z) * cos(b7F*z)" "e^(a7F*z) * sin(b7F*z)"
    default = 0
    hint = "This parameter selects which solution to the differential \
        equation y'''(z) + y(z) = 0, y'''(z) - y(z) = 0, etc., is to be \
        iterated.  a3, b3 refer to the solutions to the 3rd order differential \
        equations; a4, b4 to the 4th order solutions; a5A, a5B, b5A, etc. to \
        5th order solutions; etc."
  endparam
  param c1
    caption = "Coeff 1"
    default = (1,0)
    hint = "If param 'Solution' equals 'c1*e(...', then this is the \
        coefficient of the first term"
    visible = (@solution == 2) || (@solution == 5)
  endparam
  param c2
    caption = "Coeff 2"
    default = (1,0)
    hint = "If param 'Solution' equals 'c1*e(...', then this is the \
        coefficient of the second term"
    visible = (@solution == 2) || (@solution == 5)
  endparam
  param c3
    caption = "Coeff 3"
    default = (1,0)
    hint = "If param 'Solution' equals 'c1*e(...', then this is the \
        coefficient of the third term"
    visible = (@solution == 2) || (@solution == 5)
  endparam
  param blend
    caption = "Blend Z^Power?"
    default = FALSE
    hint = "If enabled, then each iteration the differential equation solution \
        is blended with the standard Mandelbrot function, z(n+1) = z^power + c.  \
        Set params 'Z Power', 'ODE Weight', and 'Z^Power Weight'"
  endparam
  param power
    caption = "Z Power"
    default = (2,0)
    hint = "If 'Blend' is enabled, then this is the exponent of the usual \
        Mandelbrot function"
    visible = @blend == TRUE
  endparam
  param weight1
    caption = "ODE Weight"
    default = -0.1
    hint = "If 'Blend' is enabled, this is the amount of the differential equation \
        function that is added to the standard Mandelbrot function"
    visible = @blend == TRUE
  endparam
  param weight2
    caption = "Z^Power Weight"
    default = 0.9
    hint = "If 'Blend' is enabled, this is the amount of the standard Mandelbrot function \
        that is added to the differential equation function"
    visible = @blend == TRUE
  endparam
  param pixelformula
    caption = "Pixel Formula"
    enum = "p" "p^2" "p^3" "p^4" "p^power" "1/p" "sqrt(p)" "1/p^2" "log(p)" "e^p" \
          "p^p" "sin(p)" "cos(p)" \
          "tan(p)" "asin(p)" "acos(p)" "atan(p)" "sinh(p)" "cosh(p)" "tanh(p)" \
          "asinh(p)" "acosh(p)" "atanh(p)" "log(1/p)" "log(log(p))" "e^-p" \
          "e^(1/p)" "p^-p" "sin(p)^2" "cos(p)^2" "tan(p)^2" "cot(p)" "sec(p)" \
          "csc(p)" "cot(p)^2" "sec(p)^2" "csc(p)^2" "p^p^p" "1/p^p^p" "log(-p)" \
          "1/log(p)" "plog(p)" "sin(p)/p" "cos(p)/p" "sin(p)*cos(p)" "sin(p^2)" \
          "e^(-1/p)" "pe^p" "pe^-p" "pe^(1/p)" "pe^(-1/p)" "p^3" "1/p^3" \
          "acot(p)" "asec(p)" "acsc(p)" "tan(p)/p" "cot(p)/p" "sec(p)/p" \
          "csc(p)/p" "psin(p)" "pcos(p)" "ptan(p)" "pcot(p)" "psec(p)" "pcsc(p)" \
          "sin(1/p)" "cos(1/p)" "tan(1/p)" "cot(1/p)" "sec(1/p)" "csc(1/p)" \
          "cotanh(p)" "sech(p)" "cosech(p)" "acoth(p)" "asech(p)" "acosech(p)" \
          "3-term polynomial" "sinh(p)^2" "cosh(p)^2" "tanh(p)^2" "cotanh(p)^2" \
          "sech(p)^2" "cosech(p)^2" "sinh(1/p)" "cosh(1/p)" "tanh(1/p)" \
          "cotanh(1/p)" "sech(1/p)" "cosech(1/p)" "sin(p)tan(p)" "sinh(p)tanh(p)" \
          "sinh(p)cosh(p)" "sinh(p)^2*cosh(p)^2" "sin(p)^2*cos(p)^2" \
          "sin(1/p)*cos(1/p)" "sin(1/p)^2" "sin(p)cos(1/p)" "sin(p)sin(1/p)" \
          "log(p)^2" "sin(p)sin(2p)" "e^2p" "e^-2p" "sinh(1/p)cosh(1/p)" \
          "sinh(1/p)^2" "sinh(p)cosh(1/p)" "sinh(p)sinh(1/p)" "sin(p)sinh(p)" \
          "sin(p)cosh(p)" "sin(p)^2*sinh(p)^2" "sin(p)e^p" "cos(p)e^p" \
          "sinh(p)e^p" "cosh(p)e^p" "sin(p)log(p)" "cos(p)log(p)" "sinh(p)log(p)" \
          "cosh(p)log(p)"
    default = 0
    hint = "Pixel value (Mand) or seed (Julia) can be initialized \
        before iterating. For 'p^power', set parameter 'Pixel Power'; \
        for '3-term polynomial', set 'Coeff Pa', 'Exponent Pa', 'Coeff Pb', \
        'Exponent Pb', 'Coeff Pc', 'Exponent Pc'. 'p' results in normal \
        initialization"
  endparam
  param ppower
    caption = "Pixel Power"
    default = (5,0)
    hint = "This is the power used if parameter \
        'Pixel Formula' is set to 'p^power'"
  endparam
  param coeffpa
    caption = "Coeff Pa"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 1st term"
  endparam
  param exponentpa
    caption = "Exponent Pa"
    default = (6,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 1st term"
  endparam
  param coeffpb
    caption = "Coeff Pb"
    default = (-1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 2nd term"
  endparam
  param exponentpb
    caption = "Exponent Pb"
    default = (4,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 2nd term"
  endparam
  param coeffpc
    caption = "Coeff Pc"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 3rd term"
  endparam
  param exponentpc
    caption = "Exponent Pc"
    default = (2,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 3rd term"
  endparam
  param pmode
    caption = "Pixel Mode"
    default = 0
    enum = "Post-add" "Pre-add" "Both"
    hint = "'Post-add' -- formula is executed, then pixel/constant is added to result; \
        'Pre-add' -- pixel is added to z, then formula executed; 'Both' -- pixel added, \
        formula executed, then pixel added again to result"
  endparam
  param jconstant
    caption = "Seed/Perturbation"
    default = (0,0)
    hint = "This is the seed constant for Julia-type fractals, or the initial \
          perturbation for Mandelbrot-types"
  endparam
  param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity"
  endparam
  param mandy
    caption = "Mandelbrot flag"
    default = TRUE
    hint = "Works in combination with the Julia flag for switching"
  endparam
  param julia
    caption = "Julia flag"
    default = FALSE
    hint = "Works in combination with the Mandelbrot flag for switching"
  endparam

  switch:
  type = "jam-LHODE"
  jconstant = #pixel
  bail = bail
  solution = solution
  c1 = c1
  c2 = c2
  c3 = c3
  blend = blend
  power = power
  weight1 = weight1
  weight2 = weight2
  pixelformula = pixelformula
  ppower = ppower
  coeffpa = coeffpa
  exponentpa = exponentpa
  coeffpb = coeffpb
  exponentpb = exponentpb
  coeffpc = coeffpc
  exponentpc = exponentpc
  pmode = pmode
  mandy = julia
  julia = mandy
}

jam-ShapeGuidedJulia {

; Mandelbrot/Julia incorporating two different Julia constants, J1 and J2.
; The effective Julia constant used on any given iteration is interpolated
; between (or beyond) J1 and J2 based on the distance of the current value
; of the z iterate from a user-defined shape, such as a circle.

; Switch mode can be used to select suitable values for J1 and J2, and the
; rate of interpolation can be adjusted by setting a coefficient constant for
; the linear interpolation equations.

; After switching to the 'Julia 1' mode, the selected Julia constant can be
; read from the read-only variable 'Switch Constant'.  This value should be
; manually copied to param 'Julia 1' before switching a second time (to mode
; 'Julia 2'), if you want to preserve the selected 'Julia 1' value after the
; second switch.

; Questions, comments, or problems welecomed at maddry@sri.org.

global:
  float twopi = 2.0 * #pi
  float tangle = @rotation * #pi / 180 ; rotated trap angle
  if ( tangle < 0 )
    tangle = tangle + twopi
  endif ; tangle

init:
  if @CurrentMode == "Mandelbrot"
    z =  @perturb, jc1 = #pixel, jc2 = @Julia2
  elseif @CurrentMode == "Julia 1"
    z = #pixel, jc1 = @SwitchConstant, jc2 = @Julia2
  else
    z = #pixel, jc1 = @Julia1, jc2 = @SwitchConstant
  endif ; @CurrentMode

  float distance = float zangle = float temp = 0.0
  complex ztemp = complex ttemp = (0,0)
  complex jeffective = (0,0) ; the effective Julia constant
  complex jcoeff = ( jc2 - jc1)/@ilimit ; the interpolation equation coefficient

loop:
  ; First, njormalize z to trap center, find the point on the trap closest
  ; to z, then find the distance between the iterate and the trap

  if @shape == "circle"
    distance = cabs(z - @center) - @tscale
  else
    ; Center on trap
    ztemp = z - @center
    ; Compute rotated z
    ztemp = ztemp * exp( flip(tangle))
    ; Find angle of 'rotated' z
    zangle = atan2( ztemp )
    if ( zangle < 0 )
      zangle = zangle + twopi ; 0 <= zangle <= two pi
    endif ; zangle
      if @shape == "ellipse"
        temp = abs(tan(zangle))
        temp = @twidthx * @theighty * sqrt(1 + temp * temp)/(@theighty^@texponent + \
                (@twidthx^@texponent * temp^@texponent))^(1/@texponent)
        ttemp = @tscale * temp * exp(flip(zangle))
        distance = cabs(ztemp - ttemp)
      elseif @shape == "hyperbola"
        distance = abs( imag(ztemp) * real(ztemp) - @tscale )
      endif ; @shape [inner]
  endif ; @shape [outer]

  ; Second, interpolate to find the effective Julia constant
  jeffective = jcoeff * distance + jc1

  ; Third, calculate the new z value
  z = z^@zexponent + jeffective

bailout:
  |z| < @bail

default:
  title = "Shape Guided Julia"
  center = (0,0)
  maxiter = 100
  method = multipass
  periodicity = 0

  param CurrentMode
    caption = "Current Mode"
    default = 0
    enum = "Mandelbrot" "Julia 1" "Julia 2"
    hint = "This is the current switch operating mode"
    enabled = FALSE ; visible but not directly changeable
  endparam
  param SwitchToMode
    caption = "Switch To?"
    default = 1
    enum = "Mandelbrot" "Julia 1" "Julia 2"
    hint = "This is the operating mode that will be active after a 'switch'"
  endparam
  param NextMode
    caption = "Next Mode?"
    default = 2
    enum = "Mandelbrot" "Julia 1" "Julia 2"
    hint = "This is the operating mode that will be active after a second 'switch'"
    visible = FALSE ; never visible or directly changeable
  endparam
  param SwitchConstant
    caption = "Switch Constant"
    default = (0,0)
    hint = "This is the complex value selected by the cursor after a switch.  \
          To preserve this value before another switch, manually copy this value \
          to param 'Julia 1' (if 'Switch To' is set to 'Julia 2' or 'Mandelbrot') \
          or to param 'Julia 2' (if 'Switch To' is set to 'Julia 1' or \
          'Mandelbrot').  This value should not normally be set manually"
  endparam
  param Julia1
    caption = "Julia 1"
    default = (0,0)
    hint = "This is the first Julia constant, which can be set as usual by \
          switching if param 'Switch To' is set to 'Julia 1'.  This param can also \
          be set manually, for example by copying the 'Switch Constant' before \
          setting 'Switch To' to 'Julia 2' and performing a second switch"
  endparam
  param Julia2
    caption = "Julia 2"
    default = (0,0)
    hint = "This is the second Julia constant, which can be set as usual by \
          switching if param 'Switch To' is set to 'Julia 2'.  This param can also \
          be set manually, for example by copying the 'Switch Constant' before \
          setting 'Switch To' to 'Julia 1' and performing a second switch"
  endparam
  param shape
    caption = "Guide Shape"
    default = 0
    enum = "circle" "ellipse" "hyperbola"
    hint = "This param determines the trap shape.  The distance between the chosen \
          trap and the current z is used to calculate the effective Julia constant \
          for that iteration"
  endparam
  param center
    caption = "Trap Center"
    default = (0,0)
    hint = "This is the center of the guiding shape which affects the \
          effective Julia constant used on each iteration.  The effective \
          Julia constant is calculated from params 'Julia 1' and 'Julia 2' \
          based on the distance of the current z from this trap"
  endparam
  param tscale
    caption = "Trap Scale"
    default = 0.5
    min = 0.0
    hint = "This is the scale or radius of the guiding shape which affects the \
          effective Julia constant used on each iteration.  The effective \
          Julia constant is calculated from params 'Julia 1' and 'Julia 2' \
          based on the distance of the current z from the trap shape"
  endparam
  param rotation
    caption = "Rotation Angle"
    default = 0.0
    min = -179.9
    max = 359.9
    hint = "Number of degrees (0-359) that the trap shape should be rotated from \
          its default position"
    visible = @shape != "circle"
  endparam
  param texponent
    caption = "Ellipse Exponent"
    default = 2.0
    hint = "Use 2 for ellipse, > 2 for superellipse, < 1 for astroid, 1-2 for \
          subellipse"
    visible = @shape == "ellipse"
  endparam
  param twidthx
    caption = "Trap Width"
    default = 1.0
    min = 0.0
    hint = "Trap size in x-direction"
    visible = @shape == "ellipse"
  endparam
  param theighty
    caption = "Trap Height"
    default = 0.5
    min = 0.0
    hint = "Trap size in y-direction"
    visible = @shape == "ellipse"
  endparam
  param ilimit
    caption = "Interpolation Constant"
    default = 10.0
    hint = "This coefficient value affects the rate at which the effective \
          Julia constant varies betweek the 'Julia 1' value and the 'Julia 2' value"
  endparam
  param zexponent
    caption = "Mandelbrot Power"
    default = (2,0)
    hint = "This is the exponent for the Mnadelbrot function"
  endparam
  param perturb
    caption = "Mandy Perturbation"
    default = (0,0)
    hint = "In Mandelbrot mode, this is the initial perturbation"
  endparam
  param bail
    caption = "Bailout Value"
    default = 1024.0
    hint = "This is the bailout value at which iteration ends"
  endparam

switch:
  type = "jam-ShapeGuidedJulia"
  CurrentMode = SwitchToMode
  SwitchToMode = NextMode
  NextMode = CurrentMode
  SwitchConstant = #pixel
  Julia1 = Julia1
  Julia2 = Julia2
  shape = shape
  tscale = tscale
  center = center
  rotation = rotation
  texponent = texponent
  twidthx = twidthx
  theighty = theighty
  ilimit = ilimit
  zexponent = zexponent
  perturb = perturb
  bail = bail
}

jam-itertrig { ; iterated trig functions
  ; jam 170511
  ; based on the iterative method of Otto Magus

global:
	float adjustment = @adjust/100
	halfpi = #pi/2

init:
	float x = float y = 0.0
	float a = 0.0
	int itercount = 0

	z = @pixfunction(#pixel)

loop:
while itercount < @iterations
	itercount = itercount + 1
	z = @Zfunction(z)
	x = real(z)
	y = imag(z)
	a = sqr(x) + sqr(y)
	x = x/a + real(@zperturb)
	y = y/a + imag(@zperturb)
	z = x + flip(y)
	
	if @trigfunction == "sin" ; sine function
		z = sin(z)
	elseif @trigfunction == "cos" ; cosine
		z = cos(z)
	elseif @trigfunction == "tan" ; tangent
		z = tan(z)
	elseif @trigfunction == "cot" ; cotangent
		z = cotan(z)
	elseif @trigfunction == "sec" ; secant
		z = 1/cos(z)
	elseif @trigfunction == "csc" ; cosecant
		z = 1/sin(z)
	elseif @trigfunction == "ver" ; versine
		z = 1 - cos(z)
	elseif @trigfunction == "vcs" ; vercosine
		z = 1 + cos(z)
	elseif @trigfunction == "cvs" ; coversine
		z = 1 - sin(z)
	elseif @trigfunction == "cvc" ; covercosine
		z = 1 + sin(z)
	elseif @trigfunction == "exs" ; exsecant
		z = 1/cos(z) - 1
	elseif @trigfunction == "exc" ; excosecant
		z = 1/sin(z) - 1
	elseif @trigfunction == "crd" ; chord
		z = 2 * sin(z/2)
	elseif @trigfunction == "asin" ; arcsine
		z =  asin(z - trunc(z)) 
	elseif @trigfunction == "acos" ; arccosine
		z = acos(z - trunc(z))
	elseif @trigfunction == "atan" ; arctangent
		z = atan(z)
	elseif @trigfunction == "acot" ; arccotangent
		z = halfpi - atan(z)
	elseif @trigfunction == "asec" ; arcsecant
		z = acos(1/z - trunc(1/z))
	elseif @trigfunction == "acsc" ; arccosecant
		z = asin(1/z - trunc(1/z))
	elseif @trigfunction == "aver" ; arcversine
		z = acos(1 - z - trunc(1-z))
	elseif @trigfunction == "avcs" ; arcvercosine
		z = acos(1 + z - trunc(1+z))
	elseif @trigfunction == "acvs" ; arccoversine
		z = asin(1 - z - trunc(1-z))
	elseif @trigfunction == "acvc" ; arccovercosine
		z = asin(1 + z - trunc(1+z))
	elseif @trigfunction == "aexs" ; arcexsecant
		z = acos( (1/(z+1)) - trunc( (1/(z+1)) ) )
	elseif @trigfunction == "aexc" ; arcexcosecant
		z = asin( (1/(z+1)) - trunc( (1/(z+1)) ) )
	elseif @trigfunction == "acrd" ; arcchord
		z = 2 * asin( z/2 - trunc(z/2) )
	endif ; @trigfunction

	z = @multiplier * log( abs(z))^@power + @offset
endwhile ; itercount

#z = adjustment * z

bailout:
  |z| < @bail

default:
  title = "Iterated Trig Functions"
  center = (0,0)
  maxiter = 1000
  method = multipass
  periodicity = 0

param trigfunction
	caption = "Trig Function"
	enum = "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd"
	default = 0
	hint = "This parameter chooses which function to iterate."
endparam
param zperturb
	caption = "Z Perturbation"
	default = (0,0)
	hint = "The parameter modifies #z during the arcsine iterations."
endparam
func pixfunction
	caption = "Pixel Function"
	default = ident()
	hint = "This function modifies the #pixel value before iterations begin."
endfunc
func Zfunction
	caption = "Z Function"
	default = ident()
	hint = "This function modifies #z during the arcsine iterations."
endfunc
param multiplier
	caption = "Multiplier"
	default = (1,0)
	hint = "Each iteration of arcsine(#z) is multiplied by this value."
endparam
param offset
	caption = "Offset"
	default	=	(-1,0)
	hint = "This value is added to the arcsine result each iteration."
endparam
param power
	caption	=	"Exponent"
	default	=	(1,0)
	hint = "The arcsine result is raised to this power each iteration."
endparam
param iterations
	caption	= "Iterations"
	default = 2
	min = 1
	hint = "This parameter determines how many times the arcsine function \
		is executed."
endparam
param adjust
	caption	=	"Adjustment"
	default	=	102.0
	hint = "This value scales #z after the arcsine iterations."
endparam
param bail
    caption = "Bailout Value"
    default = 4.0
    hint = "Value needed to 'escape' to infinity"
  endparam
}

jam-BernoulliPolynomials {

; Bernoulli polynomials
; Mathematica:  Table[BernoulliB[n, z], {n, 0, 20}]
; jam 7/27/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = sqr(#z) - #z + 1/6
elseif @variant == "3"
	zpolynom = #z^3 - 1.5 * #z^2 + 0.5 * #z
elseif @variant == "4"
	zpolynom = #z^4 - 2 * #z^3 + sqr(#z) - 1/30
elseif @variant == "5"
	zpolynom = #z^5 - 2.5 * #z^4 + (5/3) * #z^3 - #z/6
elseif @variant == "6"
	zpolynom = #z^6 - 3 * #z^5 + 2.5 * #z^4 - 0.5 * sqr(#z) + 1/42
elseif @variant == "7"
	zpolynom = #z^7 - 3.5 * #z^6 + 3.5 * #z^5 - (7/6) * #z^3 + #z/6
elseif @variant == "8"
	zpolynom = #z^8 - 4 * #z^7 + (14/3) * #z^6 - (7/3) * #z^4 + (2/3) * sqr(#z) - \
		1/30
elseif @variant == "9"
	zpolynom = #z^9 - 4.5 * #z^8 + 6 * #z^7 - 4.2 * #z^5 + 2 * #z^3 - 0.3 \
		* #z
elseif @variant == "10"
	zpolynom = #z^10 - 5 * #z^9 + 7.5 * #z^8 - 7 * #z^6 + 5 * #z^4 - 1.5 * sqr(#z) \
		+ 5/66
elseif @variant == "11"
	zpolynom = #z^11 - 5.5 * #z^10 + (55/6) * #z^9 - 11 * #z^7 + 11 * #z^5 - 5.5 * \
		#z^3 + (5/6) * #z
elseif @variant == "12"
	zpolynom = #z^12 - 6 * #z^11 + 11 * #z^10 - 16.5 * #z^8 + 22 * #z^6 - 16.5 * \
		#z^4 + 5 * sqr(#z) - 691/2730
elseif @variant == "13"
	zpolynom = #z^13 - 6.5 * #z^12 + 13 * #z^11 - (143/6) * #z^9 + 286/7 * #z^7 - \
		42.9 * #z^5 + 65/3 * #z^3 - 691/210
elseif @variant == "14"
	zpolynom = #z^14 - 7 * #z^13 + 91/6 * #z^12 - 1001/30 * #z^10 + 71.5 * #z^8 \
	- 100.1 * #z^6 + (455/6) * #z^4 - 691/30 * sqr(#z) + 7/6
elseif @variant == "15"
	zpolynom = #z^15 - 7.5 * #z^14 + 17.5 * #z^13 - 45.5 * #z^11 + 715/6 * #z^9 \
		- 214.5 * #z^7 + 227.5 * #z^5 - 691/6 * #z^3 + 17.5 * #z
elseif @variant == "16"
	zpolynom = #z^16 - 8 * #z^15 + 20 * #z^14 - 182/3 * #z^12 + 572/3 * #z^10 \
		- 429 * #z^8 + (1820/3) * #z^6 - 1382/3 * #z^4 + 140 * sqr(#z) - 3617/510
elseif @variant == "17"
	zpolynom = #z^17 - 8.5 * #z^16 + 68/3 * #z^15 - 238/3 * #z^13 + 884/3 * #z^11 \
		- 2431/3 * #z^9 + (4420/3) * #z^7 - 23494/15 * #z^5 + 2380/3 * #z^3 - \
		3617/30 * #z
elseif @variant == "18"
	zpolynom = #z^18 - 9 * #z^17 + 25.5 * #z^16 - 102 * #z^14 + 442 * #z^12 - 1458.6 \
		* #z^10 + 3315 * #z^8 - 4698.8 * #z^6 + 3570 * #z^4 - 1085.1 \
		* sqr(#z) + 43867/798
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Bernoulli"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-BesselPolynomials {

; Bessel polynomials
; Mathematica:  y[n_, z_] := Sqrt[2/(Pi*z)]*E^(1/z)*BesselK[-n - 1/2, 1/z]; 
;				Table[ y[n, z], {n, 0, 18}]
; jam 7/28/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = 1 + 3 * #z + 3 * sqr(#z)
elseif @variant == "3"
	zpolynom = 1 + 6 * #z + 15 * sqr(#z) + 15 * #z^3
elseif @variant == "4"
	zpolynom = 1 + 10 * #z + 45 * sqr(#z) + 105 * #z^3 + 105 * #z^4
elseif @variant == "5"
	zpolynom = 1 + 15 * #z + 105 * sqr(#z) + 420 * #z^3 + 945 * #z^4 + 945 * #z^5
elseif @variant == "6"
	zpolynom = 1 + 21 * #z + 210 * sqr(#z) + 1260 * #z^3 + 4725 * #z^4 + 10395 * \
		#z^5 + 10395 * #z^6
elseif @variant == "7"
	zpolynom = 1 + 28 * #z + 378 * sqr(#z) + 3150 * #z^3 + 17325 * #z^4 + 62370 * \
		#z^5 + 135135 * #z^6 +135135 * #z^7
elseif @variant == "8"
	zpolynom = 1 + 36 * #z + 630 * sqr(#z) + 6930 * #z^3 + 51975 * #z^4 + 270270 \
		* #z^5 + 945945 * #z^6 + 2027025 * #z^7 + 2027025 * #z^8
elseif @variant == "9"
	zpolynom = 1 + 45 * #z + 990 * sqr(#z) + 13860 * #z^3 + 135135 * #z^4 + \
		945945 * #z^5 + 4729725 * #z^6 + 16216200 * #z^7 + 34459425 * #z^8 + \
		34459425 * #z^9
elseif @variant == "10"
	zpolynom = 1 + 55 * #z + 1485 * sqr(#z) + 25740 * #z^3 + 315315 * #z^4 + \
		2837835 * #z^5 + 18918900 * #z^6 + 91891800 * #z^7 + 310134825 * #z^8 + \
		654729075 * #z^9 + 654729075 * #z^10
elseif @variant == "11"
	zpolynom = 1 + 66 * #z + 2145 * sqr(#z) + 45045 * #z^3 + 675675 * #z^4 + \
		7567560 * #z^5 + 64324260 * #z^6 + 413513100 * #z^7 + 1964187225 * \
			#z^8 + 6.547290750e9 * #z^9 + 13.749310575e9 * #z^10 + 13.749310575e9 \
			* #z^11
elseif @variant == "12"
	zpolynom = 1 + 78 * #z + 3003 * sqr(#z) + 75075 * #z^3 + 1351350 * #z^4 + \
		18378360 * #z^5 + 192972780 * #z^6 + 1571349780 * #z^7 + 9.820936125e9 * \
		#z^8 + 45.831035250e9 * #z^9 + 151.242416325e9 * #z^10 + 316.234143225e9 \
		* #z^11 + 316.234143225e9 * #z^12
elseif @variant == "13"
	zpolynom = 1 + 91 * #z + 4095 * sqr(#z) + 120120 * #z^3 + 2552550 * #z^4 + \
		41351310 * #z^5 + 523783260 * #z^6 + 5.237832600e9 * #z^7 + 41.247931725e9 \
		* #z^8 + 252.070693875e9 * #z^9 + 1.159525191825e12 * #z^10 + \
		3.794809718700e12 * #z^11 + 7.905853580625e12 * #z^12 + 7.905853580625e12 \
		* #z^13
elseif @variant == "14"
	zpolynom = 1 + 105 * #z + 5460 * sqr(#z) + 185640 * #z^3 + 4594590 * #z^4 + \
		87297210 * #z^5 + 1309458150 * #z^6 + 15.713497800e9 * #z^7 + 151.242416325e9 \
		* #z^8 + 1.159525191825e12 * #z^9 + 6.957151150950e12 * #z^10 + \
		31.623414322500e12 * #z^11 + 102.776096548125e12 * #z^12 + 213.458046676875e12 \
		* #z^13 + 213.458046676875e12 * #z^14
elseif @variant == "15"
	zpolynom = 1 + 120 * #z + 7140 * sqr(#z) + 278460 * #z^3 + 7936110 * #z^4 + \
		174594420 * #z^5 + 3.055402350e9 * #z^6 + 43.212118950e9 * #z^7 + 496.939367925e9 \
		* #z^8 + 4.638100767300e12 * #z^9 + 34.785755754750e12 * #z^10 + \
		205.552193096250e12 * #z^11 + 924.984868933125e12 * #z^12 + 2.988412653476250e15 \
		* #z^13 + 6.190283353629375e15 * #z^14 + 6.190283353629375e15 * #z^15
elseif @variant == "16"
	zpolynom = 1 + 136 * #z + 9180 * sqr(#z) + 406980 * #z^3 + 13226850 * #z^4 + \
		333316620 * #z^5 + 6.721885170e9 * #z^6 + 110.430970650e9 * #z^7 + \
		1.490818103775e12 * #z^8 + 16.564645597500e12 * #z^9 + 150.738274937250e12 \
		* #z^10 + 1.109981842719750e15 * #z^11 + 6.474894082531875e15 * #z^12 + \
		28.887988983603750e15 * #z^13 + 92.854250304440625e15 * #z^14 + \
		191.898783962510625e15 * #z^15 + 191.898783962510625e15 * #z^16
elseif @variant == "17"
	zpolynom = 1 + 153 * #z + 11628 * sqr(#z) + 581400 * #z^3 + 21366450 * #z^4 \
		+ 611080470 * #z^5 + 14.054850810e9 * #z^6 + 265.034329560e9 * #z^7 + \
		4.141161399375e12 * #z^8 + 53.835098191875e12 * #z^9 + 581.419060472250e12 \
		* #z^10 + 5.179915266025500e15 * #z^11 + 37.554385678684875e15 * \
		#z^12 + 216.659917377028125e15 * #z^13 + 959.493919812553125e15 * \
		#z^14 + 3.070380543400170000e18 * #z^15 + 6.332659870762850625e18 \
		* #z^16 + 6.332659870762850625e18 * #z^17
elseif @variant == "18"
	zpolynom = 1 + 171 * #z + 14535 * sqr(#z) + 813960 * #z^3 + 33575850 * \
		#z^4 + 1081142370 * #z^5 + 28.109701620e9 * #z^6 + 602.350749000e9 * #z^7 + \
		10.767019638375e12 * #z^8 + 161.505294575625e12 * #z^9 + \
		2.034966711652875e15 * #z^10 + 21.459648959248500e15 * #z^11 + \
		187.771928393424375e15 * #z^12 + 1.343291487737574375e18 * #z^13 + \
		7.675951358500425000e18 * #z^14 + 33.774185977401870000e18 * #z^15 + \
		107.655217802968460625e18 * #z^16 + 221.643095476699771875e18 * #z^17 + \
		221.643095476699771875e18 * #z^18
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Bessel"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-FibonacciPolynomials {

; Fibonacci polynomials
; Mathematica:  P[z, 1] = 1; P[z, 2] = z; 
;				P[z_, n_] := z* P[z, n - 1] + P[z, n - 2];
;				Table[ExpandAll[P[z, n]], {n, 1, 19}]
; jam 7/29/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = sqr(#z) + 1
elseif @variant == "3"
	zpolynom = 2 * #z + #z^3
elseif @variant == "4"
	zpolynom = 1 + 3 * #z^2 + #z^4
elseif @variant == "5"
	zpolynom = 3 * z + 4 * #z^3 + #z^5
elseif @variant == "6"
	zpolynom = 1 + 6 * #z^2 + 5 * #z^4 + #z^6
elseif @variant == "7"
	zpolynom = 4 * #z + 10 * #z^3 + 6 * #z^5 + #z^7
elseif @variant == "8"
	zpolynom = 1 + 10 * #z^2 + 15 * #z^4 + 7 * #z^6 + #z^8
elseif @variant == "9"
	zpolynom = 5 * #z + 20 * #z^3 + 21 * #z^5 + 8 * #z^7 + #z^9
elseif @variant == "10"
	zpolynom = 1 + 15 * #z^2 + 35 * #z^4 + 28 * #z^6 + 9 * #z^8 + #z^10
elseif @variant == "11"
	zpolynom = 6 * #z + 35 * #z^3 + 56 * #z^5 + 36 * #z^7 + 10 * #z^9 + \
		#z^11
elseif @variant == "12"
	zpolynom = 1 + 21 * #z^2 + 70 * #z^4 + 84 * #z^6 + 45 * #z^8 + 11 * \
		#z^10 + #z^12
elseif @variant == "13"
	zpolynom = 7 * #z + 56 * #z^3 + 126 * #z^5 + 120 * #z^7 + 55 * #z^9 + \
		12 * #z^11 + #z^13
elseif @variant == "14"
	zpolynom = 1 + 28 * #z^2 + 126 * #z^4 + 210 * #z^6 + 165 * #z^8 + 66 * \
		#z^10 + 13 * #z^12 + #z^14
elseif @variant == "15"
	zpolynom = 8 * #z + 84 * #z^3 + 252 * #z^5 + 330 * #z^7 + 220 * #z^9 + \
		78 * #z^11 + 14 * #z^13 + #z^15
elseif @variant == "16"
	zpolynom = 1 + 36 * #z^2 + 210 * #z^4 + 462 * #z^6 + 495 * #z^8 + 286 * \
		#z^10 + 91 * #z^12 + 15 * #z^14 + #z^16
elseif @variant == "17"
	zpolynom = 9 * #z + 120 * #z^3 + 462 * #z^5 + 792 * #z^7 + 715 * #z^9 + \
		364 * #z^11 + 105 * #z^13 + 16 * #z^15 + #z^17
elseif @variant == "18"
	zpolynom = 1 + 45 * #z^2 + 330 * #z^4 + 924 * #z^6 + 1287 * #z^8 + 1001 * \
		#z^10 + 455 * #z^12 + 120 * #z^14 + 17 * #z^16 + #z^18
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Fibonacci"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-TetranacciPolynomials {

; Tetranacci polynomials
; Mathematica:  P[z, 0] = 0; P[z, 1] = 0; P[z, 2] = 1; P[z, 3] = z^3;
;				P[z_, n_] := z^3* P[z, n - 1] + z^2*P[z, n - 2] + z*P[z, n - 3] + P[z, n - 4];
;				Table[ExpandAll[P[z, n], z], {n, 1, 22}]
; jam 7/30/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = #z^3
elseif @variant == "3"
	zpolynom = #z^2 + #z^6
elseif @variant == "4"
	zpolynom = #z + 2 * #z^5 + #z^9
elseif @variant == "5"
	zpolynom = 1 + 3 * #z^4 + 3 * #z^8 + #z^12
elseif @variant == "6"
	zpolynom = 4 * #z^3 + 6 * #z^7 + 4 * #z^11 + #z^15
elseif @variant == "7"
	zpolynom = 3 * #z^2 + 10 * #z^6 + 10 * #z^10 + 5 * #z^14 + #z^18
elseif @variant == "8"
	zpolynom = 2 * #z + 12 * #z^5 + 20 * #z^9 + 15 * #z^13 + 6 * #z^17 + #z^21
elseif @variant == "9"
	zpolynom = 1 + 12 * #z^4 + 31 * #z^8 + 35 * #z^12 + 21 * #z^16 + 7 * #z^20 \
		+ #z^24
elseif @variant == "10"
	zpolynom = 10 * #z^3 + 40 * #z^7 + 65 * #z^11 + 56 * #z^15 + 28 * #z^19 + 8 \
		* #z^23	+ #z^27
elseif @variant == "11"
	zpolynom = 6 * #z^2 + 44 * #z^6 + 101 * #z^10 + 120 * #z^14 + 84 * #z^18 + 36 \
		* #z^22 + 9 * #z^26 + #z^30
elseif @variant == "12"
	zpolynom = 3 * #z + 40 * #z^5 + 135 * #z^9 + 216 * #z^13 + 203 * #z^17 + 120 \
		* #z^21 + 45 * #z^25 + 10 * #z^29 + #z^33
elseif @variant == "13"
	zpolynom = 1 + 31 * #z^4 + 155 * #z^8 + 336 * #z^12 + 413 * #z^16 + 322 * \
		#z^20 + 165 * #z^24 + 55 * #z^28 + 11 * #z^32 + #z^36
elseif @variant == "14"
	zpolynom = 20 * #z^3 + 155 * #z^7 + 456 * #z^11 + 728 * #z^15 + 728 * #z^19 + \
		486 * #z^23 + 220 * #z^27 + 66 * #z^31 + 12 * #z^35 + #z^39
elseif @variant == "15"
	zpolynom = 10 * #z^2 + 135 * #z^6 + 546 * #z^10 + 1128 * #z^14 + 1428 * \
		#z^18 + 1206 * #z^22 + 705 * #z^26 + 286 * #z^30 + 78 * #z^34 + 13 * \
		#z^38 + #z^42
elseif @variant == "16"
	zpolynom = 4 * #z + 101 * #z^5 + 580 * #z^9 + 1554 * #z^13 + 2472 * #z^17 \
		+ 2598 * #z^21 + 1902 * #z^25 + 990 * #z^29 + 364 * #z^33 + 91 * #z^37 \
		+ 14 * #z^41 + #z^45
elseif @variant == "17"
	zpolynom = 1 + 65 * #z^4 + 546 * #z^8 + 1918 * #z^12 + 3823 * #z^16 + 4950 \
		* #z^20 + 4455 * #z^24 + 2882 * #z^28 + 1353 * #z^32 + 455 * #z^36 + \
		105 * #z^40 + 15 * #z^44 + #z^48
elseif @variant == "18"
	zpolynom = 35 * #z^3 + 456 * #z^7 + 2128 * #z^11 + 5328 * #z^15 + 8451 * \
		#z^19 + 9240 * #z^23 + 7282 * #z^27 + 4224 * #z^31 + 1807 * #z^35 + 560 \
		* #z^39 + 120 * #z^43 + 16 * #z^47 + #z^51
elseif @variant == "19"
	zpolynom = 15 * #z^2 + 336 * #z^6 + 2128 * #z^10 + 6728 * #z^14 + 13051 * \
		#z^18 + 17205 * #z^22 + 16302 * #z^26 + 11440 * #z^30 + 6019 * #z^34 + \
		2366 * #z^38 + 680 * #z^42 + 136 * #z^46 + 17 * #z^50 + #z^54
elseif @variant == "20"
	zpolynom = 5 * #z + 216 * #z^5 + 1918 * #z^9 + 7728 * #z^13 + 18351 * #z^17 \
		+ 29050 * #z^21 + 32802 * #z^25 + 27456 * #z^29 + 17381 * #z^33 + 8372 * \
		#z^37 + 3045 * #z^41 + 816 * #z^45 + 153 * #z^49 + 18 * #z^53 + #z^57
elseif @variant == "21"
	zpolynom = 1 + 120 * #z^4 + 1554 * #z^8 + 8092 * #z^12 + 23607 * #z^16 + \
		44803 * #z^20 + 59950 * #z^24 + 59268 * #z^28 + 44473 * #z^32 + 25662 * \
		#z^36 + 11403 * #z^40 + 3860 * #z^44 + 969 * #z^48 + 171 * #z^52 + 19 * \
		#z^56 + #z^60
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Tetranacci"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20" "21"
	default = 6
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-GeneralPolynomials {

; General polynomial formula.  Most of the other polynomial formulas in this folder, as
; well as many new ones, can be implemented here.
; jam 7/31/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == 2
	zpolynom = @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 3
	zpolynom = @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 4
	zpolynom = @coeff4 * #z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + \
		@coeff1
elseif @variant == 5
	zpolynom = @coeff5 * #z^@exp5 + @coeff4 * #z^@exp4 + @coeff3 * #z^@exp3 + \
		@coeff2 * #z^@exp2 + @coeff1
elseif @variant == 6
	zpolynom = @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * #z^@exp4 + \
		@coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 7
	zpolynom = @coeff7 * #z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + \
		@coeff4 * #z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 8
	zpolynom = @coeff8 * #z^@exp8 + @coeff7 * #z^@exp7 + @coeff6 * #z^@exp6 + \
		@coeff5 * #z^@exp5 + @coeff4 * #z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 \
		* #z^@exp2 + @coeff1
elseif @variant == 9
	zpolynom = @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * #z^@exp7 + \
		@coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * #z^@exp4 + @coeff3 \
		* #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 10
	zpolynom = @coeff10 * #z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + \
		@coeff7 * #z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 \
		* #z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 11
	zpolynom = @coeff11 * #z^@exp11 + @coeff10 * #z^@exp10 + @coeff9 * #z^@exp9 \
		+ @coeff8 * #z^@exp8 + @coeff7 * #z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 \
		* #z^@exp5 + @coeff4 * #z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * \
		#z^@exp2 + @coeff1
elseif @variant == 12
	zpolynom = @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * \
		#z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 13
	zpolynom = @coeff13 * #z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * \
		#z^@exp11 + @coeff10 * #z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * \
		#z^@exp8 + @coeff7 * #z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * \
		#z^@exp5 + @coeff4 * #z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * \
		#z^@exp2 + @coeff1
elseif @variant == 14
	zpolynom = @coeff14 * #z^@exp14 + @coeff13 * #z^@exp13 + @coeff12 * \
		#z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * #z^@exp10 + @coeff9 \
		* #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * #z^@exp7 + @coeff6 * \
		#z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * #z^@exp4 + @coeff3 * \
		#z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 15
	zpolynom = @coeff15 * #z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * \
		#z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 \
		* #z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 16
	zpolynom = @coeff16 * #z^@exp16 + @coeff15 * #z^@exp15 + @coeff14 * \
		#z^@exp14 + @coeff13 * #z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 \
		* #z^@exp11 + @coeff10 * #z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * \
		#z^@exp8 + @coeff7 * #z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * \
		#z^@exp5 + @coeff4 * #z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * \
		#z^@exp2 + @coeff1
elseif @variant == 17
	zpolynom = @coeff17 * #z^@exp17 + @coeff16 * #z^@exp16 + @coeff15 * \
		#z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * #z^@exp13 + @coeff12 * \
		#z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * #z^@exp10 + @coeff9 * \
		#z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * #z^@exp7 + @coeff6 * \
		#z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * #z^@exp4 + @coeff3 * \
		#z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 18
	zpolynom = @coeff18 * #z^@exp18 + @coeff17 * #z^@exp17 + @coeff16 * \
		#z^@exp16 + @coeff15 * #z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * \
		#z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * \
		#z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 19
	zpolynom = @coeff19 * #z^@exp19 + \
		@coeff18 * #z^@exp18 + @coeff17 * #z^@exp17 + @coeff16 * \
		#z^@exp16 + @coeff15 * #z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * \
		#z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * \
		#z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 20
	zpolynom = @coeff20 * #z^@exp20 + @coeff19 * #z^@exp19 + \
		@coeff18 * #z^@exp18 + @coeff17 * #z^@exp17 + @coeff16 * \
		#z^@exp16 + @coeff15 * #z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * \
		#z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * \
		#z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 21
	zpolynom = @coeff21 * #z^@exp21 + @coeff20 * #z^@exp20 + @coeff19 * #z^@exp19 + \
		@coeff18 * #z^@exp18 + @coeff17 * #z^@exp17 + @coeff16 * \
		#z^@exp16 + @coeff15 * #z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * \
		#z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * \
		#z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 22
	zpolynom = @coeff22 * #z^@exp22 + \
		@coeff21 * #z^@exp21 + @coeff20 * #z^@exp20 + @coeff19 * #z^@exp19 + \
		@coeff18 * #z^@exp18 + @coeff17 * #z^@exp17 + @coeff16 * \
		#z^@exp16 + @coeff15 * #z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * \
		#z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * \
		#z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 23
	zpolynom = @coeff23 * #z^@exp23 + @coeff22 * #z^@exp22 + \
		@coeff21 * #z^@exp21 + @coeff20 * #z^@exp20 + @coeff19 * #z^@exp19 + \
		@coeff18 * #z^@exp18 + @coeff17 * #z^@exp17 + @coeff16 * \
		#z^@exp16 + @coeff15 * #z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * \
		#z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * \
		#z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
elseif @variant == 24
	zpolynom = @coeff24 * #z^@exp24 + @coeff23 * #z^@exp23 + @coeff22 * #z^@exp22 + \
		@coeff21 * #z^@exp21 + @coeff20 * #z^@exp20 + @coeff19 * #z^@exp19 + \
		@coeff18 * #z^@exp18 + @coeff17 * #z^@exp17 + @coeff16 * \
		#z^@exp16 + @coeff15 * #z^@exp15 + @coeff14 * #z^@exp14 + @coeff13 * \
		#z^@exp13 + @coeff12 * #z^@exp12 + @coeff11 * #z^@exp11 + @coeff10 * \
		#z^@exp10 + @coeff9 * #z^@exp9 + @coeff8 * #z^@exp8 + @coeff7 * \
		#z^@exp7 + @coeff6 * #z^@exp6 + @coeff5 * #z^@exp5 + @coeff4 * \
		#z^@exp4 + @coeff3 * #z^@exp3 + @coeff2 * #z^@exp2 + @coeff1
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials General"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Terms"
	default = 3
	min = 2
	max = 24
	hint = "This setting selects how many terms the iterated polynomial \
		contains.  One term is always a constant term.  (2-24)"
endparam
param coeff1
	caption = "Polynom Constant Term"
	default = (0,0)
	hint = "This parameter is the final term of the iterated polynomial."
endparam
param coeff2
	caption = "2nd Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 2nd term of the iterated \
		polynomial."
endparam
param exp2
	caption = "2nd Term Power"
	default = (3,0)
	hint = "This parameter is the exponent of the 2nd term of the iterated \
		polynomial."
endparam
param coeff3
	caption = "3rd Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 3rd term of the iterated \
		polynomial."
	visible = @variant > 2
endparam
param exp3
	caption = "3rd Term Power"
	default = (6,0)
	hint = "This parameter is the exponent of the 3rd term of the iterated \
		polynomial."
	visible = @variant > 2
endparam
param coeff4
	caption = "4th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 4th term of the iterated \
		polynomial."
	visible = @variant > 3
endparam
param exp4
	caption = "4th Term Power"
	default = (7,0)
	hint = "This parameter is the exponent of the 4th term of the iterated \
		polynomial."
	visible = @variant > 3
endparam
param coeff5
	caption = "5th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 5th term of the iterated \
		polynomial."
	visible = @variant > 4
endparam
param exp5
	caption = "5th Term Power"
	default = (8,0)
	hint = "This parameter is the exponent of the 5th term of the iterated \
		polynomial."
	visible = @variant > 4
endparam
param coeff6
	caption = "6th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 6th term of the iterated \
		polynomial."
	visible = @variant > 5
endparam
param exp6
	caption = "6th Term Power"
	default = (9,0)
	hint = "This parameter is the exponent of the 6th term of the iterated \
		polynomial."
	visible = @variant > 5
endparam
param coeff7
	caption = "7th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 7th term of the iterated \
		polynomial."
	visible = @variant > 6
endparam
param exp7
	caption = "7th Term Power"
	default = (10,0)
	hint = "This parameter is the exponent of the 7th term of the iterated \
		polynomial."
	visible = @variant > 6
endparam
param coeff8
	caption = "8th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 8th term of the iterated \
		polynomial."
	visible = @variant > 7
endparam
param exp8
	caption = "8th Term Power"
	default = (11,0)
	hint = "This parameter is the exponent of the 8th term of the iterated \
		polynomial."
	visible = @variant > 7
endparam
param coeff9
	caption = "9th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 9th term of the iterated \
		polynomial."
	visible = @variant > 8
endparam
param exp9
	caption = "9th Term Power"
	default = (12,0)
	hint = "This parameter is the exponent of the 9th term of the iterated \
		polynomial."
	visible = @variant > 8
endparam
param coeff10
	caption = "10th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 10th term of the iterated \
		polynomial."
	visible = @variant > 9
endparam
param exp10
	caption = "10th Term Power"
	default = (13,0)
	hint = "This parameter is the exponent of the 10th term of the iterated \
		polynomial."
	visible = @variant > 9
endparam
param coeff11
	caption = "11th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 11th term of the iterated \
		polynomial."
	visible = @variant > 10
endparam
param exp11
	caption = "11th Term Power"
	default = (14,0)
	hint = "This parameter is the exponent of the 11th term of the iterated \
		polynomial."
	visible = @variant > 10
endparam
param coeff12
	caption = "12th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 12th term of the iterated \
		polynomial."
	visible = @variant > 11
endparam
param exp12
	caption = "12th Term Power"
	default = (15,0)
	hint = "This parameter is the exponent of the 12th term of the iterated \
		polynomial."
	visible = @variant > 11
endparam
param coeff13
	caption = "13th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 13th term of the iterated \
		polynomial."
	visible = @variant > 12
endparam
param exp13
	caption = "13th Term Power"
	default = (16,0)
	hint = "This parameter is the exponent of the 13th term of the iterated \
		polynomial."
	visible = @variant > 12
endparam
param coeff14
	caption = "14th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 14th term of the iterated \
		polynomial."
	visible = @variant > 13
endparam
param exp14
	caption = "14th Term Power"
	default = (17,0)
	hint = "This parameter is the exponent of the 14th term of the iterated \
		polynomial."
	visible = @variant > 13
endparam
param coeff15
	caption = "15th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 15th term of the iterated \
		polynomial."
	visible = @variant > 14
endparam
param exp15
	caption = "15th Term Power"
	default = (18,0)
	hint = "This parameter is the exponent of the 15th term of the iterated \
		polynomial."
	visible = @variant > 14
endparam
param coeff16
	caption = "16th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 16th term of the iterated \
		polynomial."
	visible = @variant > 15
endparam
param exp16
	caption = "16th Term Power"
	default = (19,0)
	hint = "This parameter is the exponent of the 16th term of the iterated \
		polynomial."
	visible = @variant > 15
endparam
param coeff17
	caption = "17th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 17th term of the iterated \
		polynomial."
	visible = @variant > 16
endparam
param exp17
	caption = "17th Term Power"
	default = (20,0)
	hint = "This parameter is the exponent of the 17th term of the iterated \
		polynomial."
	visible = @variant > 16
endparam
param coeff18
	caption = "18th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 18th term of the iterated \
		polynomial."
	visible = @variant > 17
endparam
param exp18
	caption = "18th Term Power"
	default = (21,0)
	hint = "This parameter is the exponent of the 18th term of the iterated \
		polynomial."
	visible = @variant > 17
endparam
param coeff19
	caption = "19th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 19th term of the iterated \
		polynomial."
	visible = @variant > 18
endparam
param exp19
	caption = "19th Term Power"
	default = (20,0)
	hint = "This parameter is the exponent of the 19th term of the iterated \
		polynomial."
	visible = @variant > 18
endparam
param coeff20
	caption = "20th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 20th term of the iterated \
		polynomial."
	visible = @variant > 19
endparam
param exp20
	caption = "20th Term Power"
	default = (20,0)
	hint = "This parameter is the exponent of the 20th term of the iterated \
		polynomial."
	visible = @variant > 19
endparam
param coeff21
	caption = "21th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 21th term of the iterated \
		polynomial."
	visible = @variant > 20
endparam
param exp21
	caption = "21th Term Power"
	default = (20,0)
	hint = "This parameter is the exponent of the 21th term of the iterated \
		polynomial."
	visible = @variant > 20
endparam
param coeff22
	caption = "22th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 22th term of the iterated \
		polynomial."
	visible = @variant > 21
endparam
param exp22
	caption = "22th Term Power"
	default = (20,0)
	hint = "This parameter is the exponent of the 22th term of the iterated \
		polynomial."
	visible = @variant > 21
endparam
param coeff23
	caption = "23th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 23th term of the iterated \
		polynomial."
	visible = @variant > 22
endparam
param exp23
	caption = "23th Term Power"
	default = (20,0)
	hint = "This parameter is the exponent of the 23th term of the iterated \
		polynomial."
	visible = @variant > 22
endparam
param coeff24
	caption = "24th Term Coefficient"
	default = (1,0)
	hint = "This constant is multiplies by the 24th term of the iterated \
		polynomial."
	visible = @variant > 23
endparam
param exp24
	caption = "24th Term Power"
	default = (20,0)
	hint = "This parameter is the exponent of the 24th term of the iterated \
		polynomial."
	visible = @variant > 23
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-polyiteratedfunctions {

; Miscellaneous functions and series
; jam 7/27/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

; declare and precompute factorials and reciprocal factorials
; used in someseries-defined functions
	float fac2 = float fac3 = float fac14 = float fac5 = 0.0
	float fac6 = float fac7 = float fac8 = float fac9 = float fac10 = 0.0
	float fac11 = float fac12 = float fac13 = float fac14 = float fac15 = 0.0
	float fac16 = float fac17 = float fac18 = float fac19 = float fac20 = 0.0
	float fac21 = float fac22 = float fac23 = float fac24 = float fac25 = 0.0
	float fac26 = float fac27 = float fac28 = float fac29 = float fac30 = 0.0
	
if (@variant == "cos3") || (@variant == "sin3A") || (@variant == "sin3B")
	fac2 = 2, fac3 = 6, fac4 = 24, fac5 = 120, fac6 = 720
	fac7 = 5040, fac8 = 40320, fac9 = 362880, fac10 = fac9*10
	fac11 = fac10*11, fac12 = fac11*12, fac13 = fac12*13
	fac14 = fac13*14, fac15 = fac14*15, fac16 = fac15*16
	fac17 = fac16*17, fac18 = fac17*18, fac18 = fac17*18
	fac19 = fac18*19, fac20 = fac19*20, fac21 = fac20*21
	fac22 = fac21*22, fac23 = fac22*23, fac24 = fac23*24
	fac25 = fac24*25, fac26 = fac25*26, fac27 = fac26*27
	fac28 = fac27*28, fac29 = fac28*29, fac30 = fac29*30
	
	fac2 = 1/fac2, fac3 = 1/fac3, fac4 = 1/fac4
	fac5 = 1/fac5, fac6 = 1/fac6, fac7 = 1/fac7
	fac8 = 1/fac8, fac9 = 1/fac9, fac10 = 1/fac10
	fac11 = 1/fac11, fac12 = 1/fac12, fac13 = 1/fac13
	fac14 = 1/fac14, fac15 = 1/fac15, fac16 = 1/fac16
	fac17 = 1/fac17, fac18 = 1/fac18, fac19 = 1/fac19
	fac20 = 1/fac20, fac21 = 1/fac21, fac22 = 1/fac22
	fac23 = 1/fac23, fac24 = 1/fac24, fac25 = 1/fac25
	fac26 = 1/fac26, fac27 = 1/fac27, fac28 = 1/fac28
	fac29 = 1/fac29, fac30 = 1/fac30
endif ; @variant

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "sin" ; sine function
	zpolynom = sin(#z)
elseif @variant == "cos" ; cosine
	zpolynom = cos(#z)
elseif @variant == "tan" ; tangent
	zpolynom = tan(#z)
elseif @variant == "cot" ; cotangent
	zpolynom = cotan(#z)
elseif @variant == "sec" ; secant
	zpolynom = 1/cos(#z)
elseif @variant == "csc" ; cosecant
	zpolynom = 1/sin(#z)
elseif @variant == "ver" ; versine
	zpolynom = 1 - cos(#z)
elseif @variant == "vcs" ; vercosine
	zpolynom = 1 + cos(#z)
elseif @variant == "cvs" ; coversine
	zpolynom = 1 - sin(#z)
elseif @variant == "cvc" ; covercosine
	zpolynom = 1 + sin(#z)
elseif @variant == "exs" ; exsecant
	zpolynom = 1/cos(#z) - 1
elseif @variant == "exc" ; excosecant
	zpolynom = 1/sin(#z) - 1
elseif @variant == "crd" ; chord function
	zpolynom = 2 * sin(#z/2)
elseif @variant == "asin" ; arcsine
	zpolynom = asin(#z - trunc(#z))
elseif @variant == "acos" ; arccosine
	zpolynom = acos(#z - trunc(#z))
elseif @variant == "atan" ; arctangent
	zpolynom = atan(#z)
elseif @variant == "acot" ; arccotangent
	zpolynom = halfpi - atan(#z)
elseif @variant == "asec" ; arcsecant
	zpolynom = acos(1/#z - trunc(1/#z))
elseif @variant == "acsc" ; arccosecant
	zpolynom = asin(1/#z - trunc(1/#z))
elseif @variant == "aver" ; arcversine
	zpolynom = acos(1 - #z - trunc(1-#z))
elseif @variant == "avcs" ; arcvercosine
	zpolynom = acos(1 + #z - trunc(1+#z))
elseif @variant == "acvs" ; arccoversine
	zpolynom = asin(1 - #z - trunc(1-#z))
elseif @variant == "acvc" ; arccovercosine
	zpolynom = asin(1 + #z - trunc(1+#z))
elseif @variant == "aexs" ; arcexsecant
	zpolynom = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
elseif @variant == "aexc" ; arcexcosecant
	zpolynom = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
elseif @variant == "acrd" ; arcchord
	zpolynom = 2 * asin( #z/2 - trunc(#z/2) )
elseif @variant == "asin 2" ; arcsine
	zpolynom = asin(#z)
elseif @variant == "acos 2" ; arccosine
	zpolynom = acos(#z)
elseif @variant == "atan 2" ; arctangent
	zpolynom = atan2(#z)
elseif @variant == "acot 2" ; arccotangent
	zpolynom = halfpi - atan2(#z)
elseif @variant == "asec 2" ; arcsecant
	zpolynom = acos(1/#z)
elseif @variant == "acsc 2" ; arccosecant
	zpolynom = asin(1/#z)
elseif @variant == "aver 2" ; arcversine
	zpolynom = acos(1 - #z)
elseif @variant == "avcs 2" ; arcvercosine
	zpolynom = acos(1 + #z)
elseif @variant == "acvs 2" ; arccoversine
	zpolynom = asin(1 - #z)
elseif @variant == "acvc 2" ; arccovercosine
	zpolynom = asin(1 + #z)
elseif @variant == "aexs 2" ; arcexsecant
	zpolynom = acos( (1/(#z+1)))
elseif @variant == "aexc 2" ; arcexcosecant
	zpolynom = asin( (1/(#z+1)))
elseif @variant == "acrd 2" ; arcchord
	zpolynom = 2 * asin( #z/2 )
elseif @variant == "exp" ; exponential function
	zpolynom = exp(#z)
elseif @variant == "exp(-z)" ; 
	zpolynom = exp(-#z)
elseif @variant == "exp(z^2)" ; 
	zpolynom = exp(sqr(#z))
elseif @variant == "exp(-z^2)" ; 
	zpolynom = exp(-sqr(#z))
elseif @variant == "exp(1/z)" ; 
	zpolynom = exp(1/#z)
elseif @variant == "exp(-1/z)" ; 
	zpolynom = exp(-1/#z)
elseif @variant == "exp(1/z^2)" ; 
	zpolynom = exp(1/sqr(#z))
elseif @variant == "exp(-1/z^2)" ; 
	zpolynom = exp(-1/sqr(#z))
elseif @variant == "cosh" ; hyperbolic cosine
	zpolynom = cosh(#z)
elseif @variant == "sinh" ; hyperbolic sine
	zpolynom = sinh(#z)
elseif @variant == "tanh" ; hyperbolic tangent
	zpolynom = tanh(#z)
elseif @variant == "cotanh" ; hyperbolic cotangent
	zpolynom = cotanh(#z)
elseif @variant == "acosh" ; archyperbolic cosine
	zpolynom = acosh(#z)
elseif @variant == "asinh" ; archyperbolic sine
	zpolynom = asinh(#z)
elseif @variant == "atanh" ; archyperbolic tangent
	zpolynom = atanh(#z)
elseif @variant == "log" ; logarithm
	zpolynom = log(#z)
elseif @variant == "log(-z)" ; 
	zpolynom = log(-#z)
elseif @variant == "log(z^2)" ; 
	zpolynom = log(sqr(#z))
elseif @variant == "log(-z^2)" ; 
	zpolynom = log(-sqr(#z))
elseif @variant == "log(1/z)" ; 
	zpolynom = log(1/#z)
elseif @variant == "log(-1/z)" ; 
	zpolynom = log(-1/#z)
elseif @variant == "log(1/z^2)" ; 
	zpolynom = log(1/sqr(#z))
elseif @variant == "log(-1/z^2)" ; 
	zpolynom = log(-1/sqr(#z))
elseif @variant == "log log" ; 
	zpolynom = log( log(#z) )
elseif @variant == "exp(exp)" ; 
	zpolynom = exp( exp(#z) )
elseif @variant == "z^z" ; 
	zpolynom = #z^#z
elseif @variant == "z^z^z" ; 
	zpolynom = #z^(#z^#z)
elseif @variant == "constant^z" ; 
	zpolynom = @zbase^#z
elseif @variant == "constant^z^z" ; 
	zpolynom = @zbase^(#z^#z)
elseif @variant == "1/z" ; 
	zpolynom = 1/#z
elseif @variant == "cos3" ; 
	zpolynom = 1 - fac3*#z^3 + fac6*#z^6 - fac9*#z^9 + fac12*#z^12 - \
		fac15*#z^15 + fac18*#z^18 - fac21*#z^21 + fac24*#z^24 - \
		fac27*#z^27 + fac30*#z^30
elseif @variant == "sin3A" ; 
	zpolynom = #z - fac4*#z^4 + fac7*#z^7 - fac10*#z^10 + fac13*#z^13 - \
		fac16*#z^16 + fac19*#z^19 - fac22*#z^22 + fac25*#z^25 - \
		fac28*#z^28
elseif @variant == "sin3B" ; 
	zpolynom = fac2*sqr(#z) - fac5*#z^5 + fac8*#z^8 - fac11*#z^11 + fac14*#z^14 - \
		fac17*#z^17 + fac20*#z^20 - fac23*#z^23 + fac26*#z^26 - \
		fac29*#z^29
endif ; @variant

	if @appendbinom
		if @appendcombo == "add"
			zpolynom = zpolynom + (@appendcoeff1 * #z^@appendpower1 + \
				@appendcoeff2 * #z^@appendpower2)
		elseif @appendcombo == "multiply"
			zpolynom = zpolynom * (@appendcoeff1 * #z^@appendpower1 + \
				@appendcoeff2 * #z^@appendpower2)
		elseif @appendcombo == "divide 1"
			zpolynom = zpolynom / (@appendcoeff1 * #z^@appendpower1 + \
				@appendcoeff2 * #z^@appendpower2)
		elseif @appendcombo == "divide 2"
			zpolynom = (@appendcoeff1 * #z^@appendpower1 + \
				@appendcoeff2 * #z^@appendpower2) / zpolynom
		elseif @appendcombo == "power 1"
			zpolynom = zpolynom^(@appendcoeff1 * #z^@appendpower1 + \
				@appendcoeff2 * #z^@appendpower2)
		elseif @appendcombo == "power 2"
			zpolynom = (@appendcoeff1 * #z^@appendpower1 + \
				@appendcoeff2 * #z^@appendpower2)^zpolynom
		endif ; @appendcombo
	endif ; @appendbinom

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "PolyIterated Functions"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Function Variant"
	enum = "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "asin 2" "acos 2" "atan 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" \
		"aexs 2" "aexc 2" "acrd 2" "exp" "exp(-z)" "exp(z^2)" "exp(-z^2)" \
		"exp(1/z)" "exp(-1/z)" "exp(1/z^2)" "exp(-1/z^2)" "cosh"  "sinh" \
		"tanh" "cotanh" "acosh" "asinh" "atanh" "log" "log(-z)" "log(z^2)" \
		"log(-z^2)" "log(1/z)" "log(-1/z)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z" "1/z" "cos3" \
		"sin3A" "sin3B"
	default = 0
	hint = "This setting selects which function equation to iterate."
endparam
param zbase
	caption = "Base Constant"
	default = (2,0)
	hint = "If 'Function Variant' is set to 'constant^z' or 'constant^z^z', \
		then this parameter is the constant."
	visible = (@variant == "constant^z") || (@variant == "constant^z^z")
endparam
param appendbinom
	caption = "Append Z^Power?"
	default = FALSE
	hint = "If enabled, then the 'Function Variant' can be combined with \
		a simple z^power binomial function.  Set parameters '1st-Term Coefficient', \
		'1st-Term Power', '2nd-Term Coefficient', and '2nd-Term Power' to define \
		the z polynomial."
endparam
param appendcoeff1
	caption = "1st-Term Coefficient"
	default = (1,0)
	hint = "This parameter is multiplied by the z^power factor defined in \
		param '1st-Term Power'."
	visible = @appendbinom
endparam
param appendpower1
	caption = "1st-Term Power"
	default = (5,0)
	hint = "This value is the exponent for the 1st #z term of the polynomial."
	visible = @appendbinom
endparam
param appendcoeff2
	caption = "2nd-Term Coefficient"
	default = (1,0)
	hint = "This parameter is multiplied by the z^power factor defined in \
		param '2nd-Term Power'."
	visible = @appendbinom
endparam
param appendpower2
	caption = "2nd-Term Power"
	default = (0,0)
	hint = "This value is the exponent for the 2nd #z term of the polynomial."
	visible = @appendbinom
endparam
param appendcombo
	caption = "Combination Mode"
	enum = "add" "multiply" "divide 1" "divide 2" "power 1" "power 2"
	default = 0
	hint = "This setting determines how the binomial result is conbined \
		with the function result."
	visible = @appendbinom
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Function Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Function Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Function Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-TribonnaciPolynomials {

; Tribonacci polynomials
; Mathematica:  P[z, 0] = 0; P[z, 1] = 1; P[z, 2] = z^2; 
;				P[z_, n_] := z^2 * P[z, n - 1] + z*P[z, n - 2] + P[z, n - 3];
;				Table[ExpandAll[P[z, n]], {n, 1, 19}];
; jam 7/31/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = #z + #z^4
elseif @variant == "3"
	zpolynom = 1 + 2 * #z^3 + #z^6
elseif @variant == "4"
	zpolynom = 3 * #z^2 + 3 * #z^5 + #z^8
elseif @variant == "5"
	zpolynom = 2 * #z + 6 * #z^4 + 4 * #z^7 + #z^10
elseif @variant == "6"
	zpolynom = 1 + 7 * #z^3 + 10 * #z^6 + 5 * #z^9 + #z^12
elseif @variant == "7"
	zpolynom = 6 * #z^2 + 16 * #z^5 + 15 * #z^8 + 6 * #z^11 + #z^14
elseif @variant == "8"
	zpolynom = 3 * #z + 19 * #z^4 + 30 * #z^7 + 21 * #z^10 + 7 * #z^13 + #z^16
elseif @variant == "9"
	zpolynom = 1 + 16 * #z^3 + 45 * #z^6 + 50 * #z^9 + 28 * #z^12 + 8 * #z^15 \
		+ #z^18
elseif @variant == "10"
	zpolynom = 10 * #z^2 + 51 * #z^5 + 90 * #z^8 + 77 * #z^11 + 36 * #z^14 + \
		9 * #z^17 + #z^20
elseif @variant == "11"
	zpolynom = 4 * #z + 45 * #z^4 + 126 * #z^7 + 161 * #z^10 + 112 * #z^13 + \
		45 * #z^16 + 10 * #z^19 + #z^22
elseif @variant == "12"
	zpolynom = 1 + 30 * #z^3 + 141 * #z^6 + 266 * #z^9 + 266 * #z^12 + 156 * \
		#z^15 + 55 * #z^18 + 11 * #z^21 + #z^24
elseif @variant == "13"
	zpolynom = 15 * #z^2 + 126 * #z^5 + 357 * #z^8 + 504 * #z^11 + 414 * \
		#z^14 + 210 * #z^17 + 66 * #z^20 + 12 * #z^23 + #z^26
elseif @variant == "14"
	zpolynom = 5 * #z + 90 * #z^4 + 393 * #z^7 + 784 * #z^10 + 882 * #z^13 + \
		615 * #z^16 + 275 * #z^19 + 78 * #z^22 + 13 * #z^25 + #z^28
elseif @variant == "15"
	zpolynom = 1 + 50 * #z^3 + 357 * #z^6 + 1016 * #z^9 + 1554 * #z^12 + 1452 * \
		#z^15 + 880 * #z^18 + 352 * #z^21 + 91 * #z^24 + 14 * #z^27 + #z^30
elseif @variant == "16"
	zpolynom = 21 * #z^2 + 266 * #z^5 + 1107 * #z^8 + 2304 * #z^11 + 2850 * #z^14 \
		+ 2277 * #z^17 + 1221 * #z^20 + 442 * #z^23 + 105 * #z^26 + 15 * #z^29 + #z^32
elseif @variant == "17"
	zpolynom = 6 * #z + 161 * #z^4 + 1016 * #z^7 + 2907 * #z^10 + 4740 * #z^13 + \
		4917 * #z^16 + 3432 * #z^19 + 1651 * #z^22 + 546 * #z^25 + 120 * #z^28 + \
		16 * #z^31 + #z^34
elseif @variant == "18"
	zpolynom = 1 + 77 * #z^3 + 784 * #z^6 + 3139 * #z^9 + 6765 * #z^12 + 9042 * \
		#z^15 + 8074 * #z^18 + 5005 * #z^21 + 2184 * #z^24 + 665 * #z^27 + 136 * \
		#z^30 + 17 * #z^33 + #z^36
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Tribonacci"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-PentanacciPolynomials {

; Pentanacci polynomials
; Mathematica:  P[z, 0] = 0; P[z, 1] = 0; P[z, 2] = 0; P[z, 3] = 0; P[z, 4] = 1; 
;				P[z, 5] = z^4;
;				P[z_, n_] := z^4* P[z, n - 1] + z^3*P[z, n - 2] + z^2*P[z, n - 3] + 
;				z*P[z, n - 4] + P[z, n - 5];
;				Table[ExpandAll[P[z, n], z], {n, 1, 25}]
; jam 8/1/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = z^3 + z^8
elseif @variant == "3"
	zpolynom = z^2 + 2 * z^7 + z^12
elseif @variant == "4"
	zpolynom = z + 3 * z^6 + 3 * z^11 + z^16
elseif @variant == "5"
	zpolynom = 1 + 4 * z^5 + 6 * z^10 + 4 * z^15 + z^20
elseif @variant == "6"
	zpolynom = 5 * z^4 + 10 * z^9 + 10 * z^14 + 5 * z^19 + z^24
elseif @variant == "7"
	zpolynom = 4 * z^3 + 15 * z^8 + 20 * z^13 + 15 * z^18 + 6 * z^23 + z^28
elseif @variant == "8"
	zpolynom = 3 * z^2 + 18 * z^7 + 35 * z^12 + 35 * z^17 + 21 * z^22 + 7 * \
		z^27 + z^32
elseif @variant == "9"
	zpolynom = 2 * z + 19 * z^6 + 52 * z^11 + 70 * z^16 + 56 * z^21 + 28 * \
		z^26 + 8 * z^31 + z^36
elseif @variant == "10"
	zpolynom = 1 + 18 * z^5 + 68 * z^10 + 121 * z^15 + 126 * z^20 + 84 * z^25 + \
		36 * z^30 +9 * z^35 + z^40
elseif @variant == "11"
	zpolynom = 15 * z^4 + 80 * z^9 + 185 * z^14 + 246 * z^19 + 210 * z^24 + \
		120 * z^29 + 45 * z^34 + 10 * z^39 + z^44
elseif @variant == "12"
	zpolynom = 10 * z^3 + 85 * z^8 + 255 * z^13 + 426 * z^18 + 455 * z^23 + \
		330 * z^28 + 165 * z^33 + 55 * z^38 + 11 * z^43 + z^48
elseif @variant == "13"
	zpolynom = 6 * z^2 + 80 * z^7 + 320 * z^12 + 666 * z^17 + 875 * z^22 + \
		784 * z^27 + 495 * z^32 + 220 * z^37 + 66 * z^42 + 12 * z^47 + z^52
elseif @variant == "14"
	zpolynom = 3 * z + 68 * z^6 + 365 * z^11 + 951 * z^16 + 1520 * z^21 + \
		1652 * z^26 + 1278 * z^31 + 715 * z^36 + 286 * z^41 + 78 * z^46 + \
		13 * z^51 + z^56
elseif @variant == "15"
	zpolynom = 1 + 52 * z^5 + 381 * z^10 + 1246 * z^15 + 2415 * z^20 + 3144 * \
		z^25 + 2922 * z^30 + 1992 * z^35 + 1001 * z^40 + 364 * z^45 + 91 * \
		z^50 + 14 * z^55 + z^60
elseif @variant == "16"
	zpolynom = 35 * z^4 + 365 * z^9 + 1506 * z^14 + 3535 * z^19 + 5475 * z^24 + \
		6030 * z^29 + 4905 * z^34 + 2992 * z^39 + 1365 * z^44 + 455 * z^49 + \
		105 * z^54 + 15 * z^59 + z^64
elseif @variant == "17"
	zpolynom = 20 * z^3 + 320 * z^8 + 1686 * z^13 + 4795 * z^18 + 8800 * z^23 + \
		11385 * z^28 +  10890 * z^33 + 7887 * z^38 + 4356 * z^43 + 1820 * z^48 + \
		560 * z^53 + 120 * z^58 + 16 * z^63 + z^68
elseif @variant == "18"
	zpolynom = 10 * z^2 + 255 * z^7 + 1751 * z^12 + 6055 * z^17 + 13140 * z^22 + \
		19855 * z^27 + 22110 * z^32 + 18722 * z^37 + 12232 * z^42 + 6175 * z^47 + \
		2380 * z^52 + 680 * z^57 + 136 * z^62 + 17 * z^67 + z^72
elseif @variant == "19"
	zpolynom = 4 * z + 185 * z^6 + 1686 * z^11 + 7140 * z^16 + 18320 * z^21 + \
		32211 * z^26 + 41470 * z^31 + 40612 * z^36 + 30888 * z^41 + 18395 * \
		z^46 + 8554 * z^51 + 3060 * z^56 + 816 * z^61 + 153 * z^66 + 18 * z^71 + \
		z^76
elseif @variant == "20"
	zpolynom = 1 + 121 * z^5 + 1506 * z^10 + 7875 * z^15 + 23940 * z^20 + 48879 * \
		z^25 + 72403 * z^30 + 81367 * z^35 + 71214 * z^40 + 49205 * z^45 + 26936 * \
		z^50 + 11613 * z^55 + 3876 * z^60 + 969 * z^65 + 171 * z^70 + 19 * \
		z^75 + z^80
elseif @variant == "21"
	zpolynom = 70 * z^4 + 1246 * z^9 + 8135 * z^14 + 29400 * z^19 + 69675 * z^24 + \
		118360 * z^29 + 151778 * z^34 + 151580 * z^39 + 120055 * z^44 + 76050 * \
		z^49 + 38535 * z^54 + 15488 * z^59 + 4845 * z^64 + 1140 * z^69 + 190 * \
		z^74 + 20 * z^79 + z^84
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Pentanacci"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20" "21"
	default = 5
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-ShapiroPPolynomials {

; Shapiro P polynomials
; Mathematica:  P[z, 0] = 1; Q[z, 0] = 1;
;				P[z_, n_] := P[z, n - 1] + z^2^(n - 1) * Q[z, n - 1];
;				Q[z_, n_] := P[z, n - 1] - z^2^(n - 1) * Q[z, n - 1];
;				Simplify[Table[P[z, n], {n, 0, 6}]]
; jam 8/3/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "1"
	zpolynom = 1 + #z
elseif @variant == "2"
	zpolynom = 1 + #z + #z^2 - #z^3
elseif @variant == "3"
	zpolynom = 1 + #z + #z^2 - #z^3 + #z^4 + #z^5 - #z^6 + #z^7
elseif @variant == "4"
	zpolynom = 1 + #z + #z^2 - #z^3 + #z^4 + #z^5 - #z^6 + #z^7 + #z^8 + \
		#z^9 + #z^10 - #z^11 - #z^12 - #z^13 + #z^14 - #z^15
elseif @variant == "5"
	zpolynom = 1 + #z + #z^2 - #z^3 + #z^4 + #z^5 - #z^6 + #z^7 + #z^8 + #z^9 + \
		#z^10 - #z^11 - #z^12 - #z^13 + #z^14 - #z^15 + #z^16 + #z^17 + #z^18 - \
		#z^19 + #z^20 + #z^21 - #z^22 + #z^23 - #z^24 - #z^25 - #z^26 + #z^27 + \
		#z^28 + #z^29 - #z^30 + #z^31
elseif @variant == "6"
	zpolynom = 1 + #z + #z^2 - #z^3 + #z^4 + #z^5 - #z^6 + #z^7 + #z^8 + #z^9 + \
		#z^10 - #z^11 - #z^12 - #z^13 + #z^14 - #z^15 + #z^16 + #z^17 + #z^18 - \
		#z^19 + #z^20 + #z^21 - #z^22 + #z^23 - #z^24 - #z^25 - #z^26 + #z^27 + \
		#z^28 + #z^29 - #z^30 + #z^31 + #z^32 + #z^33 + #z^34 - #z^35 + #z^36 + \
		#z^37 - #z^38 + #z^39 + #z^40 + #z^41 + #z^42 - #z^43 - #z^44 - #z^45 + \
		#z^46 - #z^47 - #z^48 - #z^49 - #z^50 + #z^51 - #z^52 - #z^53 + #z^54 - \
		#z^55 + #z^56 + #z^57 + #z^58 - #z^59 - #z^60 - #z^61 + #z^62 - #z^63
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials ShapiroP"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 2500

param variant
	caption = "Polynomial Variant"
	enum = "1" "2" "3" "4" "5" "6"
	default = 2
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-ShapiroQPolynomials {

; Shapiro Q polynomials (complementary Shapiro polynomials)
; Mathematica:  P[z, 0] = 1; Q[z, 0] = 1;
;				P[z_, n_] := P[z, n - 1] + z^2^(n - 1) * Q[z, n - 1];
;				Q[z_, n_] := P[z, n - 1] - z^2^(n - 1) * Q[z, n - 1];
;				Simplify[Table[Q[z, n], {n, 0, 6}]]
; jam 8/3/17
; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "1"
	zpolynom = 1 - #z
elseif @variant == "2"
	zpolynom = 1 + #z - #z^2 + #z^3
elseif @variant == "3"
	zpolynom = 1 + #z + #z^2 - #z^3 - #z^4 - #z^5 + #z^6 - #z^7
elseif @variant == "4"
	zpolynom = 1 + #z + #z^2 - #z^3 + #z^4 + #z^5 - #z^6 + #z^7 - \
		#z^8 - #z^9 - #z^10 + #z^11 + #z^12 + #z^13 - #z^14 + #z^15
elseif @variant == "5"
	zpolynom = 1 + #z + #z^2 - #z^3 + #z^4 + #z^5 - #z^6 + #z^7 + \
		#z^8 + #z^9 + #z^10 - #z^11 - #z^12 - #z^13 + #z^14 - #z^15 - \
		#z^16 - #z^17 - #z^18 + #z^19 - #z^20 - #z^21 + #z^22 - \
		#z^23 + #z^24 + #z^25 + #z^26 - #z^27 - #z^28 - #z^29 + #z^30 - #z^31
elseif @variant == "6"
	zpolynom = 1 + #z + #z^2 - #z^3 + #z^4 + #z^5 - #z^6 + #z^7 + \
		#z^8 + #z^9 + #z^10 - #z^11 - #z^12 - #z^13 + #z^14 - #z^15 + \
		#z^16 + #z^17 + #z^18 - #z^19 + #z^20 + #z^21 - #z^22 + \
		#z^23 - #z^24 - #z^25 - #z^26 + #z^27 + #z^28 + #z^29 - \
		#z^30 + #z^31 - #z^32 - #z^33 - #z^34 + #z^35 - #z^36 - \
		#z^37 + #z^38 - #z^39 - #z^40 - #z^41 - #z^42 + #z^43 + \
		#z^44 + #z^45 - #z^46 + #z^47 + #z^48 + #z^49 + #z^50 - \
		#z^51 + #z^52 + #z^53 - #z^54 + #z^55 - #z^56 - #z^57 - \
		#z^58 + #z^59 + #z^60 + #z^61 - #z^62 + #z^63
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials ShapiroQ"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 2500

param variant
	caption = "Polynomial Variant"
	enum = "1" "2" "3" "4" "5" "6"
	default = 2
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-HermitePolynomials {

; Hermite polynomials
; Mathematica:  Table[HermiteH[n, z], {n, 2, 20}]
; jam 8/3/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = -2 + 4 * #z^2
elseif @variant == "3"
	zpolynom = -12 * #z + 8 * #z^3
elseif @variant == "4"
	zpolynom = 12 - 48 * #z^2 + 16 * #z^4
elseif @variant == "5"
	zpolynom = 120 * #z - 160 * #z^3 + 32 * #z^5
elseif @variant == "6"
	zpolynom = -120 + 720 * #z^2 - 480 * #z^4 + 64 * #z^6
elseif @variant == "7"
	zpolynom = -1680 * #z + 3360 * #z^3 - 1344 * #z^5 + 128 * #z^7
elseif @variant == "8"
	zpolynom = 1680 - 13440 * #z^2 + 13440 * #z^4 - 3584 * #z^6 + 256 * #z^8
elseif @variant == "9"
	zpolynom = 30240 * #z - 80640 * #z^3 + 48384 * #z^5 - 9216 * #z^7 + \
		512 * #z^9
elseif @variant == "10"
	zpolynom = -30240 + 302400 * #z^2 - 403200 * #z^4 + 161280 * #z^6 - \
		23040 * #z^8 + 1024 * #z^10
elseif @variant == "11"
	zpolynom = -665280 * #z + 2217600 * #z^3 - 1774080 * #z^5 + 506880 * \
		#z^7 - 56320 * #z^9 + 2048 * #z^11
elseif @variant == "12"
	zpolynom = 665280 - 7983360 * #z^2 + 13305600 * #z^4 - 7096320 * #z^6 + \
		1520640 * #z^8 - 135168 * #z^10 + 4096 * #z^12
elseif @variant == "13"
	zpolynom = 17297280 * #z - 69189120 * #z^3 + 69189120 * #z^5 - 26357760 * \
		#z^7 + 4392960 * #z^9 - 319488 * #z^11 + 8192 * #z^13
elseif @variant == "14"
	zpolynom = -17297280 + 242161920 * #z^2 - 484323840 * #z^4 + 322882560 * \
		#z^6 - 92252160 * #z^8 + 12300288 * #z^10 - 745472 * #z^12 + 16384 * \
		#z^14
elseif @variant == "15"
	zpolynom = -518918400 * #z + 2.421619200e9 * #z^3 - 2.905943040e9 * #z^5 + \
		1.383782400e9 * #z^7 - 307507200 * #z^9 + 33546240 * #z^11 - 1720320 * \
		#z^13 + 32768 * #z^15
elseif @variant == "16"
	zpolynom = 518918400 - 8.302694400e9 * #z^2 + 19.372953600e9 * #z^4 - \
		15.498362880e9 * #z^6 + 5.535129600e9 * #z^8 - 984023040 * #z^10 + \
		89456640 * #z^12 - 3932160 * #z^14 + 65536 * #z^16
elseif @variant == "17"
	zpolynom = 17.643225600e9 * #z - 94.097203200e9 * #z^3 + 131.736084480e9 * \
		#z^5 - 75.277762560e9 * #z^7 + 20.910489600e9 * #z^9 - 3.041525760e9 * \
		#z^11 + 233963520 * #z^13 - 8912896 * #z^15 + 131072 * #z^17
elseif @variant == "18"
	zpolynom = -17.643225600e9 + 317.578060800e9 * #z^2 - 846.874828800e9 * #z^4 + \
		790.416506880e9 * #z^6 - 338.749931520e9 * #z^8 + 75.277762560e9 * #z^10 - \
		9.124577280e9 * #z^12 + 601620480 * #z^14 - 20054016 * #z^16 + 262144 * #z^18
elseif @variant == "19"
	zpolynom = -670.442572800e9 * #z + 4.022655436800e12 * #z^3 - 6.436248698880e12 \
		* #z^5 + 4.290832465920e12 * #z^7 - 1.430277488640e12 * #z^9 + \
		260.050452480e9 * #z^11 - 26.671841280e9 * #z^13 + 1.524105216e9 * \
		#z^15 - 44826624 * #z^17 + 524288 * #z^19
elseif @variant == "20"
	zpolynom = 670.442572800e9 - 13.408851456000e12 * #z^2 + 40.226554368000e12 \
		* #z^4 - 42.908324659200e12 * #z^6 + 21.454162329600e12 * #z^8 - \
		5.721109954560e12 * #z^10 + 866.834841600e9 * #z^12 - 76.205260800e9 * \
		#z^14 + 3.810263040e9 * #z^16 - 99614720 * #z^18 + 1048576 * #z^20
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Hermite"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20"
	default = 6
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (-8,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-CatalanPolynomials {

; for Catalan polynomials, see OEIS# A115139
; Mathematica:  p[z, 0] = 1; p[z, 1] = 1;
;				p[z_, n_] := p[z, n - 1] - z*p[z, n - 2];
;				Table[p[z, n], {n, 0, 20}] // Simplify
; jam 8/5/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = 1 - #z
elseif @variant == "3"
	zpolynom = 1 - 2 * #z
elseif @variant == "4"
	zpolynom = 1 - 3 * #z + #z^2
elseif @variant == "5"
	zpolynom = 1 - 4 * #z + 3 * #z^2
elseif @variant == "6"
	zpolynom = 1 - 5 * #z + 6 * #z^2 - #z^3
elseif @variant == "7"
	zpolynom = 1 - 6 * #z + 10 * #z^2 - 4 * #z^3
elseif @variant == "8"
	zpolynom = 1 - 7 * #z + 15 * #z^2 - 10 * #z^3 + #z^4
elseif @variant == "9"
	zpolynom = 1 - 8 * #z + 21 * #z^2 - 20 * #z^3 + 5 * #z^4
elseif @variant == "10"
	zpolynom = 1 - 9 * #z + 28 * #z^2 - 35 * #z^3 + 15 * #z^4 - #z^5
elseif @variant == "11"
	zpolynom = 1 - 10 * #z + 36 * #z^2 - 56 * #z^3 + 35 * #z^4 - 6 * #z^5
elseif @variant == "12"
	zpolynom = 1 - 11 * #z + 45 * #z^2 - 84 * #z^3 + 70 * #z^4 - 21 * \
		#z^5 + #z^6
elseif @variant == "13"
	zpolynom = 1 - 12 * #z + 55 * #z^2 - 120 * #z^3 + 126 * #z^4 - 56 * \
		#z^5 + 7 * #z^6
elseif @variant == "14"
	zpolynom = 1 - 13 * #z + 66 * #z^2 - 165 * #z^3 + 210 * #z^4 - 126 * \
		#z^5 + 28 * #z^6 - #z^7
elseif @variant == "15"
	zpolynom = 1 - 14 * #z + 78 * #z^2 - 220 * #z^3 + 330 * #z^4 - 252 * \
		#z^5 + 84 * #z^6 - 8 * #z^7
elseif @variant == "16"
	zpolynom = 1 - 15 * #z + 91 * #z^2 - 286 * #z^3 + 495 * #z^4 - 462 * \
		#z^5 + 210 * #z^6 - 36 * #z^7 + #z^8
elseif @variant == "17"
	zpolynom = 1 - 16 * #z + 105 * #z^2 - 364 * #z^3 + 715 * #z^4 - 792 * \
		#z^5 + 462 * #z^6 - 120 * #z^7 + 9 * #z^8
elseif @variant == "18"
	zpolynom = 1 - 17 * #z + 120 * #z^2 - 455 * #z^3 + 1001 * #z^4 - 1287 * \
		#z^5 + 924 * #z^6 - 330 * #z^7 + 45 * #z^8 - #z^9
elseif @variant == "19"
	zpolynom = 1 - 18 * #z + 136 * #z^2 - 560 * #z^3 + 1365 * #z^4 - 2002 * \
		#z^5 + 1716 * #z^6 - 792 * #z^7 + 165 * #z^8 - 10 * #z^9
elseif @variant == "20"
	zpolynom = 1 - 19 * #z + 153 * #z^2 - 680 * #z^3 + 1820 * #z^4 - 3003 * \
		#z^5 + 3003 * #z^6 - 1716 * #z^7 + 495 * #z^8 - 55 * #z^9 + #z^10
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Catalan"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-GeometricPolynomials {

; Geometric (or Fubini) polynomials
; Mathematica:  F[z_, n_] := Sum[ StirlingS2[n, k] * k! * z^k, {k, 0, n}];
;				Table[F[z, n], {n, 0, 20}] // Simplify
; jam 8/5/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = #z + 2 * #z^2
elseif @variant == "3"
	zpolynom = #z + 6 * #z^2 + 6 * #z^3
elseif @variant == "4"
	zpolynom = #z + 14 * #z^2 + 36 * #z^3 + 24 * #z^4
elseif @variant == "5"
	zpolynom = #z + 30 * #z^2 + 150 * #z^3 + 240 * #z^4 + 120 * #z^5
elseif @variant == "6"
	zpolynom = #z + 62 * #z^2 + 540 * #z^3 + 1560 * #z^4 + 1800 * #z^5 + 720 * \
		#z^6
elseif @variant == "7"
	zpolynom = #z + 126 * #z^2 + 1806 * #z^3 + 8400 * #z^4 + 16800 * #z^5 + \
		15120 * #z^6 + 5040 * #z^7
elseif @variant == "8"
	zpolynom = #z + 254 * #z^2 + 5796 * #z^3 + 40824 * #z^4 + 126000 * #z^5 + \
		191520 * #z^6 + 141120 * #z^7 + 40320 * #z^8
elseif @variant == "9"
	zpolynom = #z + 510 * #z^2 + 18150 * #z^3 + 186480 * #z^4 + 834120 * #z^5 + \
		1905120 * #z^6 + 2328480 * #z^7 + 1451520 * #z^8 + 362880 * #z^9
elseif @variant == "10"
	zpolynom = #z + 1022 * #z^2 + 55980 * #z^3 + 818520 * #z^4 + 5103000 * #z^5 \
		+ 16435440 * #z^6 + 29635200 * #z^7 + 30240000 * #z^8 + 16329600 * #z^9 + \
		3628800 * #z^10
elseif @variant == "11"
	zpolynom = #z + 2046 * #z^2 + 171006 * #z^3 + 3498000 * #z^4 + 29607600 * \
		#z^5 + 129230640 * #z^6 + 322494480 * #z^7 + 479001600 * #z^8 + 419126400 * \
		#z^9 + 199584000 * #z^10 + 39916800 * #z^11
elseif @variant == "12"
	zpolynom = #z + 4094 * #z^2 + 519156 * #z^3 + 14676024 * #z^4 + 165528000 * \
		#z^5 + 953029440 * #z^6 + 3.162075840e9 * #z^7 + 6.411968640e9 * #z^8 + \
		8.083152000e9 * #z^9 + 6.187104000e9 * #z^10 + 2.634508800e9 * #z^11 + \
		479001600 * #z^12
elseif @variant == "13"
	zpolynom = #z + 8190 * #z^2 + 1569750 * #z^3 + 60780720 * #z^4 + 901020120 * \
		#z^5 + 6.711344640e9 * #z^6 + 28.805736960e9 * #z^7 + 76.592355840e9 * \
		#z^8 + 130.456085760e9 * #z^9 + 142.702560000e9 * #z^10 + 97.037740800e9 * \
		#z^11 + 37.362124800e9 * #z^12 + 6.227020800e9 * #z^13
elseif @variant == "14"
	zpolynom = #z + 16382 * #z^2 + 4733820 * #z^3 + 249401880 * #z^4 + 4.809004200e9 \
		* #z^5 + 45.674188560e9 * #z^6 + 248.619571200e9 * #z^7 + 843.184742400e9 * \
		#z^8 + 1.863435974400e12 * #z^9 + 2.731586457600e12 * #z^10 + 2.637143308800e12 \
		* #z^11 + 1.612798387200e12 * #z^12 + 566.658892800e9 * #z^13 + 87.178291200e9 \
		* #z^14
elseif @variant == "15"
	zpolynom = #z + 32766 * #z^2 + 14250606 * #z^3 + 1.016542800e9 * #z^4 + \
		25.292030400e9 * #z^5 + 302.899156560e9 * #z^6 + 2.060056318320e12 * \
		#z^7 + 8.734434508800e12 * #z^8 + 24.359586451200e12 * #z^9 + 45.950224320000e12 \
		* #z^10 + 59.056027430400e12 * #z^11 + 50.999300352000e12 * #z^12 + \
		28.332944640000e12 * #z^13 + 9.153720576000e12 * #z^14 + 1.307674368000e12 * #z^15
elseif @variant == "16"
	zpolynom = #z + 65534 * #z^2 + 42850116 * #z^3 + 4.123173624e9 * #z^4 + \
		131.542866000e9 * #z^5 + 1.969147121760e12 * #z^6 + 16.540688324160e12 * \
		#z^7 + 86.355926616960e12 * #z^8 + 297.846188640000e12 * #z^9 + 703.098107712000e12 \
		* #z^10 + 1.155068769254400e15 * #z^11 + 1.320663933388800e15 * #z^12 + \
		1.031319184896000e15 * #z^13 + 524.813313024000e12 * #z^14 + 156.920924160000e12 * \
		#z^15 + 20.922789888000e12 * #z^16
elseif @variant == "17"
	zpolynom = #z + 131070 * #z^2 + 128746950 * #z^3 + 16.664094960e9 * #z^4 + \
		678.330198120e9 * #z^5 + 12.604139926560e12 * #z^6 + 129.568848121440e12 * \
		#z^7 + 823.172919528960e12 * #z^8 + 3.457819037312640e15 * #z^9 + 10.009442963520000e15 \
		* #z^10 + 20.439835646630400e15 * #z^11 + 29.708792431718400e15 * #z^12 + \
		30.575780537702400e15 * #z^13 + 21.785854970880000e15 * #z^14 + 10.226013557760000e15 * \
		#z^15 + 2.845499424768000e15 * #z^16 + 355.687428096000e12 * #z^17
elseif @variant == "18"
	zpolynom = #z + 262142 * #z^2 + 386634060 * #z^3 + 67.171367640e9 * #z^4 + \
		3.474971465400e12 * #z^5 + 79.694820748080e12 * #z^6 + 995.210916336000e12 * \
		#z^7 + 7.621934141203200e15 * #z^8 + 38.528927611574400e15 * #z^9 + 134.672620008326400e15 \
		* #z^10 + 334.942064711654400e15 * #z^11 + 601.783536940185600e15 * #z^12 + \
		783.699448602470400e15 * #z^13 + 733.062897120153600e15 * #z^14 + 480.178027929600000e15 * \
		#z^15 + 209.144207720448000e15 * #z^16 + 54.420176498688000e15 * #z^17 + \
		6.402373705728000e15 * #z^18
elseif @variant == "19"
	zpolynom = #z + 524286 * #z^2 + 1.160688606e9 * #z^3 + 270.232006800e9 * \
		#z^4 + 17.710714165200e12 * #z^5 + 499.018753280880e12 * #z^6 + \
		7.524340159588560e15 * #z^7 + 68.937160460313600e15 * #z^8 + \
		415.357755774998400e15 * #z^9 + 1.732015476199008000e18 * #z^10 + \
		5.165761531919788800e18 * #z^11 + 11.240707219822080000e18 * #z^12 + \
		18.011278812054528000e18 * #z^13 + 21.234672840116736000e18 * \
		#z^14 + 18.198613875746304000e18 * #z^15 + 11.029155770400768000e18 * \
		#z^16 + 4.480594531725312000e18 * #z^17 + 1.094805903679488000e18 * \
		#z^18 + 121.645100408832000e15 * #z^19
elseif @variant == "20"
	zpolynom = #z + 1048574 * #z^2 + 3.483638676e9 * #z^3 + 1.085570781624e12 * \
		#z^4 + 89.904730860000e12 * #z^5 + 3.100376804676480e15 * #z^6 + \
		56.163512390086080e15 * #z^7 + 611.692004959217280e15 * #z^8 + \
		4.358654246117808000e18 * #z^9 + 21.473732319740064000e18 * #z^10 + \
		75.875547089306764800e18 * #z^11 + 196.877625020902425600e18 * #z^12 + \
		380.275818414395904000e18 * #z^13 + 549.443323130397696000e18 * #z^14 + \
		591.499300737945600000e18 * #z^15 + 467.644314338353152000e18 * #z^16 \
		+ 263.665755136143360000e18 * #z^17 + 100.357207837286400000e18 * \
		#z^18 + 23.112569077678080000e18 * #z^19 + 2.432902008176640000e18 * #z^20
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Geometric"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-HexanacciPolynomials {

; Hexanacci polynomials
; Mathematica:  P[z, 0] = 0; P[z, 1] = 0; P[z, 2] = 0; P[z, 3] = 0; P[z, 4] = 0; 
;				P[z, 5] = 1; P[z, 6] = z^5;
;				P[z_, n_] := z^5* P[z, n - 1] + z^4*P[z, n - 2] + z^3*P[z, n - 3] + 
;				z^2*P[z, n - 4] + z*P[z, n - 5] + P[z, n - 6];
;				Table[ExpandAll[P[z, n], z], {n, 0, 25}]
; jam 8/5/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = #z^5
elseif @variant == "3"
	zpolynom = #z^4 + #z^10
elseif @variant == "4"
	zpolynom = #z^3 + 2 * #z^9 + #z^15
elseif @variant == "5"
	zpolynom = #z^2 + 3 * #z^8 + 3 * #z^14 + #z^20
elseif @variant == "6"
	zpolynom = #z + 4 * #z^7 + 6 * #z^13 + 4 * #z^19 + #z^25
elseif @variant == "7"
	zpolynom = 1 + 5 * #z^6 + 10 * #z^12 + 10 * #z^18 + 5 * #z^24 + #z^30
elseif @variant == "8"
	zpolynom = 6 * #z^5 + 15 * #z^11 + 20 * #z^17 + 15 * #z^23 + 6 * #z^29 + \
		#z^35
elseif @variant == "9"
	zpolynom = 5 * #z^4 + 21 * #z^10 + 35 * #z^16 + 35 * #z^22 + 21 * #z^28 + \
		7 * #z^34 + #z^40
elseif @variant == "10"
	zpolynom = 4 * #z^3 + 25 * #z^9 + 56 * #z^15 + 70 * #z^21 + 56 * #z^27 + \
		28 * #z^33 + 8 * #z^39 + #z^45
elseif @variant == "11"
	zpolynom = 3 * #z^2 + 27 * #z^8 + 80 * #z^14 + 126 * #z^20 + 126 * #z^26 + \
		84 * #z^32 + 36 * #z^38 + 9 * #z^44 + #z^50
elseif @variant == "12"
	zpolynom = 2 * #z + 27 * #z^7 + 104 * #z^13 + 205 * #z^19 + 252 * #z^25 + \
		210 * #z^31 + 120 * #z^37 + 45 * #z^43 + 10 * #z^49 + #z^55
elseif @variant == "13"
	zpolynom = 1 + 25 * #z^6 + 125 * #z^12 + 305 * #z^18 + 456 * #z^24 + 462 * \
		#z^30 + 330 * #z^36 + 165 * #z^42 + 55 * #z^48 + 11 * #z^54 + #z^60
elseif @variant == "14"
	zpolynom = 21 * #z^5 + 140 * #z^11 + 420 * #z^17 + 756 * #z^23 + 917 * \
		#z^29 + 792 * #z^35 + 495 * #z^41 + 220 * #z^47 + 66 * #z^53 + 12 * \
		#z^59 + #z^65
elseif @variant == "15"
	zpolynom = 15 * #z^4 + 146 * #z^10 + 540 * #z^16 + 1161 * #z^22 + 1667 * \
		#z^28 + 1708 * #z^34 + 1287 * #z^40 + 715 * #z^46 + 286 * #z^52 + 78 * \
		#z^58 + 13 * #z^64 + #z^70
elseif @variant == "16"
	zpolynom = 10 * #z^3 + 140 * #z^9 + 651 * #z^15 + 1666 * #z^21 + 2807 * \
		#z^27 + 3368 * #z^33 + 2994 * #z^39 + 2002 * #z^45 + 1001 * #z^51 + \
		364 * #z^57 + 91 * #z^63 + 14 * #z^69 + #z^75
elseif @variant == "17"
	zpolynom = 6 * #z^2 + 125 * #z^8 + 735 * #z^14 + 2247 * #z^20 + 4417 * \
		#z^26 + 6147 * #z^32 + 6354 * #z^38 + 4995 * #z^44 + 3003 * #z^50 + 1365 * \
		#z^56 + 455 * #z^62 + 105 * #z^68 + 15 * #z^74 + #z^80
elseif @variant == "18"
	zpolynom = 3 * #z + 104 * #z^7 + 780 * #z^13 + 2856 * #z^19 + 6538 * #z^25 + \
		10480 * #z^31 + 12465 * #z^37 + 11340 * #z^43 + 7997 * #z^49 + 4368 * \
		#z^55 + 1820 * #z^61 + 560 * #z^67 + 120 * #z^73 + 16 * #z^79 + #z^85
elseif @variant == "19"
	zpolynom = 1 + 80 * #z^6 + 780 * #z^12 + 3431 * #z^18 + 9142 * #z^24 + \
		16808 * #z^30 + 22825 * #z^36 + 23760 * #z^42 + 19327 * #z^48 + \
		12364 * #z^54 + 6188 * #z^60 + 2380 * #z^66 + 680 * #z^72 + 136 * \
		#z^78 + 17 * #z^84 + #z^90
elseif @variant == "20"
	zpolynom = 56 * #z^5 + 735 * #z^11 + 3906 * #z^17 + 12117 * #z^23 + \
		25488 * #z^29 + 39303 * #z^35 + 46420 * #z^41 + 43032 * #z^47 + \
		31680 * #z^53 + 18551 * #z^59 + 8568 * #z^65 + 3060 * #z^71 + \
		816 * #z^77 + 153 * #z^83 + 18 * #z^89 + #z^95
elseif @variant == "21"
	zpolynom = 35 * #z^4 + 651 * #z^10 + 4221 * #z^16 + 15267 * #z^22 + \
		36688 * #z^28 + 63999 * #z^34 + 85228 * #z^40 + 89232 * #z^46 + \
		74646 * #z^52 + 50219 * #z^58 + 27118 * #z^64 + 11628 * #z^70 + \
		3876 * #z^76 + 969 * #z^82 + 171 * #z^88 + 19 * #z^94 + #z^100
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Hexanacci"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20" "21"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-LaguerrePolynomials {

; Laguerre polynomials
; Mathematica:  Expand[Table[LaguerreL[n, z], {n, 0, 20}]]
; jam 8/8/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = 1 - #z
elseif @variant == "3"
	zpolynom = 1 - 2 * #z + 0.5 * #z^2
elseif @variant == "4"
	zpolynom = 1 - 3 * #z + 1.5 * #z^2 - #z^3/6
elseif @variant == "5"
	zpolynom = 1 - 4 * #z + 3 * #z^2 - (2 * #z^3)/3 + #z^4/24
elseif @variant == "6"
	zpolynom = 1 - 5 * #z + 5 * #z^2 - (5 * #z^3)/3 + (5 * #z^4)/24 - \
		#z^5/120
elseif @variant == "7"
	zpolynom = 1 - 6 * #z + 7.5 * #z^2 - (10 * #z^3)/3 + 0.625 * #z^4 - \
		#z^5/20 + #z^6/720
elseif @variant == "8"
	zpolynom = 1 - 7 * #z + 10.5 * #z^2 - (35 * #z^3)/6 + (35 * #z^4)/24 - \
		0.175 * #z^5 + (7 * #z^6)/720 - #z^7/5040
elseif @variant == "9"
	zpolynom = 1 - 8 * #z + 14 * #z^2 - (28 * #z^3)/3 + (35 * #z^4)/12 - \
		(7 * #z^5)/15 + (7 * #z^6)/180 - #z^7/630 + #z^8/40320
elseif @variant == "10"
	zpolynom = 1 - 9 * #z + 18 * #z^2 - 14 * #z^3 + 5.25 * #z^4 - 1.05 * \
		#z^5 + (7 * #z^6)/60 - #z^7/140 + #z^8/4480 - #z^9/362880
elseif @variant == "11"
	zpolynom = 1 - 10 * #z + 22.5 * #z^2 - 20 * #z^3 + 8.75 * #z^4 - 2.1 * \
		#z^5 + (7 * #z^6)/24 - #z^7/42 + #z^8/896 - #z^9/36288 + #z^10/3628800
elseif @variant == "12"
	zpolynom = 1 - 11 * #z + 27.5 * #z^2 - 27.5 * #z^3 + 13.75 * #z^4 - \
		3.85 * #z^5 + (77 * #z^6)/120 - (11 * #z^7)/168 + (11 * #z^8)/2688 - \
		(11 * #z^9)/72576 + (11 * #z^10)/3628800 - #z^11/39916800
elseif @variant == "13"
	zpolynom = 1 - 12 * #z + 33 * #z^2 - (110 * #z^3)/3 + 20.625 * #z^4 - \
		6.6 * #z^5 + (77 * #z^6)/60 - (11 * #z^7)/70 + (11 * #z^8)/896 - \
		(11 * #z^9)/18144 + (11 * #z^10)/604800 - #z^11/3326400 + #z^12/479001600
elseif @variant == "14"
	zpolynom = 1 - 13 * #z + 39 * #z^2 - (143 * #z^3)/3 + (715 * \
		#z^4)/24 - 10.725 * #z^5 + (143 * #z^6)/60 - (143 * #z^7)/420 + \
		(143 * #z^8)/4480 - (143 * #z^9)/72576 + (143 * #z^10)/1814400 - \
		(13 * #z^11)/6652800 + (13 * #z^12)/479001600 - #z^13/6.227020800e9
elseif @variant == "15"
	zpolynom = 1 - 14 * #z + 45.5 * #z^2 - (182 * #z^3)/3 + (1001 * #z^4)/24 - \
		(1001 * #z^5)/60 + (1001 * #z^6)/240 - (143 * #z^7)/210 + (143 * \
		#z^8)/1920 - (143 * #z^9)/25920 + (143 * #z^10)/518400 - (13 * \
		#z^11)/1425600 + (13 * #z^12)/68428800 - #z^13/444787200 + \
		#z^14/87.178291200e9
elseif @variant == "16"
	zpolynom = 1 - 15 * #z + 52.5 * #z^2 - (455 * #z^3)/6 + 56.875 * #z^4 - \
		25.025 * #z^5 + (1001 * #z^6)/144 - (143 * #z^7)/112 + (143 * \
		#z^8)/896 - (143 * #z^9)/10368 + (143 * #z^10)/172800 - (13 * \
		#z^11)/380160 + (13 * #z^12)/13685760 - #z^13/59304960 + \
		#z^14/5.811886080e9 - #z^15/1.307674368000e12
elseif @variant == "17"
	zpolynom = 1 - 16 * #z + 60 * #z^2 - (280 * #z^3)/3 + (455 * #z^4)/6 - \
		36.4 * #z^5 + (1001 * #z^6)/90 - (143 * #z^7)/63 + (143 * \
		#z^8)/448 - (143 * #z^9)/4536 + (143 * #z^10)/64800 - (13 * \
		#z^11)/118800 + (13 * #z^12)/3421440 - #z^13/11119680 + #z^14/726485760 - \
		#z^15/81.729648000e9 + #z^16/20.922789888000e12
elseif @variant == "18"
	zpolynom = 1 - 17 * #z + 68 * #z^2 - (340 *  #z^3)/3 + (595 * #z^4)/6 - \
		(1547 * #z^5)/30 + (1547 * #z^6)/90 - (2431 * #z^7)/630 + (2431 * \
		#z^8)/4032 - (2431 * #z^9)/36288 + (2431 * #z^10)/453600 - (221 * \
		#z^11)/712800 + (221 * #z^12)/17107200 - (17 * #z^13)/44478720 + \
		(17 * #z^14)/2.179457280e9 - (17 * #z^15)/163.459296000e9 + (17 * \
		#z^16)/20.922789888000e12 - #z^17/355.687428096000e12
elseif @variant == "19"
	zpolynom = 1 - 18 * #z + 76.5 * #z^2 - 136 * #z^3 + 127.5 * #z^4 - \
		71.4 * #z^5 + (1547 * #z^6)/60 - (221 * #z^7)/35 + (2431 * \
		#z^8)/2240 - (2431 * #z^9)/18144 + (2431 * #z^10)/201600 - (221 * \
		#z^11)/277200 + (221 * #z^12)/5702400 - (17 * #z^13)/12355200 + \
		(17 * #z^14)/484323840 - (17 * #z^15)/27.243216000e9 + (17 * \
		#z^16)/2.324754432000e12 - #z^17/19.760412672000e12 + \
		#z^18/6.402373705728000e15
elseif @variant == "20"
	zpolynom = 1 - 19 * #z + 85.5 * #z^2 - 161.5 * #z^3 + 161.5 * #z^4 - \
		96.9 * #z^5 + (2261 * #z^6)/60 - (4199 * #z^7)/420 + (4199 * \
		#z^8)/2240 - (46189 * #z^9)/181440 + (46189 * #z^10)/1814400 - \
		(4199 * #z^11)/2217600 + (4199 * #z^12)/39916800 - (323 * \
		#z^13)/74131200 + (323 * #z^14)/2.421619200e9 - (323 * \
		#z^15)/108.972864000e9 + (323 * #z^16)/6.974263296000e12 - \
		(19 * #z^17)/39.520825344000e12 + (19 * #z^18)/6.402373705728000e15 \
		- #z^19/121.645100408832000e15
elseif @variant == "21"
	zpolynom = 1 - 20 * #z + 95 * #z^2 - 190 * #z^3 + 201.875 * #z^4 - \
		129.2 * #z^5 + (323 * #z^6)/6 - (323 * #z^7)/21 + (4199 * #z^8)/1344 \
		- (4199 * #z^9)/9072 + (46189 * #z^10)/907200 - (4199 * \
		#z^11)/997920 + (4199 * #z^12)/15966720 - (323 * #z^13)/25945920 + \
		(323 * #z^14)/726485760 - (323 * #z^15)/27.243216000e9 + \
		(323 * #z^16)/1.394852659200e12 - (19 * #z^17)/5.928123801600e12 + \
		(19 * #z^18)/640.237370572800e12 - #z^19/6.082255020441600e15 + \
		#z^20/2.432902008176640000e18
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Laguerre"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20" "21"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-AssocLaguerrePolynomials {

; Associated Laguerre Polynomials
; Standard Laguerre polynomials are obtained by setting parameter
; 'Laguerre Constant' to zero.
; Mathematica:  Expand[Simplify[Table[LaguerreL[n, k, z], {n, 0, 17}]]]
; jam 8/8/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2
	complex lkterm2 = 0.5 * sqr(@lconst) + 1.5 * @lconst
	complex lkterm3 = @lconst * sqr(@lconst)/6 + sqr(@lconst) + 11 * \
		@lconst/6
	complex lkterm4 = 25*@lconst/12 + 35*sqr(@lconst)/24 + 5*@lconst^3/12 + \
		sqr(sqr(@lconst))/24
	complex lkterm5 = 137*@lconst/60 + 15*sqr(@lconst)/8 + 17*@lconst^3/24 \
		+ sqr(sqr(@lconst))/8 + @lconst^5/120
	complex lkterm6 = 49*@lconst/20 + 203*sqr(@lconst)/90 + 49*@lconst^3/48 + \
		35*sqr(sqr(@lconst))/144 + 7*@lconst^5/240 + @lconst^6/720

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "1"
	zpolynom = 1 - #z + @lconst
elseif @variant == "2"
	zpolynom = 1 - 2 * #z + 0.5 * #z^2 + lkterm2 - @lconst*#z
elseif @variant == "3"
	zpolynom = 1 - 3 * #z + 1.5 * #z^2 - #z^3/6 + lkterm3 - 2.5*@lconst*#z - \
		0.5*sqr(@lconst)*#z + 0.5*@lconst*sqr(#z)
elseif @variant == "4"
	zpolynom = 1 - 4 * #z + 3 * #z^2 - (2 * #z^3)/3 + #z^4/24 + lkterm4 - \
		13*@lconst*#z/3 - 1.5*sqr(@lconst)*#z - @lconst^3*#z/6 + \
		7*@lconst*sqr(#z)/4 + sqr(@lconst)*sqr(#z)/4 - @lconst*#z^3/6
elseif @variant == "5"
	zpolynom = 1 - 5 * #z + 5 * #z^2 - (5 * #z^3)/3 + (5 * #z^4)/24 - \
		#z^5/120 + lkterm5 - 77*@lconst*#z/12 - 71*sqr(@lconst)*#z/24 - \
		7*@lconst^3*#z/12 - sqr(sqr(@lconst))*#z/24 + 47*@lconst*sqr(#z)/12 \
		+ sqr(@lconst)*sqr(#z) + @lconst^3*sqr(#z)/12 - 0.75*@lconst*#z^3 \
		- sqr(@lconst)*#z^3/12 + @lconst*sqr(sqr(#z))/24
elseif @variant == "6"
	zpolynom = 1 - 6 * #z + 7.5 * #z^2 - (10 * #z^3)/3 + 0.625 * #z^4 - \
		#z^5/20 + #z^6/720 + lkterm6 - 8.7*@lconst*#z - 29*sqr(@lconst)*#z/6 \
		- 31*lconst^3*#z/24 - sqr(sqr(@lconst))*#z/6 - @lconst^5*#z/120 + \
		7.125*@lconst*sqr(#z) + 119*sqr(@lconst)*sqr(#z)/48 + \
		0.375*@lconst^3*sqr(#z) + sqr(sqr(@lconst))*sqr(#z)/48 - \
		37*@lconst*#z^3/18 - 5*sqr(@lconst)*#z^3/12 - @lconst^3*#z^3/36 + \
		11*@lconst*sqr(sqr(#z))/48 + sqr(@lconst)*sqr(sqr(#z))/48 - @lconst*#z^5/120
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Assoc Laguerre"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "1" "2" "3" "4" "5" "6"
	default = 2
	hint = "This setting selects which polynomial equation to iterate."
endparam
param lconst
	caption = "Laguerre Constant"
	default = (1,0)
	hint = "This parameter selects which family of associated Laguerre polynomials \
		to iterate.  Setting this parameter to zero results in the ordinary Laguerre \
		polynomials."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-SwissKnifePolynomials {

; Mathematica:  Expand[Simplify[CoefficientList[Series[Exp[z*t]*Sech[t],
;				{t, 0, 20}], t] * Range[0, 20]!]]
; jam 8/8/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = -1 + #z^2
elseif @variant == "3"
	zpolynom = -3 * #z + #z^3
elseif @variant == "4"
	zpolynom = 5 - 6 * #z^2 + #z^4
elseif @variant == "5"
	zpolynom = 25 * #z - 10 * #z^3 + #z^5
elseif @variant == "6"
	zpolynom = -61 + 75 * #z^2 - 15 * #z^4 + #z^6
elseif @variant == "7"
	zpolynom = -427 * #z + 175 * #z^3 - 21 * #z^5 + #z^7
elseif @variant == "8"
	zpolynom = 1385 - 1708 * #z^2 + 350 * #z^4 - 28 * #z^6 + #z^8
elseif @variant == "9"
	zpolynom = 12465 * #z - 5124 * #z^3 + 630 * #z^5 - 36 * #z^7 + #z^9
elseif @variant == "10"
	zpolynom = -50521 + 62325 * #z^2 - 12810 * #z^4 + 1050 * #z^6 - 45 * \
		#z^8 + #z^10
elseif @variant == "11"
	zpolynom = -555731 * #z + 228525 * #z^3 - 28182 * #z^5 + 1650 * \
		#z^7 - 55 * #z^9 + #z^11
elseif @variant == "12"
	zpolynom = 2702765 - 3334386 * #z^2 + 685575 * #z^4 - 56364 * #z^6 + \
		2475 * #z^8 - 66 * #z^10 + #z^12
elseif @variant == "13"
	zpolynom = 35135945 * #z - 14449006 * #z^3 + 1782495 * #z^5 - 104676 * \
		#z^7 + 3575 * #z^9 - 78 * #z^11 + #z^13
elseif @variant == "14"
	zpolynom = -199360981 + 245951615 * #z^2 - 50571521 * #z^4 + 4159155 * \
		#z^6 - 183183 * #z^8 + 5005 * #z^10 - 91 * #z^12 + #z^14
elseif @variant == "15"
	zpolynom = -2.990414715e9 * #z + 1.229758075e9 * #z^3 - 151714563 * \
		#z^5 + 8912475*  #z^7 - 305305 * #z^9 + 6825 * #z^11 - 105 * #z^13 \
		+ #z^15
elseif @variant == "16"
	zpolynom = 19.391512145e9 - 23.923317720e9 * #z^2 + 4.919032300e9 * \
		#z^4 - 404572168 * #z^6 + 17824950 * #z^8 - 488488 * #z^10 + 9100 * \
		#z^12 - 120 * #z^14 + #z^16
elseif @variant == "17"
	zpolynom = 329.655706465e9 * #z - 135.565467080e9 * #z^3 + 16.724709820e9 \
		* #z^5 - 982532408 * #z^7 + 33669350 * #z^9 - 754936 * #z^11 + 11900 * \
		#z^13 - 136 * #z^15 + #z^17
elseif @variant == "18"
	zpolynom = -2.404879675441e12 + 2.966901358185e12 * #z^2 - 610.044601860e9 \
		* #z^4 + 50.174129460e9 * #z^6 - 2.210697918e9 * #z^8 + 60604830 * \
		#z^10 - 1132404 * #z^12 + 15300 * #z^14 - 153 * #z^16 + #z^18
elseif @variant == "19"
	zpolynom = -45.692713833379e12 * #z + 18.790375268505e12 * #z^3 - \
		2.318169487068e12 * #z^5 + 136.186922820e9 * #z^7 - 4.667028938e9 * \
		#z^9 + 104681070 * #z^11 - 1655052 * #z^13 + 19380 * #z^15 - 171 * \
		#z^17 + #z^19
elseif @variant == "20"
	zpolynom = 370.371188237525e12 - 456.927138333790e12 * #z^2 + \
		93.951876342525e12 * #z^4 - 7.727231623560e12 * #z^6 + 340.467307050e9 \
		* #z^8 - 9.334057876e9 * #z^10 + 174468450 * #z^12 - 2364360 * \
		#z^14 + 24225 * #z^16 - 190 * #z^18 + #z^20
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Swiss Knife"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20"
	default = 6
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (-7,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-CompSwissKnifePolynomials {

; Complementary Swiss Knife Polynomials
; jam 8/9/17
; Mathematica:  skp[n_, x_] := Sum[Binomial[n, k]*EulerE[k]*x^(n - k), {k, 0, n}]; 
;				v[n_, x_] := (skp[n, x + 1] - skp[n, x - 1])/2;
;				Expand[Simplify[Table[v[n, x], {n, 0, 20}]]]

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = -2 + 3 * #z^2
elseif @variant == "3"
	zpolynom = -8 * #z + 4 * #z^3
elseif @variant == "4"
	zpolynom = 16 - 20 * #z^2 + 5 * #z^4
elseif @variant == "5"
	zpolynom = 96 * #z - 40 * #z^3 + 6 * #z^5
elseif @variant == "6"
	zpolynom = -272 + 336 * #z^2 - 70 * #z^4 + 7 * #z^6
elseif @variant == "7"
	zpolynom = -2176 * #z + 896 * #z^3 - 112 * #z^5 + 8 * #z^7
elseif @variant == "8"
	zpolynom = 7936 - 9792 * #z^2 + 2016 * #z^4 - 168 * #z^6 + 9 * #z^8
elseif @variant == "9"
	zpolynom = 79360 * #z - 32640 * #z^3 + 4032 * #z^5 - 240 * #z^7 + \
		10 * #z^9
elseif @variant == "10"
	zpolynom = -353792 + 436480 * #z^2 - 89760 * #z^4 + 7392 * #z^6 - \
		330 * #z^8 + 11 * #z^10
elseif @variant == "11"
	zpolynom = -4245504 * #z + 1745920 * #z^3 - 215424 * #z^5 + 12672 * \
		#z^7 - 440 * #z^9 + 12 * #z^11
elseif @variant == "12"
	zpolynom = 22368256 - 27595776 * #z^2 + 5674240 * #z^4 - 466752 * \
		#z^6 + 20592 * #z^8 - 572 * #z^10 + 13 * #z^12
elseif @variant == "13"
	zpolynom = 313155584 * #z - 128780288 * #z^3 + 15887872 * #z^5 - \
		933504 * #z^7 + 32032 * #z^9 - 728 * #z^11 + 14 * #z^13
elseif @variant == "14"
	zpolynom = -1.903757312e9 + 2.348666880e9 * #z^2 - 482926080 * \
		#z^4 + 39719680 * #z^6 - 1750320 * #z^8 + 48048 * #z^10 - 910 * \
		#z^12 + 15 * #z^14
elseif @variant == "15"
	zpolynom = -30.460116992e9 * #z + 12.526223360e9 * #z^3 - 1.545363456e9 * \
		#z^5 + 90787840 * #z^7 - 3111680 * #z^9 + 69888 * #z^11 - 1120 * \
		#z^13 + 16 * #z^15
elseif @variant == "16"
	zpolynom = 209.865342976e9 - 258.910994432e9 * #z^2 + 53.236449280e9 * \
		#z^4 - 4.378529792e9 * #z^6 + 192924160 * #z^8 - 5289856 * #z^10 + \
		99008 * #z^12 - 1360 * #z^14 + 17 * #z^16
elseif @variant == "17"
	zpolynom = 3.777576173568e12 * #z - 1.553465966592e12 * #z^3 + \
		191.651217408e9 * #z^5 - 11.259076608e9 * #z^7 + 385848320 * \
		#z^9 - 8656128 * #z^11 + 137088 * #z^13 - 1632 * #z^15 + 18 * \
		#z^17
elseif @variant == "18"
	zpolynom = -29.088885112832e12 + 35.886973648896e12 * #z^2 - \
		7.378963341312e12 * #z^4 + 606.895521792e9 * #z^6 - 26.740306944e9 * \
		#z^8 + 733111808 * #z^10 - 13705536 * #z^12 + 186048 * #z^14 - \
		1938 * #z^16 + 19 * #z^18
elseif @variant == "19"
	zpolynom = -581.777702256640e12 * #z + 239.246490992640e12 * #z^3 - \
		29.515853365248e12 * #z^5 + 1.733987205120e12 * #z^7 - 59.422904320e9 * \
		#z^9 + 1.332930560e9 * #z^11 - 21085440 * #z^13 + 248064 * #z^15 - \
		2280 * #z^17 + 20 * #z^19
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynoms Comp Swiss Knife"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19"
	default = 10
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (-16,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-HeptanacciPolynomials {

; jam 8/8/17
; Mathematica:  P[z, 0] = 0; P[z, 1] = 0; P[z, 2] = 0; P[z, 3] = 0; P[z, 4] = 0; 
;				P[z, 5] = 0; P[z, 6] = 1; P[z, 7] = z^6;
;				P[z_, n_] := z^6* P[z, n - 1] + z^5*P[z, n - 2] + z^4*P[z, n - 3] + 
;				z^3*P[z, n - 4] + z^2*P[z, n - 5] + z*P[z, n - 6] + 
;				P[z, n - 7];
;				Table[ExpandAll[P[z, n], z], {n, 0, 25}]

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = #z^6
elseif @variant == "3"
	zpolynom = #z^5 + #z^12
elseif @variant == "4"
	zpolynom = #z^4 + 2 * #z^11 + #z^18
elseif @variant == "5"
	zpolynom = #z^3 + 3 * #z^10 + 3 * #z^17 + #z^24
elseif @variant == "6"
	zpolynom = #z^2 + 4 * #z^9 + 6 * #z^16 + 4 * #z^23 + #z^30
elseif @variant == "7"
	zpolynom = #z + 5 * #z^8 + 10 * #z^15 + 10 * #z^22 + 5 * #z^29 + #z^36
elseif @variant == "8"
	zpolynom = 1 + 6 * #z^7 + 15 * #z^14 + 20 * #z^21 + 15 * #z^28 + 6 * \
		#z^35 + #z^42
elseif @variant == "9"
	zpolynom = 7 * #z^6 + 21 * #z^13 + 35 * #z^20 + 35 * #z^27 + 21 * \
		#z^34 + 7 * #z^41 + #z^48
elseif @variant == "10"
	zpolynom = 6 * #z^5 + 28 * #z^12 + 56 * #z^19 + 70 * #z^26 + 56 * \
		#z^33 + 28 * #z^40 + 8 * #z^47 + #z^54
elseif @variant == "11"
	zpolynom = 5 * #z^4 + 33 * #z^11 + 84 * #z^18 + 126 * #z^25 + 126 * \
		#z^32 + 84 * #z^39 + 36 * #z^46 + 9 * #z^53 + #z^60
elseif @variant == "12"
	zpolynom = 4 * #z^3 + 36 * #z^10 + 116 * #z^17 + 210 * #z^24 + 252 * \
		#z^31 + 210 * #z^38 + 120 * #z^45 + 45 * #z^52 + 10 * #z^59 + #z^66
elseif @variant == "13"
	zpolynom = 3 * #z^2 + 37 * #z^9 + 149 * #z^16 + 325 * #z^23 + 462 * \
		#z^30 + 462 * #z^37 + 330 * #z^44 + 165 * #z^51 + 55 * #z^58 + \
		11 * #z^65 + #z^72
elseif @variant == "14"
	zpolynom = 2 * #z + 36 * #z^8 + 180 * #z^15 + 470 * #z^22 + 786 * \
		#z^29 + 924 * #z^36 + 792 * #z^43 + 495 * #z^50 + 220 * #z^57 + \
		66 * #z^64 + 12 * #z^71 + #z^78
elseif @variant == "15"
	zpolynom = 1 + 33 * #z^7 + 206 * #z^14 + 640 * #z^21 + 1251 * #z^28 + \
		1709 * #z^35 + 1716 * #z^42 + 1287 * #z^49 + 715 * #z^56 + 286 * \
		#z^63 + 78 * #z^70 + 13 * #z^77 + #z^84
elseif @variant == "16"
	zpolynom = 28 * #z^6 + 224 * #z^13 + 826 * #z^20 + 1876 * #z^27 + 2954 * \
		#z^34 + 3424 * #z^41 + 3003 * #z^48 + 2002 * #z^55 + 1001 * #z^62 + \
		364 * #z^69 + 91 * #z^76 + 14 * #z^83 + #z^90
elseif @variant == "17"
	zpolynom = 21 * #z^5 + 231 * #z^12 + 1015 * #z^19 + 2667 * #z^26 + 4809 * \
		#z^33 + 6371 * #z^40 + 6426 * #z^47 + 5005 * #z^54 + 3003 * #z^61 + \
		1365 * #z^68 + 455 * #z^75 + 105 * #z^82 + 15 * #z^89 + #z^96
elseif @variant == "18"
	zpolynom = 15 * #z^4 + 224 * #z^11 + 1190 * #z^18 + 3612 * #z^25 + 7420 * \
		#z^32 + 11152 * #z^39 + 12789 * #z^46 + 11430 * #z^53 + 8008 * #z^60 + \
		4368 * #z^67 + 1820 * #z^74 + 560 * #z^81 + 120 * #z^88 + 16 * #z^95 + \
		#z^102
elseif @variant == "19"
	zpolynom = 10 * #z^3 + 206 * #z^10 + 1330 * #z^17 + 4676 * #z^24 + 10906 * \
		#z^31 + 18488 * #z^38 + 23905 * #z^45 + 24210 * #z^52 + 19437 * #z^59 + \
		12376 * #z^66 + 6188 * #z^73 + 2380 * #z^80 + 680 * #z^87 + 136 * \
		#z^94 + 17 * #z^101 + #z^108
elseif @variant == "20"
	zpolynom = 6 * #z^2 + 180 * #z^9 + 1420 * #z^16 + 5796 * #z^23 + 15330 * \
		#z^30 + 29184 * #z^37 + 42273 * #z^44 + 48070 * #z^51 + 43637 * \
		#z^58 + 31812 * #z^65 + 18564 * #z^72 + 8568 * #z^79 + 3060 * \
		#z^86 + 816 * #z^93 + 153 * #z^100 + 18 * #z^107 + #z^114
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Heptanacci"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19" "20"
	default = 8
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (3,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-NorlundPolynomials {

; Norlund Polynomials or Generalized Bernoulli Polynomials
; jam 8/10/17
; Standard Bernoulli polynomials are obtained by setting parameter
; 'Norlund Constant' to one.
; Mathematica:  Expand[Table[ExpandAll[NorlundB[n, a, z], z], {n, 0, 8}]]

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

	complex nor2 = sqr(@norconst)
	complex nor3 = @norconst*nor2
	complex nor4 = @norconst*nor3
	complex nor5 = @norconst*nor4
	complex nor6 = @norconst*nor5
	
	complex norterm2 = 0.25*nor2-@norconst/12
	complex norterm3 = 0.125*(nor3-nor2)
	complex norterm4 = 0.0625*nor4-0.125*nor3+nor2/48+@norconst/120
	complex norterm5 = -0.03125*nor5+5*nor4/48-5*nor3/96-nor2/48
	complex norterm6 = 0.015625*nor6-0.078125*nor5+0.078125*nor4+\
		13*nor3/576-nor2/96-@norconst/252

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)
	
	complex z2 = complex z3 = complex z4 = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "1"
	zpolynom = #z - 0.5*@norconst
elseif @variant == "2"
	zpolynom = sqr(#z) - @norconst*#z + norterm2
elseif @variant == "3"
	zpolynom = #z^3 - 1.5*@norconst*sqr(#z) + 0.75*nor2*#z - 0.25*@norconst*#z + norterm3
elseif @variant == "4"
	z2 = sqr(#z)
	zpolynom = sqr(z2) - 2*@norconst*#z^3 + 1.5*nor2*z2 - 0.5*@norconst*z2 - 0.5*nor3*#z + 0.5*nor2*#z + norterm4
elseif @variant == "5"
	z2 = sqr(#z)
	z3 = #z*z2
	zpolynom = #z^5 - 2.5*@norconst*sqr(z2)+ 2.5*nor2*z3 - 5*@norconst*z3/6 - 1.25*nor3*z2 + 1.25*nor2*z2 + 0.3125*nor4*#z - 0.625*nor3*#z + 5*nor2*#z/48 + @norconst*#z/24 + norterm5
elseif @variant == "6"
	z2 = sqr(#z)
	z3 = #z*z2
	z4 = sqr(z2)
	zpolynom = #z^6 - 3*@norconst*#z^5 + 3.75*nor2*z4 - 1.25*@norconst*z4 - 2.5*nor3*z3 + 2.5*nor2*z3 + 0.9375*nor4*z2 - 1.875*nor3*z2 + 0.3125*nor2*z2 + 0.125*@norconst*z2 - 0.1875*nor5*#z + 0.625*nor4*#z - 0.3125*nor3*#z - 0.125*nor2*#z + norterm6
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Norlund"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "1" "2" "3" "4" "5" "6"
	default = 2
	hint = "This setting selects which polynomial equation to iterate."
endparam
param norconst
	caption = "Norlund Constant"
	default = (1.5,0)
	hint = "This parameter selects which family of Norlund polynomials \
		to iterate.  Setting this parameter to 1.0 results in the ordinary Bernoulli \
		polynomials."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-ZetaPolynomials {

; jam 8/16/17
; See http://www.luschny.de/math/seq/ZetaPolynomials.htm
; Mathematica:  h[n_, z_] := Sum[Sum[Abs[StirlingS1[n, n - i]] * z^(n - k - 1),
;				{i, 0, k}], {k, 0, n - 1}]
; 				zeta[n_, z_] := Sum[Sum[(-1)^v * Binomial[k, v] * h[k + 1, z]/
;				(k + 1)! * (z + v + 1)^n, {v, 0, k}], {k, 0, n}]
;				Simplify[Table[zeta[n, z], {n, 1, 19}]]

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = (-#z + 2 * sqr(#z))/6
elseif @variant == "3"
	zpolynom = (-1 + #z) * #z^2/4
elseif @variant == "4"
	zpolynom = #z * (1 + #z - 9 * #z^2 + 6 * #z^3)/30
elseif @variant == "5"
	zpolynom = #z^2 * (1 + #z - 4 * #z^2 + 2 * #z^3)/12
elseif @variant == "6"
	zpolynom = #z * (-1 - #z + 6 * #z^2 + 6 * #z^3 - 15 * #z^4 + 6 * #z^5)/42
elseif @variant == "7"
	zpolynom = #z^2 * (-2 - 2 * #z + 5 * #z^2 + 5 * #z^3 - 9 * #z^4 + 3 * \
		#z^5)/24
elseif @variant == "8"
	zpolynom = #z * (3 + 3 * #z - 17 * #z^2 - 17 * #z^3 + 25 * #z^4 + 25 * \
		#z^5 - 35 * #z^6 + 10 * #z^7)/90
elseif @variant == "9"
	zpolynom = #z^2 * (3 + 3 * #z - 7 * #z^2 - 7 * #z^3 + 7 * #z^4 + 7 * #z^5 \
		- 8 * #z^6 + 2 * #z^7)/20
elseif @variant == "10"
	zpolynom = #z * (-5 - 5 * #z + 28 * #z^2 + 28 * #z^3 - 38 * #z^4 - 38 * \
		#z^5 + 28 * #z^6 + 28 * #z^7 - 27 * #z^8 + 6 * #z^9)/66
elseif @variant == "11"
	zpolynom = #z^2 * (-10 - 10 * #z + 23 * #z^2 + 23 * #z^3 - 21 * #z^4 - \
		21 * #z^5 + 12 * #z^6 + 12 * #z^7 - 10 * #z^8 + 2 * #z^9)/24
elseif @variant == "12"
	zpolynom = #z * (691 + 691 * #z - 3859 * #z^2 - 3859 * #z^3 + 5150 * #z^4 \
		+ 5150 * #z^5 - 3430 * #z^6 - 3430 * #z^7 + 1575 * #z^8 + 1575 * #z^9 - \
		1155 * #z^10 + 210 * #z^11)/2730
elseif @variant == "13"
	zpolynom = #z^2 * (691 + 691 * #z - 1584 * #z^2 - 1584 * #z^3 + 1419 * #z^4 \
		+ 1419 * #z^5 - 726 * #z^6 - 726 * #z^7 + 275 * #z^8 + 275 * #z^9 - 180 * \
		#z^10 + 30 * #z^11)/420
elseif @variant == "14"
	zpolynom = #z * (-105 - 105 * #z + 586 * #z^2 + 586 * #z^3 - 779 * #z^4 - \
		779 * #z^5 + 508 * #z^6 + 508 * #z^7 - 207 * #z^8 - 207 * #z^9 + 66 * \
		#z^10 + 66 * #z^11 - 39 * #z^12 + 6 * #z^13)/90
elseif @variant == "15"
	zpolynom = #z^2 * (-420 - 420 * #z + 962 * #z^2 + 962 * #z^3 - 858 * #z^4 - \
		858 * #z^5 + 429 * #z^6 + 429 * #z^7 - 143 * #z^8 - 143 * #z^9 + 39 * \
		#z^10 + 39 * #z^11 - 21 * #z^12 + 3 * #z^13)/48
elseif @variant == "16"
	zpolynom = #z * (3617 + 3617 * #z - 20183 * #z^2 - 20183 * #z^3 + 26805 * \
		#z^4 + 26805 * #z^5 - 17395 * #z^6 - 17395 * #z^7 + 6915 * #z^8 + 6915 * \
		#z^9 - 1925 * #z^10 - 1925 * #z^11 + 455 * #z^12 + 455 * #z^13 - 225 * \
		#z^14 + 30 * #z^15)/510
elseif @variant == "17"
	zpolynom = #z^2 * (10851 + 10851 * #z - 24849 * #z^2 - 24849 * #z^3 + 22139 \
		* #z^4 + 22139 * #z^5 - 11011 * #z^6 - 11011 * #z^7 + 3575 * #z^8 + 3575 \
		* #z^9 - 845 * #z^10 - 845 * #z^11 + 175 * #z^12 + 175 * #z^13 - 80 * \
		#z^14 + 10 * #z^15)/180
elseif @variant == "18"
	zpolynom = #z * (-219335 - 219335 * #z + 1223848 * #z^2 + 1223848 * #z^3 - \
		1625012 * #z^4 - 1625012 * #z^5 + 1053304 * #z^6 + 1053304 * #z^7 - \
		416346 * #z^8 - 416346 * #z^9 + 112728 * #z^10 + 112728 * #z^11 - 22932 * \
		#z^12 - 22932 * #z^13 + 4200 * #z^14 + 4200 * #z^15 - 1785 * #z^16 + 210 * \
		#z^17)/3990
elseif @variant == "19"
	zpolynom = #z^2 * (-438670 - 438670 * #z + 1004513 * #z^2 + 1004513 * #z^3 - \
		894727 * #z^4 - 894727 * #z^5 + 444431 * #z^6 + 444431 * #z^7 - 143429 * \
		#z^8 - 143429 * #z^9 + 32929 * #z^10 + 32929 * #z^11 - 5831 * #z^12 - \
		5831 * #z^13 + 952 * #z^14 + 952 * #z^15 - 378 * #z^16 + 42 * #z^17)/840
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Zeta"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19"
	default = 7
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (4,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-HarmonicPolynomials {

; Harmonic polynomials
; These are not harmonic polynomials in the traditional mathematical sense of "harmonic",
; but rather related to the harmonic numbers and zeta polynomials.
; See http://www.luschny.de/math/seq/ZetaPolynomials.htm
; Mathematica:  h[n_, z_] := Sum[Sum[Abs[StirlingS1[n, n - i]] * z^(n - k - 1),
;				{i, 0, k}], {k, 0, n - 1}]
;				Table[h[n, z], {n, 1, 20}]
; jam 8/17/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "2"
	zpolynom = 6 + 4 * #z + #z^2
elseif @variant == "3"
	zpolynom = 24 + 18 * #z + 7 * #z^2 + #z^3
elseif @variant == "4"
	zpolynom = 120 + 96 * #z + 46 * #z^2 + 11 * #z^3 + #z^4
elseif @variant == "5"
	zpolynom = 720 + 600 * #z + 326 * #z^2 + 101 * #z^3 + 16 * #z^4 + #z^5
elseif @variant == "6"
	zpolynom = 5040 + 4320 * #z + 2556 * #z^2 + 932 * #z^3 + 197 * #z^4 + \
		22 * #z^5 + #z^6
elseif @variant == "7"
	zpolynom = 40320 + 35280 * #z + 22212 * #z^2 + 9080 * #z^3 + 2311 * \
		#z^4 + 351 * #z^5 + 29 * #z^6 + #z^7
elseif @variant == "8"
	zpolynom = 362880 + 322560 * #z + 212976 * #z^2 + 94852 * #z^3 + 27568 * \
		#z^4 + 5119 * #z^5 + 583 * #z^6 + 37 * #z^7 + #z^8
elseif @variant == "9"
	zpolynom = 3628800 + 3265920 * #z + 2239344 * #z^2 + 1066644 * #z^3 + \
		342964 * #z^4 + 73639 * #z^5 + 10366 * #z^6 + 916 * #z^7 + 46 * \
		#z^8 + #z^9
elseif @variant == "10"
	zpolynom = 39916800 + 36288000 * #z + 25659360 * #z^2 + 12905784 * #z^3 + \
		4496284 * #z^4 + 1079354 * #z^5 + 177299 * #z^6 + 19526 * #z^7 + \
		1376 * #z^8 + 56 * #z^9 + #z^10
elseif @variant == "11"
	zpolynom = 479001600 + 439084800 * #z + 318540960 * #z^2 + 167622984 * \
		#z^3 + 62364908 * #z^4 + 16369178 * #z^5 + 3029643 * #z^6 + 392085 * \
		#z^7 + 34662 * #z^8 + 1992 * #z^9 + 67 * #z^10 + #z^11
elseif @variant == "12"
	zpolynom = 6.227020800e9 + 5.748019200e9 * #z + 4.261576320e9 * #z^2 + \
		2.330016768e9 * #z^3 + 916001880 * #z^4 + 258795044 * #z^5 + 52724894 * \
		#z^6 + 7734663 * #z^7 + 808029 * #z^8 + 58566 * #z^9 + 2796 * #z^10 + \
		79 * #z^11 + #z^12
elseif @variant == "13"
	zpolynom = 87.178291200e9 + 80.951270400e9 * #z + 61.148511360e9 * #z^2 + \
		34.551794304e9 * #z^3 + 14.238041208e9 * #z^4 + 4.280337452e9 * #z^5 + \
		944218666 * #z^6 + 153275513 * #z^7 + 18239040 * #z^8 + 1569387 * \
		#z^9 + 94914 * #z^10 + 3823 * #z^11 + 92 * #z^12 + #z^13
elseif @variant == "14"
	zpolynom = 1.307674368000e12 + 1.220496076800e12 * #z + 937.030429440e9 * \
		#z^2 + 544.873631616e9 * #z^3 + 233.884371216e9 * #z^4 + 74.162765536e9 * \
		#z^5 + 17.499398776e9 * #z^6 + 3.090075848e9 * #z^7 + 408622073 * #z^8 + \
		40210458 * #z^9 + 2898183 * #z^10 + 148436 * #z^11 + 5111 * #z^12 + 106 * \
		#z^13 + #z^14
elseif @variant == "15"
	zpolynom = 20.922789888000e12 + 19.615115520000e12 * #z + 15.275952518400e12 * \
		#z^2 + 9.110134903680e12 * #z^3 + 4.053139199856e12 * #z^4 + \
		1.346325854256e12 * #z^5 + 336.653747176e9 * #z^6 + 63.850536496e9 * \
		#z^7 + 9.219406943e9 * #z^8 + 1.011778943e9 * #z^9 + 83683203 * #z^10 + \
		5124723 * #z^11 + 225101 * #z^12 + 6701 * #z^13 + 121 * #z^14 + #z^15
elseif @variant == "16"
	zpolynom = 355.687428096000e12 + 334.764638208000e12 * #z + \
		264.030355814400e12 * #z^2 + 161.038110977280e12 * #z^3 +\
		73.960362101376e12 * #z^4 + 25.594352867952e12 * #z^5 + \
		6.732785809072e12 * #z^6 + 1.358262331112e12 * #z^7 + 211.361047584e9 *\
		#z^8 + 25.407870031e9 * #z^9 + 2.350710191e9 * #z^10 + 165678771 * \
		#z^11 + 8726339 * #z^12 + 332317 * #z^13 + 8637 * #z^14 + 137 * #z^15 + \
		#z^16
elseif @variant == "17"
	zpolynom = 6.402373705728000e15 + 6.046686277632000e15 * #z + \
		4.823280687052800e15 * #z^2 + 3.001678242428160e15 * #z^3 + \
		1.418364266700672e15 * #z^4 + 509.064360856560e12 * #z^5 + \
		140.051711622176e12 * #z^6 + 29.823245437976e12 * #z^7 + \
		4.951400140040e12 * #z^8 + 643.294838111e9 * #z^9 + 65.369943278e9 * \
		#z^10 + 5.167249298e9 * #z^11 + 314026534 * #z^12 + 14375728 * #z^13 + \
		479146 * #z^14 + 10966 * #z^15 + 154 * #z^16 + #z^17
elseif @variant == "18"
	zpolynom = 121.645100408832000e15 + 115.242726703104000e15 * #z + \
		92.865738644582400e15 * #z^2 + 58.853489050759680e15 * #z^3 + \
		28.532235043040256e15 * #z^4 + 10.581522762118752e15 * #z^5 + \
		3.029995170055728e15 * #z^6 + 676.870129505744e12 * #z^7 + \
		118.948447958696e12 * #z^8 + 16.530707226038e12 * #z^9 + 1.819953817115e12 * \
		#z^10 + 158.380430642e9 * #z^11 + 10.819726910e9 * #z^12 + 572789638 * \
		#z^13 + 23000356 * #z^14 + 676534 * #z^15 + 13738 * #z^16 + 172 * #z^17 + #z^18
elseif @variant == "19"
	zpolynom = 2.432902008176640000e18 + 2.311256907767808000e18 * #z + \
		1.879691760950169600e18 * #z^2 + 1.211082030609016320e18 * #z^3 + \
		600.965954868524544e15 * #z^4 + 229.581167523296544e15 * #z^5 + \
		68.151430993177584e15 * #z^6 + 15.890527630664864e15 * #z^7 + \
		2.936890640720968e15 * #z^8 + 433.031885253418e12 * #z^9 + \
		51.109829751223e12 * #z^10 + 4.829181999313e12 * #z^11 + \
		363.955241932e9 * #z^12 + 21.702730032e9 * #z^13 + 1.009796402e9 * \
		#z^14 + 35854502 * #z^15 + 937556 * #z^16 + 17006 * #z^17 + 191 * \
		#z^18 + #z^19
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "Polynomials Harmonic"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 1000

param variant
	caption = "Polynomial Variant"
	enum = "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" \
		"13" "14" "15" "16" "17" "18" "19"
	default = 3
	hint = "This setting selects which polynomial equation to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (-6.6,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-polySeriesExponentials {

; Partial series expansions of the exponential function
; Mathematica:  expn[n_, z_] := Normal[Series[Exp[z], {z, 0, n}]]
; jam 8/24/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	halfpi = #pi/2

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @variant == "3"
	zpolynom = 1 + #z + 0.5*#z^2 + #z^3/6
elseif @variant == "4"
	zpolynom = 1 + #z + 0.5*#z^2 + #z^3/6 + #z^4/24
elseif @variant == "5"
	zpolynom = 1 + #z + 0.5*#z^2 + #z^3/6 + #z^4/24 + #z^5/120
elseif @variant == "6"
	zpolynom = 1 + #z + 0.5*#z^2 + #z^3/6 + #z^4/24 + #z^5/120 + \
		#z^6/720
elseif @variant == "7"
	zpolynom = 1 + #z + 0.5*#z^2 + #z^3/6 + #z^4/24 + #z^5/120 + \
		#z^6/720 + #z^7/5040
elseif @variant == "8"
	zpolynom = 1 + #z + 0.5*#z^2 + #z^3/6 + #z^4/24 + #z^5/120 + \
		#z^6/720 + #z^7/5040 + #z^8/40320
endif ; @variant

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			zpolynom = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "PolySeries Exponential"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Series Variant"
	enum = "3" "4" "5" "6" "7" "8"
	default = 3
	hint = "This setting selects the number of terms in the series expansion \
		of the function to iterate."
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-PolySeqPolygonal {

; Repeated iteration of polynomials based on sequences of polygonal numbers
; Mathematica:  Table[PolygonalNumber[n, j], {j, 0, 20}]
; for the initial 20 members of the sequence of n-gonal numbers.
; jam 8/29/17

; The earliest reference I can find (2011) of the use of the underlying
; algorithms implemented in these formulas can be found on Fractal Forums here:
; http://www.fractalforums.com/new-theories-and-research/very-simple-formula-for-fractal-patterns/

; Around the same time, Sam Monier described and used the labs() and similar functions
; to produce dense fractal patterns (see description here:
; http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227).
; These and other 'Ducky' type formulas had a long history of use
; in Fractal Explorer, as described by Ed Algra at the Monier link cited above.

; Otto Magus used these ideas together in his wonderful set of polynomial
; formulas found in om.ufm.  Well worth exploring!  These formed the
; basis for these current formulas.

; Having long worked with polynomial formulas myself (e.g., see jam.ufm),
; and inspired by Otto's work, I have produced these extensions and
; elaborations, with various modifications, tweaks, and bells & whistles, 
; along with new polynomials, functions, algorithms, and variants.
; I've decided that the new functionality is significant enough to
; warrant sharing in the public database.  Enjoy!

global:
	float zadjust = @zadjustment/100
	float halfpi = #pi/2
	int gindex = 0 ; loop index, global section
	int maxterms = 17 ; maximum number of sequence terms allowed
	complex sequence[17] ; for holding members of the defining sequence
	sequence[0] = 0, sequence[1] = 1
	if @variant == "3" ; triangular numbers
		sequence[2] = 3, sequence[3] = 6, sequence[4] = 10
		sequence[5] = 15, sequence[6] = 21, sequence[7] = 28
		sequence[8] = 36, sequence[9] = 45, sequence[10] = 55
		sequence[11] = 66, sequence[12] = 78, sequence[13] = 91
		sequence[14] = 105, sequence[15] = 120, sequence[16] = 136
	elseif @variant == "4" ; square numbers
		sequence[2] = 4, sequence[3] = 9, sequence[4] = 16
		sequence[5] = 25, sequence[6] = 36, sequence[7] = 49
		sequence[8] = 64, sequence[9] = 81, sequence[10] = 100
		sequence[11] = 121, sequence[12] = 144, sequence[13] = 169
		sequence[14] = 196, sequence[15] = 225, sequence[16] = 256
	elseif @variant == "5" ; pentagonal numbers
		sequence[2] = 5, sequence[3] = 12, sequence[4] = 22
		sequence[5] = 35, sequence[6] = 51, sequence[7] = 70
		sequence[8] = 92, sequence[9] =117, sequence[10] = 145
		sequence[11] = 176, sequence[12] = 210, sequence[13] = 247
		sequence[14] = 287, sequence[15] = 330, sequence[16] = 376
	elseif @variant == "6" ; hexagonal numbers
		sequence[2] = 6, sequence[3] = 15, sequence[4] = 28
		sequence[5] = 45, sequence[6] = 66, sequence[7] = 91
		sequence[8] = 120, sequence[9] = 153, sequence[10] = 190
		sequence[11] = 231, sequence[12] = 276, sequence[13] = 325
		sequence[14] = 378, sequence[15] = 435, sequence[16] = 496
	elseif @variant == "7" ; heptagonal numbers
		sequence[2] = 7, sequence[3] = 18, sequence[4] = 34
		sequence[5] = 55, sequence[6] = 81, sequence[7] = 112
		sequence[8] = 148, sequence[9] = 189, sequence[10] = 235
		sequence[11] = 286, sequence[12] = 342, sequence[13] = 403
		sequence[14] = 469, sequence[15] = 540, sequence[16] = 616
	elseif @variant == "8" ; octagonal numbers
		sequence[2] = 8, sequence[3] = 21, sequence[4] = 40
		sequence[5] = 65, sequence[6] = 96, sequence[7] = 133
		sequence[8] = 176, sequence[9] = 225, sequence[10] = 280
		sequence[11] = 341, sequence[12] = 408, sequence[13] = 481
		sequence[14] = 560, sequence[15] = 645, sequence[16] = 736
	elseif @variant == "9" ; nonagonal numbers
		sequence[2] = 9, sequence[3] = 24, sequence[4] = 46
		sequence[5] = 75, sequence[6] = 111, sequence[7] = 154
		sequence[8] = 204, sequence[9] = 261, sequence[10] = 325
		sequence[11] = 396, sequence[12] = 474, sequence[13] = 559
		sequence[14] = 651, sequence[15] = 750, sequence[16] = 856
	elseif @variant == "10" ; decagonal numbers
		sequence[2] = 10, sequence[3] = 27, sequence[4] = 52
		sequence[5] = 85, sequence[6] = 126, sequence[7] = 175
		sequence[8] = 232, sequence[9] = 297, sequence[10] = 370
		sequence[11] = 451, sequence[12] = 540, sequence[13] = 637
		sequence[14] = 742, sequence[15] = 855, sequence[16] = 976
	elseif @variant == "11" ; undecagonal numbers
		sequence[2] = 11, sequence[3] = 30, sequence[4] = 58
		sequence[5] = 95, sequence[6] = 141, sequence[7] = 196
		sequence[8] = 260, sequence[9] = 333, sequence[10] = 415
		sequence[11] = 506, sequence[12] = 606, sequence[13] = 715
		sequence[14] = 833, sequence[15] = 960, sequence[16] = 1096
	elseif @variant == "12" ; dodecagonal numbers
		sequence[2] = 12, sequence[3] = 33, sequence[4] = 64
		sequence[5] = 105, sequence[6] = 156, sequence[7] = 217
		sequence[8] = 288, sequence[9] = 369, sequence[10] = 460
		sequence[11] = 561, sequence[12] = 672, sequence[13] = 793
		sequence[14] = 924, sequence[15] = 1065, sequence[16] = 1216
	endif ; @variant

	gindex = @seqterms + 1
	while gindex < maxterms
		sequence[gindex] = 0 ; set unused terms to zero
		gindex = gindex + 1
	endwhile ; gindex

init:
	int cindex = int iindex = 0
	float xz = float yz = 0.0
	float magn = 0.0
	complex zpolynom = (0,0)

	if @innerpixfunc == "ident"
		#z = #pixel
	elseif @innerpixfunc == "sin" ; sine function
		#z = sin(#pixel)
	elseif @innerpixfunc == "cos" ; cosine
		#z = cos(#pixel)
	elseif @innerpixfunc == "tan" ; tangent
		#z = tan(#pixel)
	elseif @innerpixfunc == "cot" ; cotangent
		#z = cotan(#pixel)
	elseif @innerpixfunc == "sec" ; secant
		#z = 1/cos(#pixel)
	elseif @innerpixfunc == "csc" ; cosecant
		#z = 1/sin(#pixel)
	elseif @innerpixfunc == "ver" ; versine
		#z = 1 - cos(#pixel)
	elseif @innerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#pixel)
	elseif @innerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#pixel)
	elseif @innerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#pixel)
	elseif @innerpixfunc == "exs" ; exsecant
		#z = 1/cos(#pixel) - 1
	elseif @innerpixfunc == "exc" ; excosecant
		#z = 1/sin(#pixel) - 1
	elseif @innerpixfunc == "crd" ; chord
		#z = 2 * sin(#pixel/2)
	elseif @innerpixfunc == "asin" ; arcsine
		#z =  asin(#pixel - trunc(#pixel)) 
	elseif @innerpixfunc == "acos" ; arccosine
		#z = acos(#pixel - trunc(#pixel))
	elseif @innerpixfunc == "atan" ; arctangent
		#z = atan(#pixel)
	elseif @innerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#pixel)
	elseif @innerpixfunc == "asec" ; arcsecant
		#z = acos(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#pixel - trunc(1/#pixel))
	elseif @innerpixfunc == "aver" ; arcversine
		#z = acos(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #pixel - trunc(1-#pixel))
	elseif @innerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #pixel - trunc(1+#pixel))
	elseif @innerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#pixel+1)) - trunc( (1/(#pixel+1)) ) )
	elseif @innerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #pixel/2 - trunc(#pixel/2) )
	elseif @innerpixfunc == "exp" ; exponential
		#z = exp(#pixel)
	elseif @innerpixfunc == "exp(-pixel)" ; negative exponential
		#z = exp(-#pixel)
	elseif @innerpixfunc == "exp(1/pixel)" ; recip exponential
		#z = exp(1/#pixel)
	elseif @innerpixfunc == "exp(-1/pixel)" ; neg recip exponential
		#z = exp(-1/#pixel)
	elseif @innerpixfunc == "exp(pixel^2)" ; pix^2 exponential
		#z = exp(sqr(#pixel))
	elseif @innerpixfunc == "exp(-pixel^2)" ; -pix^2 exponential
		#z = exp(-sqr(#pixel))
	elseif @innerpixfunc == "exp(1/pixel^2)" ; recip pix^2 exponential
		#z = exp(1/sqr(#pixel))
	elseif @innerpixfunc == "exp(-1/pixel^2)" ; -recip pix^2 exponential
		#z = exp(-1/sqr(#pixel))
	elseif @innerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#pixel)
	elseif @innerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#pixel)
	elseif @innerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#pixel)
	elseif @innerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#pixel)
	elseif @innerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#pixel)
	elseif @innerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#pixel)
	elseif @innerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#pixel)
	elseif @innerpixfunc == "sqr" ; square
		#z = sqr(#pixel)
	elseif @innerpixfunc == "sqrt" ; square root
		#z = sqrt(#pixel)
	elseif @innerpixfunc == "power" ; power
		#z = #pixel^@innerpixpower
	elseif @innerpixfunc == "log" ; logarithm
		#z = log(#pixel)
	elseif @innerpixfunc == "log(-pixel)" ;
		#z = log(-#pixel)
	elseif @innerpixfunc == "log(1/pixel)" ;
		#z = log(1/#pixel)
	elseif @innerpixfunc == "log(-1/pixel)" ;
		#z = log(-1/#pixel)
	elseif @innerpixfunc == "1/pixel" ; reciprocal
		#z = 1/#pixel
	elseif @innerpixfunc == "absolute value" ; absolute value
		#z = abs(#pixel)
	elseif @innerpixfunc == "conjugation" ; conjugate
		#z = conj(#pixel)
	elseif @innerpixfunc == "flip" ; flip
		#z = flip(#pixel)
	elseif @innerpixfunc == "ceiling" ; ceiling
		#z = ceil(#pixel)
	elseif @innerpixfunc == "floor" ; floor
		#z = floor(#pixel)
	elseif @innerpixfunc == "truncation" ; truncation
		#z = trunc(#pixel)
	elseif @innerpixfunc == "rounding" ; rounding
		#z = round(#pixel)
	elseif @innerpixfunc == "asin 2" ; arcsine
		#z = asin(#pixel)
	elseif @innerpixfunc == "acos 2" ; arccosine
		#z = acos(#pixel)
	elseif @innerpixfunc == "atan 2" ; arctangent
		#z = atan2(#pixel)
	elseif @innerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#pixel)
	elseif @innerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#pixel)
	elseif @innerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#pixel)
	elseif @innerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #pixel)
	elseif @innerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #pixel)
	elseif @innerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #pixel)
	elseif @innerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #pixel)
	elseif @innerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#pixel+1)))
	elseif @innerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#pixel+1)))
	elseif @innerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #pixel/2 )
	elseif @innerpixfunc == "log(pixel^2)" ; 
		#z = log(sqr(#pixel))
	elseif @innerpixfunc == "log(-pixel^2)" ; 
		#z = log(-sqr(#pixel))
	elseif @innerpixfunc == "log(1/pixel^2)" ; 
		#z = log(1/sqr(#pixel))
	elseif @innerpixfunc == "log(-1/pixel^2)" ; 
		#z = log(-1/sqr(#pixel))
	elseif @innerpixfunc == "log log" ; 
		#z = log( log(#pixel) )
	elseif @innerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#pixel) )
	elseif @innerpixfunc == "pixel^pixel" ; 
		#z = #pixel^#pixel
	elseif @innerpixfunc == "pixel^pixel^pixel" ; 
		#z = #pixel^(#pixel^#pixel)
	elseif @innerpixfunc == "constant^pixel" ; 
		#z = @pbase^#pixel
	elseif @innerpixfunc == "constant^pixel^pixel" ; 
		#z = @pbase^(#pixel^#pixel)
	endif ; @innerpixfunc

if @innerpixfunc != "ident"
	#z = @pixmultiplier1 * #z + @pixoffset1
	if @outerpixfunc == "ident"
		#z = #z
	elseif @outerpixfunc == "sin" ; sine function
		#z = sin(#z)
	elseif @outerpixfunc == "cos" ; cosine
		#z = cos(#z)
	elseif @outerpixfunc == "tan" ; tangent
		#z = tan(#z)
	elseif @outerpixfunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @outerpixfunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @outerpixfunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @outerpixfunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @outerpixfunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @outerpixfunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @outerpixfunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @outerpixfunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @outerpixfunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @outerpixfunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @outerpixfunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @outerpixfunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @outerpixfunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @outerpixfunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @outerpixfunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @outerpixfunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @outerpixfunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @outerpixfunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @outerpixfunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @outerpixfunc == "exp" ; exponential
		#z = exp(#z)
	elseif @outerpixfunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @outerpixfunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @outerpixfunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @outerpixfunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @outerpixfunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @outerpixfunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @outerpixfunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @outerpixfunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @outerpixfunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @outerpixfunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @outerpixfunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @outerpixfunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @outerpixfunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @outerpixfunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @outerpixfunc == "sqr" ; square
		#z = sqr(#z)
	elseif @outerpixfunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @outerpixfunc == "power" ; power
		#z = #z^@cyclepower
	elseif @outerpixfunc == "log" ; logarithm
		#z = log(#z)
	elseif @outerpixfunc == "log(-z)" ;
		#z = log(-#z)
	elseif @outerpixfunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @outerpixfunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @outerpixfunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @outerpixfunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @outerpixfunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @outerpixfunc == "flip" ; flip
		#z = flip(#z)
	elseif @outerpixfunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @outerpixfunc == "floor" ; floor
		#z = floor(#z)
	elseif @outerpixfunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @outerpixfunc == "rounding" ; rounding
		#z = round(#z)
	elseif @outerpixfunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @outerpixfunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @outerpixfunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @outerpixfunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @outerpixfunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @outerpixfunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @outerpixfunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @outerpixfunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @outerpixfunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @outerpixfunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @outerpixfunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @outerpixfunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @outerpixfunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @outerpixfunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @outerpixfunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @outerpixfunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @outerpixfunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @outerpixfunc == "log log" ; 
		#z = log( log(#z) )
	elseif @outerpixfunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @outerpixfunc == "z^z" ; 
		#z = #z^#z
	elseif @outerpixfunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @outerpixfunc == "constant^z" ; 
		#z = @pbase2^#z
	elseif @outerpixfunc == "constant^z^z" ; 
		#z = @pbase2^(#z^#z)
	endif ; @outerpixfunc
endif ; @innerpixfunc

if (@outerpixfunc != "ident") && (@innerpixfunc != "ident")
	#z = @pixmultiplier2 * #z + @pixoffset2
endif ; (@outerpixfunc

loop:
if cindex < @cycles
	cindex = cindex + 1 ; increment cycle index

	if (@cyclefunc != 0) && @absolute
		#z = abs(#z)
	endif ; @cyclefunc

	if @cyclefunc == "ident"
		#z = #z
	elseif @cyclefunc == "sin" ; sine function
		#z = sin(#z)
	elseif @cyclefunc == "cos" ; cosine
		#z = cos(#z)
	elseif @cyclefunc == "tan" ; tangent
		#z = tan(#z)
	elseif @cyclefunc == "cot" ; cotangent
		#z = cotan(#z)
	elseif @cyclefunc == "sec" ; secant
		#z = 1/cos(#z)
	elseif @cyclefunc == "csc" ; cosecant
		#z = 1/sin(#z)
	elseif @cyclefunc == "ver" ; versine
		#z = 1 - cos(#z)
	elseif @cyclefunc == "vcs" ; vercosine
		#z = 1 + cos(#z)
	elseif @cyclefunc == "cvs" ; coversine
		#z = 1 - sin(#z)
	elseif @cyclefunc == "cvc" ; covercosine
		#z = 1 + sin(#z)
	elseif @cyclefunc == "exs" ; exsecant
		#z = 1/cos(#z) - 1
	elseif @cyclefunc == "exc" ; excosecant
		#z = 1/sin(#z) - 1
	elseif @cyclefunc == "crd" ; chord
		#z = 2 * sin(#z/2)
	elseif @cyclefunc == "asin" ; arcsine
		#z =  asin(#z - trunc(#z)) 
	elseif @cyclefunc == "acos" ; arccosine
		#z = acos(#z - trunc(#z))
	elseif @cyclefunc == "atan" ; arctangent
		#z = atan(#z)
	elseif @cyclefunc == "acot" ; arccotangent
		#z = halfpi - atan(#z)
	elseif @cyclefunc == "asec" ; arcsecant
		#z = acos(1/#z - trunc(1/#z))
	elseif @cyclefunc == "acsc" ; arccosecant
		#z = asin(1/#z - trunc(1/#z))
	elseif @cyclefunc == "aver" ; arcversine
		#z = acos(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "avcs" ; arcvercosine
		#z = acos(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "acvs" ; arccoversine
		#z = asin(1 - #z - trunc(1-#z))
	elseif @cyclefunc == "acvc" ; arccovercosine
		#z = asin(1 + #z - trunc(1+#z))
	elseif @cyclefunc == "aexs" ; arcexsecant
		#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "aexc" ; arcexcosecant
		#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
	elseif @cyclefunc == "acrd" ; arcchord
		#z = 2 * asin( #z/2 - trunc(#z/2) )
	elseif @cyclefunc == "exp" ; exponential
		#z = exp(#z)
	elseif @cyclefunc == "exp(-z)" ; negative exponential
		#z = exp(-#z)
	elseif @cyclefunc == "exp(1/z)" ; recip exponential
		#z = exp(1/#z)
	elseif @cyclefunc == "exp(-1/z)" ; neg recip exponential
		#z = exp(-1/#z)
	elseif @cyclefunc == "exp(z^2)" ; z^2 exponential
		#z = exp(sqr(#z))
	elseif @cyclefunc == "exp(-z^2)" ; -z^2 exponential
		#z = exp(-sqr(#z))
	elseif @cyclefunc == "exp(1/z^2)" ; recip z^2 exponential
		#z = exp(1/sqr(#z))
	elseif @cyclefunc == "exp(-1/z^2)" ; -recip z^2 exponential
		#z = exp(-1/sqr(#z))
	elseif @cyclefunc == "sinh" ; hyperbolic sine
		#z = sinh(#z)
	elseif @cyclefunc == "asinh" ; inverse hyperbolic sine
		#z = asinh(#z)
	elseif @cyclefunc == "cosh" ; hyperbolic cosine
		#z = cosh(#z)
	elseif @cyclefunc == "acosh" ; inverse hyperbolic cosine
		#z = acosh(#z)
	elseif @cyclefunc == "tanh" ; hyperbolic tangent
		#z = tanh(#z)
	elseif @cyclefunc == "atanh" ; inverse hyperbolic tangent
		#z = atanh(#z)
	elseif @cyclefunc == "cotanh" ; hyperbolic cotangent
		#z = cotanh(#z)
	elseif @cyclefunc == "sqr" ; square
		#z = sqr(#z)
	elseif @cyclefunc == "sqrt" ; square root
		#z = sqrt(#z)
	elseif @cyclefunc == "power" ; power
		#z = #z^@cyclepower
	elseif @cyclefunc == "log" ; logarithm
		#z = log(#z)
	elseif @cyclefunc == "log(-z)" ;
		#z = log(-#z)
	elseif @cyclefunc == "log(1/z)" ;
		#z = log(1/#z)
	elseif @cyclefunc == "log(-1/z)" ;
		#z = log(-1/#z)
	elseif @cyclefunc == "1/z" ; reciprocal
		#z = 1/#z
	elseif @cyclefunc == "absolute value" ; absolute value
		#z = abs(#z)
	elseif @cyclefunc == "conjugation" ; conjugate
		#z = conj(#z)
	elseif @cyclefunc == "flip" ; flip
		#z = flip(#z)
	elseif @cyclefunc == "ceiling" ; ceiling
		#z = ceil(#z)
	elseif @cyclefunc == "floor" ; floor
		#z = floor(#z)
	elseif @cyclefunc == "truncation" ; truncation
		#z = trunc(#z)
	elseif @cyclefunc == "rounding" ; rounding
		#z = round(#z)
	elseif @cyclefunc == "asin 2" ; arcsine
		#z = asin(#z)
	elseif @cyclefunc == "acos 2" ; arccosine
		#z = acos(#z)
	elseif @cyclefunc == "atan 2" ; arctangent
		#z = atan2(#z)
	elseif @cyclefunc == "acot 2" ; arccotangent
		#z = halfpi - atan2(#z)
	elseif @cyclefunc == "asec 2" ; arcsecant
		#z = acos(1/#z)
	elseif @cyclefunc == "acsc 2" ; arccosecant
		#z = asin(1/#z)
	elseif @cyclefunc == "aver 2" ; arcversine
		#z = acos(1 - #z)
	elseif @cyclefunc == "avcs 2" ; arcvercosine
		#z = acos(1 + #z)
	elseif @cyclefunc == "acvs 2" ; arccoversine
		#z = asin(1 - #z)
	elseif @cyclefunc == "acvc 2" ; arccovercosine
		#z = asin(1 + #z)
	elseif @cyclefunc == "aexs 2" ; arcexsecant
		#z = acos( (1/(#z+1)))
	elseif @cyclefunc == "aexc 2" ; arcexcosecant
		#z = asin( (1/(#z+1)))
	elseif @cyclefunc == "acrd 2" ; arcchord
		#z = 2 * asin( #z/2 )
	elseif @cyclefunc == "log(z^2)" ; 
		#z = log(sqr(#z))
	elseif @cyclefunc == "log(-z^2)" ; 
		#z = log(-sqr(#z))
	elseif @cyclefunc == "log(1/z^2)" ; 
		#z = log(1/sqr(#z))
	elseif @cyclefunc == "log(-1/z^2)" ; 
		#z = log(-1/sqr(#z))
	elseif @cyclefunc == "log log" ; 
		#z = log( log(#z) )
	elseif @cyclefunc == "exp(exp)" ; 
		#z = exp( exp(#z) )
	elseif @cyclefunc == "z^z" ; 
		#z = #z^#z
	elseif @cyclefunc == "z^z^z" ; 
		#z = #z^(#z^#z)
	elseif @cyclefunc == "constant^z" ; 
		#z = @cbase^#z
	elseif @cyclefunc == "constant^z^z" ; 
		#z = @cbase^(#z^#z)
	endif ; @cyclefunc

	iindex = 0 ; reset iterations index
	if @seqreverse ; and reset sequence index
		seqindex = @iterations
	else
		seqindex = 0
	endif ; @seqreverse	
	while iindex < @iterations
		iindex = iindex + 1 ; increment iteration index

		if @innerzfunc == "ident"
			#z = #z
		elseif @innerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @innerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @innerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @innerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @innerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @innerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @innerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @innerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @innerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @innerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @innerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @innerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @innerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @innerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @innerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @innerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @innerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @innerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @innerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @innerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @innerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @innerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @innerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @innerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @innerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @innerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @innerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @innerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @innerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @innerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @innerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @innerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @innerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @innerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @innerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @innerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @innerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @innerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @innerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @innerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @innerzfunc == "power" ; power
			#z = #z^@innerzpower
		elseif @innerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @innerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @innerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @innerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @innerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @innerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @innerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @innerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @innerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @innerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @innerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @innerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @innerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @innerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @innerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @innerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @innerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @innerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @innerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @innerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @innerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @innerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @innerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @innerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @innerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @innerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @innerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @innerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @innerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @innerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @innerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @innerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @innerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @innerzfunc == "constant^z" ; 
			#z = @izbase^#z
		elseif @innerzfunc == "constant^z^z" ; 
			#z = @izbase^(#z^#z)
		endif ; @innerzfunc

if @innerzfunc != "ident"
		#z = @izmultiplier * #z + @izoffset
		if @outerzfunc == "ident"
			#z = #z
		elseif @outerzfunc == "sin" ; sine function
			#z = sin(#z)
		elseif @outerzfunc == "cos" ; cosine
			#z = cos(#z)
		elseif @outerzfunc == "tan" ; tangent
			#z = tan(#z)
		elseif @outerzfunc == "cot" ; cotangent
			#z = cotan(#z)
		elseif @outerzfunc == "sec" ; secant
			#z = 1/cos(#z)
		elseif @outerzfunc == "csc" ; cosecant
			#z = 1/sin(#z)
		elseif @outerzfunc == "ver" ; versine
			#z = 1 - cos(#z)
		elseif @outerzfunc == "vcs" ; vercosine
			#z = 1 + cos(#z)
		elseif @outerzfunc == "cvs" ; coversine
			#z = 1 - sin(#z)
		elseif @outerzfunc == "cvc" ; covercosine
			#z = 1 + sin(#z)
		elseif @outerzfunc == "exs" ; exsecant
			#z = 1/cos(#z) - 1
		elseif @outerzfunc == "exc" ; excosecant
			#z = 1/sin(#z) - 1
		elseif @outerzfunc == "crd" ; chord
			#z = 2 * sin(#z/2)
		elseif @outerzfunc == "asin" ; arcsine
			#z =  asin(#z - trunc(#z)) 
		elseif @outerzfunc == "acos" ; arccosine
			#z = acos(#z - trunc(#z))
		elseif @outerzfunc == "atan" ; arctangent
			#z = atan(#z)
		elseif @outerzfunc == "acot" ; arccotangent
			#z = halfpi - atan(#z)
		elseif @outerzfunc == "asec" ; arcsecant
			#z = acos(1/#z - trunc(1/#z))
		elseif @outerzfunc == "acsc" ; arccosecant
			#z = asin(1/#z - trunc(1/#z))
		elseif @outerzfunc == "aver" ; arcversine
			#z = acos(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "avcs" ; arcvercosine
			#z = acos(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "acvs" ; arccoversine
			#z = asin(1 - #z - trunc(1-#z))
		elseif @outerzfunc == "acvc" ; arccovercosine
			#z = asin(1 + #z - trunc(1+#z))
		elseif @outerzfunc == "aexs" ; arcexsecant
			#z = acos( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "aexc" ; arcexcosecant
			#z = asin( (1/(#z+1)) - trunc( (1/(#z+1)) ) )
		elseif @outerzfunc == "acrd" ; arcchord
			#z = 2 * asin( #z/2 - trunc(#z/2) )
		elseif @outerzfunc == "exp" ; exponential
			#z = exp(#z)
		elseif @outerzfunc == "exp(-z)" ; negative exponential
			#z = exp(-#z)
		elseif @outerzfunc == "exp(1/z)" ; recip exponential
			#z = exp(1/#z)
		elseif @outerzfunc == "exp(-1/z)" ; neg recip exponential
			#z = exp(-1/#z)
		elseif @outerzfunc == "exp(z^2)" ; z^2 exponential
			#z = exp(sqr(#z))
		elseif @outerzfunc == "exp(-z^2)" ; -z^2 exponential
			#z = exp(-sqr(#z))
		elseif @outerzfunc == "exp(1/z^2)" ; recip z^2 exponential
			#z = exp(1/sqr(#z))
		elseif @outerzfunc == "exp(-1/z^2)" ; -recip z^2 exponential
			#z = exp(-1/sqr(#z))
		elseif @outerzfunc == "sinh" ; hyperbolic sine
			#z = sinh(#z)
		elseif @outerzfunc == "asinh" ; inverse hyperbolic sine
			#z = asinh(#z)
		elseif @outerzfunc == "cosh" ; hyperbolic cosine
			#z = cosh(#z)
		elseif @outerzfunc == "acosh" ; inverse hyperbolic cosine
			#z = acosh(#z)
		elseif @outerzfunc == "tanh" ; hyperbolic tangent
			#z = tanh(#z)
		elseif @outerzfunc == "atanh" ; inverse hyperbolic tangent
			#z = atanh(#z)
		elseif @outerzfunc == "cotanh" ; hyperbolic cotangent
			#z = cotanh(#z)
		elseif @outerzfunc == "sqr" ; square
			#z = sqr(#z)
		elseif @outerzfunc == "sqrt" ; square root
			#z = sqrt(#z)
		elseif @outerzfunc == "power" ; power
			#z = #z^@outerzpower
		elseif @outerzfunc == "log" ; logarithm
			#z = log(#z)
		elseif @outerzfunc == "log(-z)" ;
			#z = log(-#z)
		elseif @outerzfunc == "log(1/z)" ;
			#z = log(1/#z)
		elseif @outerzfunc == "log(-1/z)" ;
			#z = log(-1/#z)
		elseif @outerzfunc == "1/z" ; reciprocal
			#z = 1/#z
		elseif @outerzfunc == "absolute value" ; absolute value
			#z = abs(#z)
		elseif @outerzfunc == "conjugation" ; conjugate
			#z = conj(#z)
		elseif @outerzfunc == "flip" ; flip
			#z = flip(#z)
		elseif @outerzfunc == "ceiling" ; ceiling
			#z = ceil(#z)
		elseif @outerzfunc == "floor" ; floor
			#z = floor(#z)
		elseif @outerzfunc == "truncation" ; truncation
			#z = trunc(#z)
		elseif @outerzfunc == "rounding" ; rounding
			#z = round(#z)
		elseif @outerzfunc == "asin 2" ; arcsine
			#z = asin(#z)
		elseif @outerzfunc == "acos 2" ; arccosine
			#z = acos(#z)
		elseif @outerzfunc == "atan 2" ; arctangent
			#z = atan2(#z)
		elseif @outerzfunc == "acot 2" ; arccotangent
			#z = halfpi - atan2(#z)
		elseif @outerzfunc == "asec 2" ; arcsecant
			#z = acos(1/#z)
		elseif @outerzfunc == "acsc 2" ; arccosecant
			#z = asin(1/#z)
		elseif @outerzfunc == "aver 2" ; arcversine
			#z = acos(1 - #z)
		elseif @outerzfunc == "avcs 2" ; arcvercosine
			#z = acos(1 + #z)
		elseif @outerzfunc == "acvs 2" ; arccoversine
			#z = asin(1 - #z)
		elseif @outerzfunc == "acvc 2" ; arccovercosine
			#z = asin(1 + #z)
		elseif @outerzfunc == "aexs 2" ; arcexsecant
			#z = acos( (1/(#z+1)))
		elseif @outerzfunc == "aexc 2" ; arcexcosecant
			#z = asin( (1/(#z+1)))
		elseif @outerzfunc == "acrd 2" ; arcchord
			#z = 2 * asin( #z/2 )
		elseif @outerzfunc == "log(z^2)" ; 
			#z = log(sqr(#z))
		elseif @outerzfunc == "log(-z^2)" ; 
			#z = log(-sqr(#z))
		elseif @outerzfunc == "log(1/z^2)" ; 
			#z = log(1/sqr(#z))
		elseif @outerzfunc == "log(-1/z^2)" ; 
			#z = log(-1/sqr(#z))
		elseif @outerzfunc == "log log" ; 
			#z = log( log(#z) )
		elseif @outerzfunc == "exp(exp)" ; 
			#z = exp( exp(#z) )
		elseif @outerzfunc == "z^z" ; 
			#z = #z^#z
		elseif @outerzfunc == "z^z^z" ; 
			#z = #z^(#z^#z)
		elseif @outerzfunc == "constant^z" ; 
			#z = @ozbase^#z
		elseif @outerzfunc == "constant^z^z" ; 
			#z = @ozbase^(#z^#z)
		endif ; @outerzfunc
		if @outerzfunc != "ident"
			#z = @ozmultiplier * #z + @ozoffset
		endif ; @outerzfunc
endif ; @innerzfunc

		xz = real(#z)
		yz = imag(#z)
		magn = xz^@xpower + yz^@ypower
		xz = xz/magn + real(@xyoffset)
		yz = yz/magn + imag(@xyoffset)
		#z = xz + flip(yz)

if @seqmode == "coefficient" ; use sequence members as coefficients of polynomial terms
	if @seqalternate
		if @seqreverse

zpolynom = sequence[0]* #z^16 - sequence[1]* #z^15 + sequence[2]* #z^14 - \
	sequence[3]* #z^13 + sequence[4]* #z^12 - sequence[5]* #z^11 + sequence[6]* \
	#z^10 - sequence[7]* #z^9 + sequence[8]* #z^8 - sequence[9]* #z^7 +\
	sequence[10]* #z^6 - sequence[11]* #z^5 + sequence[12]* #z^4 - \
	sequence[13]* #z^3 + sequence[14]* sqr(#z) - sequence[15]* #z + sequence[16]

		else ; do not reverse sequence of polynomial terms

zpolynom = sequence[0] - sequence[1]* #z + sequence[2]* sqr(#z) - sequence[3]* #z^3 \
	+ sequence[4]* #z^4 - sequence[5]* #z^5 + sequence[6]* #z^6 - sequence[7]* \
	#z^7 + sequence[8]* #z^8 - sequence[9]* #z^9 + sequence[10]* #z^10 - \
	sequence[11]* #z^11 + sequence[12]* #z^12 - sequence[13]* #z^13 + \
	sequence[14]* #z^14 - sequence[15]* #z^15 + sequence[16]* #z^16

		endif ; @seqreverse

;!!!!!
	else ; do not alternate sign of polynomial terms
		if @seqreverse

zpolynom = sequence[0]* #z^16 + sequence[1]* #z^15 + sequence[2]* #z^14 + \
	sequence[3]* #z^13 + sequence[4]* #z^12 + sequence[5]* #z^11 + sequence[6]* \
	#z^10 + sequence[7]* #z^9 + sequence[8]* #z^8 + sequence[9]* #z^7 +\
	sequence[10]* #z^6 + sequence[11]* #z^5 + sequence[12]* #z^4 + \
	sequence[13]* #z^3 + sequence[14]* sqr(#z) + sequence[15]* #z + sequence[16]

		else ; do not reverse sequence of polynomial terms

zpolynom = sequence[0] + sequence[1]* #z + sequence[2]* sqr(#z) + sequence[3]* #z^3 \
	+ sequence[4]* #z^4 + sequence[5]* #z^5 + sequence[6]* #z^6 + sequence[7]* \
	#z^7 + sequence[8]* #z^8 + sequence[9]* #z^9 + sequence[10]* #z^10 + \
	sequence[11]* #z^11 + sequence[12]* #z^12 + sequence[13]* #z^13 + \
	sequence[14]* #z^14 + sequence[15]* #z^15 + sequence[16]* #z^16
	
		endif ; @seqreverse
	endif ; @seqalternate

;!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
elseif @seqmode == "exponent" ; use sequence members as exponents of polynomial terms
	if @seqalternate
		if @seqreverse

zpolynom = #z^sequence[0] - #z^sequence[1] + #z^sequence[2] - #z^sequence[3] \
	+ #z^sequence[4] - #z^sequence[5] + #z^sequence[6] - #z^sequence[7] \
	+ #z^sequence[8] - #z^sequence[9] + #z^sequence[10] - \
	#z^sequence[11] + #z^sequence[12] - #z^sequence[13] + \
	#z^sequence[14] - #z^sequence[15] + #z^sequence[16]

		else ; do not reverse sequence of polynomial terms

zpolynom = #z^sequence[0] - #z^sequence[1] + #z^sequence[2] - #z^sequence[3] \
	+ #z^sequence[4] - #z^sequence[5] + #z^sequence[6] - #z^sequence[7] \
	+ #z^sequence[8] - #z^sequence[9] + #z^sequence[10] - \
	#z^sequence[11] + #z^sequence[12] - #z^sequence[13] + \
	#z^sequence[14] - #z^sequence[15] + #z^sequence[16]

		endif ; @seqreverse

;!!!!!
	else ; do not alternate sign of polynomial terms
		if @seqreverse

zpolynom = #z^sequence[0] + #z^sequence[1] + #z^sequence[2] + #z^sequence[3] \
	+ #z^sequence[4] + #z^sequence[5] + #z^sequence[6] + #z^sequence[7] \
	+ #z^sequence[8] + #z^sequence[9] + #z^sequence[10] + \
	#z^sequence[11] + #z^sequence[12] + #z^sequence[13] + \
	#z^sequence[14] + #z^sequence[15] + #z^sequence[16]

		else ; do not reverse sequence of polynomial terms

zpolynom = #z^sequence[0] + #z^sequence[1] + #z^sequence[2] + #z^sequence[3] \
	+ #z^sequence[4] + #z^sequence[5] + #z^sequence[6] + #z^sequence[7] \
	+ #z^sequence[8] + #z^sequence[9] + #z^sequence[10] + \
	#z^sequence[11] + #z^sequence[12] + #z^sequence[13] + \
	#z^sequence[14] + #z^sequence[15] + #z^sequence[16]

		endif ; @seqreverse
	endif ; @seqalternate
endif ; @seqmode

	if @lvariant == "log"
		#z = @zmultiplier * log(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "sqrt"
		#z = @zmultiplier * sqrt(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "power"
		#z = @zmultiplier * (abs(zpolynom)^@lpower)^@zpower + @zoffset
	elseif @lvariant == "labs"
		if imag(zpolynom) < 0
			#z = conj(zpolynom)
		endif ; imag
		#z = @zmultiplier * log(zpolynom)^@zpower + @zoffset
	elseif @lvariant == "sine"
		#z = @zmultiplier * sin(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log sine"
		#z = @zmultiplier * log(abs(sin(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip abs"
		#z = @zmultiplier * (abs(zpolynom) + (1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "recip log 2"
		#z = @zmultiplier * (log(log(abs(zpolynom))) + log(1/abs(zpolynom)))^@zpower + @zoffset
	elseif @lvariant == "log log"
		#z = @zmultiplier * log(abs(log(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "recip log"
		#z = @zmultiplier * log(1/abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "atan"
		#z = @zmultiplier * atan(abs(zpolynom))^@zpower + @zoffset
	elseif @lvariant == "log atan"
		#z = @zmultiplier * log(abs(atan(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log sqrt"
		#z = @zmultiplier * log(abs(sqrt(abs(zpolynom))))^@zpower + @zoffset
	elseif @lvariant == "log power"
		#z = @zmultiplier * log(abs(abs(zpolynom)^@lpower))^@zpower + @zoffset
	endif ; @lvariant

	endwhile ; iindex
endif ; cindex

#z = zadjust * #z

bailout:
|z|<@bail

default:
title = "PolySequence Polygonal"
center = (0.001, 0.001)
magn = 0.25
method = multipass
periodicity = 0
maxiter = 500

param variant
	caption = "Sequence Variant"
	enum = "3" "4" "5" "6" "7" "8" "9" "10" "11" "12"
	default = 3
	hint = "This setting selects which polygonal number sequence to iterate. \
		'3' = triangular numbers, '4' = square numbers, etc."
endparam
param seqterms
	caption = "Number of Terms"
	default = 5
	min = 2
	max = 16
	hint = "This parameter determines how many terms from the defining sequence \
		'Sequence Variant' are used to build the iterated polynomial (2-16)."
endparam
param seqmode
	caption = "Sequence Mode"
	enum = "coefficient" "exponent"
	default = 0
	hint = "'coefficient' means that the sequence members are used as coefficients \
		of a polynomial in successive powers of #z; 'exponent' means that the \
		polynomial is constructed using terms based on #z^sequence member."
endparam
param seqalternate
	caption = "Alternate Terms?"
	default = FALSE
	hint = "If enabled, the terms of the polynomial alternate in sign."
endparam
param seqreverse
	caption = "Reverse Terms?"
	default = FALSE
	hint = "If enabled, the sequence is applied to the terms of the polynomial \
		in reverse order."
	visible = @seqmode == "coefficient"
endparam
param innerpixfunc
	caption = "Inner Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-pixel)" "exp(1/pixel)" \
		"exp(-1/pixel)" "exp(pixel^2)" "exp(-pixel^2)" "exp(1/pixel^2)" "exp(-1/pixel^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-pixel)" "log(1/pixel)" "log(-1/pixel)" "1/pixel" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(pixel^2)" "log(-pixel^2)" "log(1/pixel^2)" "log(-1/pixel^2)" "log log" \
		"exp(exp)" "pixel^pixel" "pixel^pixel^pixel" "constant^pixel" "constant^pixel^pixel"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed BEFORE 'Outer Pixel Function'."
endparam
param innerpixpower
	caption = "Inner Pixel Exponent"
	default = (3,0)
	hint = "If the 'Inner Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerpixfunc == "power"
endparam
param pbase
	caption = "Pixel Base"
	default = (2,0)
	hint = "If the 'Inner Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc == "constant^pixel")  || (@innerpixfunc == \
		"constant^pixel^pixel")
endparam
param pixmultiplier1
	caption = "Pixel Multiplier 1"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param pixoffset1
	caption = "Pixel Offset 1"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the inner pixel function."
	visible = @innerpixfunc != "ident"
endparam
param outerpixfunc
	caption = "Outer Pixel Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "Before any iterations, the #pixel value is modified by this \
		function. This function is executed AFTER 'Inner Pixel Function'."
	visible = @innerpixfunc != "ident"
endparam
param outerpixpower
	caption = "Outer Pixel Exponent"
	default = (3,0)
	hint = "If the 'Outer Pixel Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc == "power")
endparam
param pbase2
	caption = "Outer Pixel Base"
	default = (2,0)
	hint = "If the 'Outer Pixel Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerpixfunc != "ident") && ((@outerpixfunc == "constant^z")  || \
		(@outerpixfunc == "constant^z^z"))
endparam
param pixmultiplier2
	caption = "Pixel Multiplier 2"
	default = (1,0)
	hint = "This constant is multiplied by the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param pixoffset2
	caption = "Pixel Offset 2"
	default = (0,0)
	hint = "This constant is added to the #pixel value after the outer pixel function, \
		prior to the iteration loops."
	visible = (@innerpixfunc != "ident") && (@outerpixfunc != "ident")
endparam
param cycles
	caption = "Cycles per Loop"
	default = 1
	min = 1
	hint = "This parameter determines how many iterations of #z are affected by \
		the 'Variant' equation."
endparam
param cyclefunc
	caption = "Cycle Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "This parameter chooses an optional function that is iterated \
		once each cycle."
endparam
param cbase
	caption = "Cycle Base"
	default = (4,0)
	hint = "If the 'Cycle Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@cyclefunc == "constant^z")  || (@cyclefunc == \
		"constant^z^z")
endparam
param absolute
	caption = "Absolute Value?"
	default = FALSE
	hint = "If enabled, the 'Cycle Function' uses the absolute value of #z."
	visible = @cyclefunc != 0
endparam
param cyclepower
	caption = "Cycle Exponent"
	default = (3,0)
	hint = "If the 'Cycle Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @cyclefunc == "power"
endparam
param iterations
	caption = "Iterations per Cycle"
	default = 3
	min = 1
	max = 16
	hint = "During each of the #z iterations set by param 'Number of Cycles', #z is \
		iterated through the 'Variant' equation this many times."
endparam
param innerzfunc
	caption = "Inner Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this \
		function. This function is executed BEFORE 'Outer Z Function'."
endparam
param innerzpower
	caption = "Inner Z Exponent"
	default = (3,0)
	hint = "If the 'Inner Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = @innerzfunc == "power"
endparam
param izbase
	caption = "Inner Z Base"
	default = (4,0)
	hint = "If the 'Inner Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc == "constant^z")  || (@innerzfunc == \
		"constant^z^z")
endparam
param izmultiplier
	caption = "Inner Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param izoffset
	caption = "Inner Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the inner #z function."
	visible = @innerzfunc != "ident"
endparam
param outerzfunc
	caption = "Outer Z Function"
	enum = "ident" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-z)" "exp(1/z)" \
		"exp(-1/z)" "exp(z^2)" "exp(-z^2)" "exp(1/z^2)" "exp(-1/z^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-z)" "log(1/z)" "log(-1/z)" "1/z" "absolute value" "conjugation" \
		"flip" "ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(z^2)" "log(-z^2)" "log(1/z^2)" "log(-1/z^2)" "log log" \
		"exp(exp)" "z^z" "z^z^z" "constant^z" "constant^z^z"
	default = 0
	hint = "During the iterations, the #z value is modified by this function. \
		This function is executed AFTER 'Inner Z Function'."
	visible = @innerzfunc != "ident"
endparam
param outerzpower
	caption = "Outer Z Exponent"
	default = (3,0)
	hint = "If the 'Outer Z Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@innerzfunc != "ident") && (@outerzfunc == "power")
endparam
param ozbase
	caption = "Outer Z Base"
	default = (4,0)
	hint = "If the 'Outer Z Function' is set to 'constant^z' or 'constant^z^z', \
		then this is the constant that is used."
	visible = (@innerzfunc != "ident") && ((@outerzfunc == "constant^z")  || \
		(@outerzfunc == "constant^z^z"))
endparam
param ozmultiplier
	caption = "Outer Z Multiplier"
	default = (1,0)
	hint = "This constant is multiplied by #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param ozoffset
	caption = "Outer Z Offset"
	default = (0,0)
	hint = "This constant is added to #z value after the outer #z function."
	visible = (@innerzfunc != "ident") && (@outerzfunc != "ident")
endparam
param xpower
	caption = "X Exponent"
	default = 2.0
	hint = "Real(z) is raised to this power for calculation \
		of the magnitude."
endparam
param ypower
	caption = "Y Exponent"
	default = 2.0
	hint = "Imag(z) is raised to this power for calculation \
		of the magnitude."
endparam
param xyoffset
	caption = "XY Offset"
	default = (0,0)
	hint = "The real part of this parameter is added to real(z), the imaginary \
		part to imag(z)."
endparam
param lvariant
	caption = "Labs Function"
	enum = "log" "sqrt" "log sqrt" "power" "log power" "labs" "sine" "log sine"\
		 "log log" "recip log" "recip log 2" "recip abs" "atan" "log atan"
	default = 0
	hint = "This setting how the polynomial iteration is processed."
endparam
param lpower
	caption = "Labs Exponent"
	default = (0.25,0)
	hint = "If 'Labs Function' is set to 'power', then this parameter \
		is the exponent that is used."
	visible = (@lvariant == "power") || (@lvariant == "log power")
endparam
param zpower
	caption = "Z Exponent"
	default = (1,0)
	hint = "The 'Polynomial Variant' expression is raised to this power before \
		modification by the 'Z Multiplier' and 'Z Offset'."
endparam
param zmultiplier
	caption = "Z Multiplier"
	default = (1,0)
	hint = "This value is multiplied by the equation selected by parameter \
		'Variant' during each iteration."
endparam
param zoffset
	caption = "Z Offset"
	default = (0,0)
	hint = "This value is added to the equation selected by parameter 'Variant' \
		during each iteration."
endparam
param zadjustment
	caption = "Z Adjustment"
	default = 102.0
	hint = "This setting affects how many total #z iterations are executed."
endparam
param bail
	caption = "Bailout"
	default = 1e7
	hint = "This setting determines when the iteration of #z ends."
endparam
}

jam-UnityRootBarnsley {

; jam 12/20/2018
; Based on variations of the traditional Barnsley formulas.
; Some ideas from Michèle Dessureault, Ed Algra, Sam Monnier, and many others.
; The complex plane is divided into N sectors defined by the Nth roots of unity.
; Variant equations are executed each loop, determined by which sector contains
; the current #z value.

global:
;	maxroots = 4 ; set to maximum number of roots of unity - 1, since root (1,0) is never used

	float twopi = 2 * #pi
    float degconversion = twopi/360
	float unityroots[4] ; dimension to size maxroots

	; Constants for CCW and CW rotations
	complex rotation90 = exp(1i * #pi / 2)
	complex rotation180 = exp(1i * #pi)
	complex rotation270 = exp(1i * 3 * #pi / 2)

	; If a global rotation for the sectors has been given, calculate that now
	float rotation = @rotate * degconversion
	if ( rotation < 0 )
		rotation = rotation + twopi
	endif ; rotation

	int glindex = int glindex2 = 0 ; loop indices for the global section
	int tempint = 0

	; Store the boundary values for the various sectors
	tempint = @numberofroots - 1
	while glindex < tempint
		glindex2 = glindex + 1
		unityroots[glindex] = glindex2 * twopi / @numberofroots + rotation
		glindex = glindex + 1
	endwhile ; glindex

init:

	complex juliaconst = (0,0)
	bool dontbail = TRUE
	float tempfloat = float tempfloat2 = float tempx = float tempy = 0.0
	float zangle = float zangletemp = 0.0
	complex z1 = complex z2 = (0,0)

	if @mandy
		#z = #pixel, juliaconst = #pixel
	else ; Julia
		#z = #pixel, juliaconst = @jconstant
	endif

loop:
	zangle = atan2(#z)
	if zangle < 0
		zangle = zangle + twopi
	endif ; zangle

	if @numberofroots == 2
		if @barnsleytype2 == "1"
			if zangle <= unityroots[0] && zangle > rotation ; default is upper half-plane (when no rotation)
				#z = (#z - flip(1)+ @barnconst1) * juliaconst
			else ; lower half-plane
				#z = (#z + flip(1) + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "2"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (#z - 1 + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = (#z + 1 + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "3"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = #z * juliaconst - 1 + @barnconst1
			else ; lower half-plane
				#z = #z * juliaconst + 1 + @barnconst2
			endif ; zangle
		elseif @barnsleytype2 == "4"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = #z * juliaconst - (0,1) + @barnconst1
			else ; lower half-plane
				#z = #z * juliaconst + (0,1) + @barnconst2
			endif ; zangle
		elseif @barnsleytype2 == "5"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (sqr(#z) - (0,1) + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = (sqr(#z) + (0,1) + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "6"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (sqr(#z) - 1 + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = (sqr(#z) + 1 + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "7"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = sqr(#z) * juliaconst - (0,1) + @barnconst1
			else ; lower half-plane
				#z = sqr(#z) * juliaconst + (0,1) + @barnconst2
			endif ; zangle
		elseif @barnsleytype2 == "8"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = sqr(#z) * juliaconst - 1 + @barnconst1
			else ; lower half-plane
				#z = sqr(#z) * juliaconst + 1 + @barnconst2
			endif ; zangle
		elseif @barnsleytype2 == "9"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (#z - 1 + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = (#z + 1 + @barnconst2) * conj(juliaconst)
			endif ; zangle
		elseif @barnsleytype2 == "10"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (#z - 1 + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = (#z + 1 + @barnconst2) * flip(juliaconst)
			endif ; zangle
		elseif @barnsleytype2 == "11"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = (#z + (0,1) + @barnconst2) * conj(juliaconst)
			endif ; zangle
		elseif @barnsleytype2 == "12"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = (#z + (0,1) + @barnconst2) * flip(juliaconst)
			endif ; zangle
		elseif @barnsleytype2 == "13"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (#z - (0,1) + @barnconst1) / juliaconst
			else ; lower half-plane
				#z = (#z + (0,1) + @barnconst2) / juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "14"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (#z - 1 + @barnconst1) / juliaconst
			else ; lower half-plane
				#z = (#z + 1 + @barnconst2) / juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "15"
			tempfloat = 0.5 * real(#z)
			tempfloat2 = 0.5 * imag(#z)
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				tempx = tempfloat - tempfloat2
				tempy = tempfloat + tempfloat2 
				#z = (tempx + flip(tempy) + @barnconst1) * juliaconst
			else ; lower half-plane
				tempx = -tempfloat - tempfloat2 + 1
				tempy = tempfloat - tempfloat2 
				#z = (tempx + flip(tempy) + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "16"
			tempfloat = 0.5 * real(#z)
			tempfloat2 = 0.5 * imag(#z)
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				tempx = tempfloat - tempfloat2
				tempy = tempfloat + tempfloat2 
				#z = (tempx + flip(tempy) + @barnconst1) * real(juliaconst)
			else ; lower half-plane
				tempx = -tempfloat - tempfloat2 + 1
				tempy = tempfloat - tempfloat2 
				#z = (tempx + flip(tempy) + @barnconst2) * flip(imag(juliaconst))
			endif ; zangle
		elseif @barnsleytype2 == "17"
			tempfloat = real(#z)
			tempfloat2 = imag(#z)
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				tempx = 2 * tempfloat
				tempy = 0.5 * tempfloat2 
				#z = (tempx + flip(tempy) + @barnconst1) * juliaconst
			else ; lower half-plane
				tempx = 2 * (1 - tempfloat)
				tempy = 1 - 0.5 * tempfloat2 
				#z = (tempx + flip(tempy) + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "18"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = (@barnsleymult * #z - (0,1) + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = ((0,1) - @barnsleymult * #z + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "19"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ( (#z - 1) * log(#z) + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = ( (#z + 1) * log(#z) + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "20"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ( (#z - (0,1)) * log(#z) + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = ( (#z + (0,1)) * log(#z) + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "21"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ( #z * log(#z-1) + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = ( #z * log(#z+1) + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "22"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ( #z * log(#z-(0,1)) + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = ( #z * log(#z+(0,1)) + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "23"
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ( #z * rotation90 + @barnconst1) * juliaconst ; counterclockwise rotation 90
			else ; lower half-plane ; clockwise rotation by 90
				#z = ( #z * rotation270 + @barnconst2) * juliaconst ; CW rotation
			endif ; zangle
		elseif @barnsleytype2 == "24"
			if zangle <= unityroots[0] && zangle > rotation ; x-axis reflection
				#z = ( (real(#z) + flip(-imag(#z))) + @barnconst1) * juliaconst ; 
			else ; lower half-plane ; CCW rotation by 90
				#z = ( #z * rotation90 + @barnconst2) * juliaconst ; 
			endif ; zangle
		elseif @barnsleytype2 == "25"
			if zangle <= unityroots[0] && zangle > rotation ; y-axis reflection
				#z = ( (-real(#z) + flip(imag(#z))) + @barnconst1) * juliaconst ; 
			else ; lower half-plane ; CCW rotation by 90
				#z = ( #z * rotation90 + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "26"
			z1 = #z ; save current z
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ( #z * rotation90 + z1 + @barnconst1) * juliaconst
			else ; lower half-plane ; clockwise rotation by 90
				#z = ( #z * rotation270 - z1 + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "27"
			z2 = z1 ; save previous z
			z1 = #z ; save current z
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ( #z * rotation90 + z1 + @barnconst1) * juliaconst
			else ; lower half-plane ; clockwise rotation by 90
				#z = ( #z * rotation270 + z2 + @barnconst2) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "28" ; rotation by 180 degrees
;			tempfloat = #pi + (real(#z) % twopi)
;			tempfloat2 = #pi + (imag(#z) % twopi)
			tempfloat = cabs(#z) % twopi
			tempfloat2 = -tempfloat
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ((#z + @barnconst1 + 0.25) *  exp(1.0i * tempfloat)) * juliaconst
			else ; lower half-plane
				#z = ((#z + @barnconst2 - 0.25) *  exp(1.0i * tempfloat2)) * juliaconst
			endif ; zangle
		elseif @barnsleytype2 == "29" ; rotation by 180 degrees
;			tempfloat = cabs(#z) % twopi
;			tempfloat2 = -tempfloat
			if zangle <= unityroots[0] && zangle > rotation ; upper half-plane
				#z = ((#z - (0,1)) *  exp(1.0i * #pi)  + @barnconst1) * juliaconst
			else ; lower half-plane
				#z = ((#z + (0,1)) *  exp(1.0i * #pi)  + @barnconst2) * juliaconst
			endif ; zangle
		endif ; @barnsleytype2
	elseif @numberofroots == 3
		if @barnsleytype3 == "1"
			if zangle <= unityroots[0] && zangle > rotation ; default, #z is in first 120-degree sector
				#z = (#z - flip(1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + 1 + @barnconst2) * juliaconst
			else ; third sector
				#z = (#z + flip(1) + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "2"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + (0,1) + @barnconst2) * juliaconst
			else ; third sector
				#z = (#z + 1 + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "3"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (sqr(#z) - flip(1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (sqr(#z) + 1 + @barnconst2) * juliaconst
			else ; third sector
				#z = (sqr(#z) + flip(1) + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "4"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (sqr(#z) - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (sqr(#z) + (0,1) + @barnconst2) * juliaconst
			else ; third sector
				#z = (sqr(#z) + 1 + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "5"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - flip(1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + @barnconst2) * juliaconst
			else ; third sector
				#z = (#z + flip(1) + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "6"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + @barnconst2) * juliaconst
			else ; third sector
				#z = (#z + 1 + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "7"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (sqr(#z) - flip(1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (sqr(#z) + @barnconst2) * juliaconst
			else ; third sector
				#z = (sqr(#z) + flip(1) + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "8"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (sqr(#z) - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (sqr(#z) + @barnconst2) * juliaconst
			else ; third sector
				#z = (sqr(#z) + 1 + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "9"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - flip(1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + @barnconst2) * conj(juliaconst)
			else ; third sector
				#z = (#z + flip(1) + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "10"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + @barnconst2) * conj(juliaconst)
			else ; third sector
				#z = (#z + 1 + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "11"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - flip(1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + @barnconst2) * flip(juliaconst)
			else ; third sector
				#z = (#z + flip(1) + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "12"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + @barnconst2) * flip(juliaconst)
			else ; third sector
				#z = (#z + 1 + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "13"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - flip(1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + 1 + @barnconst2) * conj(juliaconst)
			else ; third sector
				#z = (#z + flip(1) + @barnconst3) * flip(juliaconst)
			endif ; zangle
		elseif @barnsleytype3 == "14"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + (0,1) + @barnconst2) * conj(juliaconst)
			else ; third sector
				#z = (#z + 1 + @barnconst3) * flip(juliaconst)
			endif ; zangle
		elseif @barnsleytype3 == "15"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - flip(1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + 1 + @barnconst2) / juliaconst
			else ; third sector
				#z = (#z + flip(1) + @barnconst3) * flip(juliaconst)
			endif ; zangle
		elseif @barnsleytype3 == "16"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + (0,1) + @barnconst2) / juliaconst
			else ; third sector
				#z = (#z + 1 + @barnconst3) * conj(juliaconst)
			endif ; zangle
		elseif @barnsleytype3 == "17"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (conj(#z) + 1 + @barnconst2) * juliaconst
			else ; third sector
				#z = (#z + (0,1) + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "18"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (flip(#z) + 1 + @barnconst2) * juliaconst
			else ; third sector
				#z = (#z + (0,1) + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "19"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (conj(#z) + 1 + @barnconst2) * juliaconst
			else ; third sector
				#z = (#z + 1 + @barnconst3) * juliaconst
			endif ; zangle
		elseif @barnsleytype3 == "20"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first 120-degree sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (flip(#z) + 1 + @barnconst2) * juliaconst
			else ; third sector
				#z = (#z + 1 + @barnconst3) * juliaconst
			endif ; zangle
		endif ; @barnsleytype3
	elseif @numberofroots == 4
		if @barnsleytype4 == "1"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z + (-1,-1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (#z + (1,-1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z + (1,1) + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (#z + (-1,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "2"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (sqr(#z) + (-1,-1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (sqr(#z) + (1,-1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (sqr(#z) + (1,1) + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (sqr(#z) + (-1,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "3"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z  * juliaconst) + (-1,-1) + @barnconst1
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (#z * juliaconst) + (1,-1) + @barnconst2
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z * juliaconst) + (1,1) + @barnconst3
			else ; fourth quadrant
				#z = (#z * juliaconst) + (-1,1) + @barnconst4
			endif ; zangle
		elseif @barnsleytype4 == "4"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (sqr(#z) * juliaconst) + (-1,-1) + @barnconst1
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (sqr(#z) * juliaconst) + (1,-1) + @barnconst2
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (sqr(#z) * juliaconst) + (1,1) + @barnconst3
			else ; fourth quadrant
				#z = (sqr(#z) * juliaconst) + (-1,1) + @barnconst4
			endif ; zangle
		elseif @barnsleytype4 == "5"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (conj(#z) - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z + (0,1) + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (conj(#z) + (0,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "6"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (conj(#z) + 1 + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z + 1 + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (conj(#z) - 1 + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "7"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (flip(#z) - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z + (0,1) + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (flip(#z) + (0,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "8"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (flip(#z) + 1 + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z + 1 + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (flip(#z) - 1 + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "9"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (conj(#z) - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (conj(#z) + (0,1) + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (#z + (0,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "10"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (conj(#z) - 1 + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (conj(#z) + 1 + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (#z + 1 + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "11"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (flip(#z) - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (flip(#z) + (0,1) + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (#z + (0,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "12"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (flip(#z) - 1 + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (flip(#z) + 1 + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (#z + 1 + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "13"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (#z - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z + 1 + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (#z + (0,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "14"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (conj(#z) - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z + 1 + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (conj(#z) + (0,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "15"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (conj(#z) - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (#z - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (conj(#z) + 1 + @barnconst3) * juliaconst
			else ; fourth quadrant
				#z = (#z + (0,1) + @barnconst4) * juliaconst
			endif ; zangle
		elseif @barnsleytype4 == "16"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first quadrant
				#z = (#z  * juliaconst) - (1,0) + @barnconst1
			elseif zangle <= unityroots[1] ; second quadrant
				#z = (#z * juliaconst) - (0,1) + @barnconst2
			elseif zangle <= unityroots[2] ; third quadrant
				#z = (#z * juliaconst) + (1,0) + @barnconst3
			else ; fourth quadrant
				#z = (#z * juliaconst) + (0,1) + @barnconst4
			endif ; zangle
		endif ; @barnsleytype4
	elseif @numberofroots == 5
		if @barnsleytype5 == "1"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first sector
				#z = (#z + (-1,-1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z + (1,-1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third sector
				#z = (#z + (1,0) + @barnconst3) * juliaconst
			elseif zangle <= unityroots[3] ; fourth sector
				#z = (#z + (1,1) + @barnconst4) * juliaconst
			else ; fifth sector
				#z = (#z + (-1,1) + @barnconst5) * juliaconst
			endif ; zangle
		elseif @barnsleytype5 == "2"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third sector
				#z = (conj(#z) + (1,0) + @barnconst3) * juliaconst
			elseif zangle <= unityroots[3] ; fourth sector
				#z = (#z + (0,1) + @barnconst4) * juliaconst
			else ; fifth sector
				#z = (#z + 1 + @barnconst5) * juliaconst
			endif ; zangle
		elseif @barnsleytype5 == "3"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (#z - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third sector
				#z = (flip(#z) + (1,0) + @barnconst3) * juliaconst
			elseif zangle <= unityroots[3] ; fourth sector
				#z = (#z + (0,1) + @barnconst4) * juliaconst
			else ; fifth sector
				#z = (#z + 1 + @barnconst5) * juliaconst
			endif ; zangle
		elseif @barnsleytype5 == "4"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first sector
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (conj(#z) - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third sector
				#z = (#z + (1,0) + @barnconst3) * juliaconst
			elseif zangle <= unityroots[3] ; fourth sector
				#z = (conj(#z) + (0,1) + @barnconst4) * juliaconst
			else ; fifth sector
				#z = (#z + (0,1) + @barnconst5) * juliaconst
			endif ; zangle
		elseif @barnsleytype5 == "5"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first sector
				#z = (#z - (0,1) + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (flip(#z) - (0,1) + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third sector
				#z = (#z + (1,0) + @barnconst3) * juliaconst
			elseif zangle <= unityroots[3] ; fourth sector
				#z = (flip(#z) + (0,1) + @barnconst4) * juliaconst
			else ; fifth sector
				#z = (#z + (0,1) + @barnconst5) * juliaconst
			endif ; zangle
		elseif @barnsleytype5 == "6"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (conj(#z) - 1 + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third sector
				#z = (#z + (0,1) + @barnconst3) * juliaconst
			elseif zangle <= unityroots[3] ; fourth sector
				#z = (conj(#z) + 1 + @barnconst4) * juliaconst
			else ; fifth sector
				#z = (#z + 1 + @barnconst5) * juliaconst
			endif ; zangle
		elseif @barnsleytype5 == "7"
			if zangle <= unityroots[0] && zangle > rotation ; #z is in first sector
				#z = (#z - 1 + @barnconst1) * juliaconst
			elseif zangle <= unityroots[1] ; second sector
				#z = (flip(#z) - 1 + @barnconst2) * juliaconst
			elseif zangle <= unityroots[2] ; third sector
				#z = (#z + (0,1) + @barnconst3) * juliaconst
			elseif zangle <= unityroots[3] ; fourth sector
				#z = (flip(#z) + 1 + @barnconst4) * juliaconst
			else ; fifth sector
				#z = (#z + 1 + @barnconst5) * juliaconst
			endif ; zangle
		endif ; @barnsleytype5
	endif ; @numberofroots
	
	if @bailtest == "mod"
		dontbail = (|#z| <= @bailout)
	elseif @bailtest == "real"
		dontbail = (sqr(real(#z)) <= @bailout)
	elseif @bailtest == "imag"
		dontbail = (sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "and"
		dontbail = (sqr(real(#z)) <= @bailout && sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "or"
		dontbail = (sqr(real(#z)) <= @bailout || sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "eor"
		if sqr(real(#z)) <= @bailout
			dontbail = (sqr(imag(#z)) > @bailout)
		else
			dontbail = (sqr(imag(#z)) <= @bailout)
		endif ; sqr()
	elseif @bailtest == "manh"
		dontbail = (sqr(abs(real(#z)) + abs(imag(#z))) <= @bailout)
	elseif @bailtest == "manr"
		dontbail = (sqr(real(#z) + imag(#z)) <= @bailout)
	elseif @bailtest == "real 2"
		dontbail = (abs(real(#z)) <= @bailout)
	elseif @bailtest == "imag 2"
		dontbail = (abs(imag(#z)) <= @bailout)
	elseif @bailtest == "sum"
		dontbail = (abs(real(#z) + imag(#z)) <= @bailout)
	elseif @bailtest == "sum 2"
		dontbail = (abs(real(#z)) + abs(imag(#z)) <= @bailout)
	elseif @bailtest == "product"
		dontbail = (abs(real(#z) * imag(#z)) <= @bailout)
	elseif @bailtest == "difference"
		dontbail = (abs(real(#z)) - abs(imag(#z)) <= @bailout)
	elseif @bailtest == "difference 2"
		dontbail = (abs(real(#z) - imag(#z)) <= @bailout)
	elseif @bailtest == "difference 3"
		dontbail = (abs(imag(#z)) - abs(real(#z)) <= @bailout)
	elseif @bailtest == "quotient"
		dontbail = (abs(real(#z)) / abs(imag(#z)) <= @bailout)
	elseif @bailtest == "quotient 2"
		dontbail = (abs(imag(#z)) / abs(real(#z)) <= @bailout)
	endif ; @bailtest

bailout:
	dontbail

default:
	title = "Barnsley - Sectors"
	center = (0,0)
	maxiter = 500
	method = multipass
	periodicity = 0
	magn = 0.75

param numberofroots
	caption = "Number of Roots"
	default = 3
	min = 2
	max = 5
	hint = "This parameter determines the number of roots of unity to use \
		in order to divide the complex plane into sectors (2-5)."
endparam
param rotate
	caption = "Rotation Angle"
	default = 0.0
	min = -179.99
	max = 359.99
	hint = "Number of degrees (0-359) that the sectoral divisions should be rotated \
		from their default, roots of unity, positions."
endparam
param barnsleytype2
	caption = "Barnsley Type"
	enum = "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15" "16" \
		"17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29"
	hint = "This setting determines which set of equations is used."
	visible = @numberofroots == 2
endparam
param barnsleymult
	caption = "Barnsley Multiplier"
	default = (2,0)
	hint = "This parameter is used as the multiplier of #z in some of the Barnsley equations."
	visible = @barnsleytype2 == "18"
endparam
;param zpower
;	caption = "Z Power"
;	default = (3,0)
;	hint = "This parameter is the exponent used by some of the Barnsley equations."
;	visible = FALSE
;endparam
param barnsleytype3
	caption = "Barnsley Type"
	enum = "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15" "16" \
		"17" "18" "19" "20"
	hint = "This setting determines which set of equations is used."
	visible = @numberofroots == 3
endparam
param barnsleytype4
	caption = "Barnsley Type"
	enum = "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15" "16"
	hint = "This setting determines which set of equations is used."
	visible = @numberofroots == 4
endparam
param barnsleytype5
	caption = "Barnsley Type"
	enum = "1" "2" "3" "4" "5" "6" "7"
	hint = "This setting determines which set of equations is used."
	visible = @numberofroots == 5
endparam
param barnconst1
	caption = "1st Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 1st Barnsley equation."
endparam
param barnconst2
	caption = "2nd Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 2nd Barnsley equation."
endparam
param barnconst3
	caption = "3rd Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 3rd Barnsley equation."
	visible = @numberofroots > 2
endparam
param barnconst4
	caption = "4th Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 4th Barnsley equation."
	visible = @numberofroots > 3
endparam
param barnconst5
	caption = "5th Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 5th Barnsley equation."
	visible = @numberofroots > 4
endparam
param bailtest
	caption = "Bailout Test"
	enum = "mod" "real" "imag" "and" "or" "eor" "manh" "manr" "real 2" "imag 2" \
		"sum" "sum 2" "product" "difference" "difference 2" "difference 3" \
		"quotient" "quotient 2"
	default = 0
endparam
param bailout 
	caption = "Bailout Value"
	default = 4.0
	min = 0.001
endparam
param jconstant 
	caption = "Seed/Perturbation"
	default = (0,0)
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
	type = "jam-UnityRootBarnsley"
	numberofroots = numberofroots
	rotate = rotate
	barnsleytype2 = barnsleytype2
	barnsleytype3 = barnsleytype3
	barnsleytype4 = barnsleytype4
	barnsleytype5 = barnsleytype5
	barnconst1 = barnconst1
	barnconst2 = barnconst2
	barnconst3 = barnconst3
	barnconst4 = barnconst4
	barnconst5 = barnconst5
	barnsleymult = barnsleymult
	bailtest = bailtest
	bailout = bailout
	zpower = zpower
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-FunctionBarnsley {

; jam 12/21/2018
; Based on variations of the traditional Barnsley formulas.
; Some ideas from Michèle Dessureault, Ed Algra, Sam Monnier, and many others.
; The various Barnsley equations are executed based on the value of a function \
; of the current #z value.

global:
	float halfpi = #pi/2

init:
	complex juliaconst = (0,0)
	bool dontbail = TRUE
	float testvalue = float barnsleyvalue = 0.0
	float equation1 = float equation2 = 0.0 ; for heatmap option
	complex currentz = (0,0)

	if @mandy
		#z = #pixel, juliaconst = #pixel
	else ; Julia
		#z = #pixel, juliaconst = @jconstant
	endif

loop:
	if @heatmap
		#z = currentz ; restore proper z value
	endif ; @heatmap

	if @functionmode == "cabs"
		testvalue = |#z|
	elseif @functionmode == "real"
		testvalue = abs(real(#z))
	elseif @functionmode == "imag"
		testvalue = abs(imag(#z))
	elseif @functionmode == "real 2"
		testvalue = real(#z)
	elseif @functionmode == "imag 2"
		testvalue = imag(#z)
	elseif @functionmode == "sum"
		testvalue = real(#z) + imag(#z)
	elseif @functionmode == "sum 2"
		testvalue = abs(real(#z)) + abs(imag(#z))
	elseif @functionmode == "sum 3"
		testvalue = sqr(real(#z)) + sqr(imag(#z))
	elseif @functionmode == "product"
		testvalue = real(#z) * imag(#z)
	elseif @functionmode == "product 2"
		testvalue = abs(real(#z)) * abs(imag(#z))
	elseif @functionmode == "product 3"
		testvalue = sqr(real(#z) * imag(#z))
	elseif @functionmode == "difference"
		testvalue = real(#z) - imag(#z)
	elseif @functionmode == "difference 2"
		testvalue = abs(real(#z) - imag(#z))
	elseif @functionmode == "difference 3"
		testvalue = sqr(real(#z) - imag(#z))
	endif ; @functionmode

	if @testfunction == "sin" ; sine function
		testvalue = sin(testvalue)
	elseif @testfunction == "cos" ; cosine
		testvalue = cos(testvalue)
	elseif @testfunction == "tan" ; tangent
		testvalue = tan(testvalue)
	elseif @testfunction == "cot" ; cotangent
		testvalue = cotan(testvalue)
	elseif @testfunction == "sec" ; secant
		testvalue = 1/cos(testvalue)
	elseif @testfunction == "csc" ; cosecant
		testvalue = 1/sin(testvalue)
	elseif @testfunction == "ver" ; versine
		testvalue = 1 - cos(testvalue)
	elseif @testfunction == "vcs" ; vercosine
		testvalue = 1 + cos(testvalue)
	elseif @testfunction == "cvs" ; coversine
		testvalue = 1 - sin(testvalue)
	elseif @testfunction == "cvc" ; covercosine
		testvalue = 1 + sin(testvalue)
	elseif @testfunction == "exs" ; exsecant
		testvalue = 1/cos(testvalue) - 1
	elseif @testfunction == "exc" ; excosecant
		testvalue = 1/sin(testvalue) - 1
	elseif @testfunction == "crd" ; chord
		testvalue = 2 * sin(testvalue/2)
	elseif @testfunction == "asin" ; arcsine
		testvalue =  asin(testvalue - trunc(testvalue)) 
	elseif @testfunction == "acos" ; arccosine
		testvalue = acos(testvalue - trunc(testvalue))
	elseif @testfunction == "atan" ; arctangent
		testvalue = atan(testvalue)
	elseif @testfunction == "acot" ; arccotangent
		testvalue = halfpi - atan(testvalue)
	elseif @testfunction == "asec" ; arcsecant
		testvalue = acos(1/testvalue - trunc(1/testvalue))
	elseif @testfunction == "acsc" ; arccosecant
		testvalue = asin(1/testvalue - trunc(1/testvalue))
	elseif @testfunction == "aver" ; arcversine
		testvalue = acos(1 - testvalue - trunc(1-testvalue))
	elseif @testfunction == "avcs" ; arcvercosine
		testvalue = acos(1 + testvalue - trunc(1+testvalue))
	elseif @testfunction == "acvs" ; arccoversine
		testvalue = asin(1 - testvalue - trunc(1-testvalue))
	elseif @testfunction == "acvc" ; arccovercosine
		testvalue = asin(1 + testvalue - trunc(1+testvalue))
	elseif @testfunction == "aexs" ; arcexsecant
		testvalue = acos( (1/(testvalue+1)) - trunc( (1/(testvalue+1)) ) )
	elseif @testfunction == "aexc" ; arcexcosecant
		testvalue = asin( (1/(testvalue+1)) - trunc( (1/(testvalue+1)) ) )
	elseif @testfunction == "acrd" ; arcchord
		testvalue = 2 * asin( testvalue/2 - trunc(testvalue/2) )
	elseif @testfunction == "exp" ; exponential
		testvalue = exp(testvalue)
	elseif @testfunction == "exp(-n)" ; negative exponential
		testvalue = exp(-testvalue)
	elseif @testfunction == "exp(1/n)" ; recip exponential
		testvalue = exp(1/testvalue)
	elseif @testfunction == "exp(-1/n)" ; neg recip exponential
		testvalue = exp(-1/testvalue)
	elseif @testfunction == "exp(n^2)" ; z^2 exponential
		testvalue = exp(sqr(testvalue))
	elseif @testfunction == "exp(-n^2)" ; -z^2 exponential
		testvalue = exp(-sqr(testvalue))
	elseif @testfunction == "exp(1/n^2)" ; recip z^2 exponential
		testvalue = exp(1/sqr(testvalue))
	elseif @testfunction == "exp(-1/n^2)" ; -recip z^2 exponential
		testvalue = exp(-1/sqr(testvalue))
	elseif @testfunction == "sinh" ; hyperbolic sine
		testvalue = sinh(testvalue)
	elseif @testfunction == "asinh" ; inverse hyperbolic sine
		testvalue = asinh(testvalue)
	elseif @testfunction == "cosh" ; hyperbolic cosine
		testvalue = cosh(testvalue)
	elseif @testfunction == "acosh" ; inverse hyperbolic cosine
		testvalue = acosh(testvalue)
	elseif @testfunction == "tanh" ; hyperbolic tangent
		testvalue = tanh(testvalue)
	elseif @testfunction == "atanh" ; inverse hyperbolic tangent
		testvalue = atanh(testvalue)
	elseif @testfunction == "cotanh" ; hyperbolic cotangent
		testvalue = cotanh(testvalue)
	elseif @testfunction == "sqr" ; square
		testvalue = sqr(testvalue)
	elseif @testfunction == "sqrt" ; square root
		testvalue = sqrt(testvalue)
	elseif @testfunction == "power" ; power
		testvalue = testvalue^@testpower
	elseif @testfunction == "log" ; logarithm
		testvalue = log(testvalue)
	elseif @testfunction == "log(-n)" ;
		testvalue = log(-testvalue)
	elseif @testfunction == "log(1/n)" ;
		testvalue = log(1/testvalue)
	elseif @testfunction == "log(-1/n)" ;
		testvalue = log(-1/testvalue)
	elseif @testfunction == "1/n" ; reciprocal
		testvalue = 1/testvalue
	elseif @testfunction == "absolute value" ; absolute value
		testvalue = abs(testvalue)
	elseif @testfunction == "ceiling" ; ceiling
		testvalue = ceil(testvalue)
	elseif @testfunction == "floor" ; floor
		testvalue = floor(testvalue)
	elseif @testfunction == "truncation" ; truncation
		testvalue = trunc(testvalue)
	elseif @testfunction == "rounding" ; rounding
		testvalue = round(testvalue)
	elseif @testfunction == "asin 2" ; arcsine
		testvalue = asin(testvalue)
	elseif @testfunction == "acos 2" ; arccosine
		testvalue = acos(testvalue)
	elseif @testfunction == "atan 2" ; arctangent
		testvalue = atan2(testvalue)
	elseif @testfunction == "acot 2" ; arccotangent
		testvalue = halfpi - atan2(testvalue)
	elseif @testfunction == "asec 2" ; arcsecant
		testvalue = acos(1/testvalue)
	elseif @testfunction == "acsc 2" ; arccosecant
		testvalue = asin(1/testvalue)
	elseif @testfunction == "aver 2" ; arcversine
		testvalue = acos(1 - testvalue)
	elseif @testfunction == "avcs 2" ; arcvercosine
		testvalue = acos(1 + testvalue)
	elseif @testfunction == "acvs 2" ; arccoversine
		testvalue = asin(1 - testvalue)
	elseif @testfunction == "acvc 2" ; arccovercosine
		testvalue = asin(1 + testvalue)
	elseif @testfunction == "aexs 2" ; arcexsecant
		testvalue = acos( (1/(testvalue+1)))
	elseif @testfunction == "aexc 2" ; arcexcosecant
		testvalue = asin( (1/(testvalue+1)))
	elseif @testfunction == "acrd 2" ; arcchord
		testvalue = 2 * asin( testvalue/2 )
	elseif @testfunction == "log(n^2)" ; 
		testvalue = log(sqr(testvalue))
	elseif @testfunction == "log(-n^2)" ; 
		testvalue = log(-sqr(testvalue))
	elseif @testfunction == "log(1/n^2)" ; 
		testvalue = log(1/sqr(testvalue))
	elseif @testfunction == "log(-1/n^2)" ; 
		testvalue = log(-1/sqr(testvalue))
	elseif @testfunction == "log log" ; 
		testvalue = log( log(testvalue) )
	elseif @testfunction == "exp(exp)" ; 
		testvalue = exp( exp(testvalue) )
	elseif @testfunction == "n^n" ; 
		testvalue = testvalue^testvalue
	elseif @testfunction == "n^n^n" ; 
		testvalue = testvalue^(testvalue^testvalue)
	elseif @testfunction == "constant^n" ; 
		testvalue = @testbase^testvalue
	elseif @testfunction == "constant^n^n" ; 
		testvalue = @testbase^(testvalue^testvalue)
	endif ; @testfunction

	testvalue = testvalue + @testadjustment

	if @barnsleymode == "cabs"
		barnsleyvalue = |#z|
	elseif @barnsleymode == "real"
		barnsleyvalue = abs(real(#z))
	elseif @barnsleymode == "imag"
		barnsleyvalue = abs(imag(#z))
	elseif @barnsleymode == "real 2"
		barnsleyvalue = real(#z)
	elseif @barnsleymode == "imag 2"
		barnsleyvalue = imag(#z)
	elseif @barnsleymode == "sum"
		barnsleyvalue = real(#z) + imag(#z)
	elseif @barnsleymode == "sum 2"
		barnsleyvalue = abs(real(#z)) + abs(imag(#z))
	elseif @barnsleymode == "sum 3"
		barnsleyvalue = sqr(real(#z)) + sqr(imag(#z))
	elseif @barnsleymode == "product"
		barnsleyvalue = real(#z) * imag(#z)
	elseif @barnsleymode == "product 2"
		barnsleyvalue = abs(real(#z)) * abs(imag(#z))
	elseif @barnsleymode == "product 3"
		barnsleyvalue = sqr(real(#z) * imag(#z))
	elseif @barnsleymode == "difference"
		barnsleyvalue = real(#z) - imag(#z)
	elseif @barnsleymode == "difference 2"
		barnsleyvalue = abs(real(#z) - imag(#z))
	elseif @barnsleymode == "difference 3"
		barnsleyvalue = sqr(real(#z) - imag(#z))
	elseif @barnsleymode == "test constant"
		barnsleyvalue = @barntestconst
	endif ; @barnsleymode

	if @barnsleytype == "1"
		if barnsleyvalue <= testvalue
			#z = (#z - flip(1)+ @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (#z + flip(1) + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif ; barnsleyvalue
	elseif @barnsleytype == "2"
		if barnsleyvalue <= testvalue
			#z = (#z - 1 + @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (#z + 1 + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "3"
		if barnsleyvalue <= testvalue
			#z = #z * juliaconst - 1 + @barnconst1
			equation1 = equation1 + 1
		else
			#z = #z * juliaconst + 1 + @barnconst2
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "4"
		if barnsleyvalue <= testvalue
			#z = #z * juliaconst - (0,1) + @barnconst1
			equation1 = equation1 + 1
		else
			#z = #z * juliaconst + (0,1) + @barnconst2
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "5"
		if barnsleyvalue <= testvalue
			#z = (sqr(#z) - (0,1) + @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (sqr(#z) + (0,1) + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "6"
		if barnsleyvalue <= testvalue
			#z = (sqr(#z) - 1 + @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (sqr(#z) + 1 + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "7"
		if barnsleyvalue <= testvalue
			#z = sqr(#z) * juliaconst - (0,1) + @barnconst1
			equation1 = equation1 + 1
		else
			#z = sqr(#z) * juliaconst + (0,1) + @barnconst2
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "8"
		if barnsleyvalue <= testvalue
			#z = sqr(#z) * juliaconst - 1 + @barnconst1
			equation1 = equation1 + 1
		else
			#z = sqr(#z) * juliaconst + 1 + @barnconst2
			equation2 = equation2 + 1
		endif
	endif ; @barnsleytype
	
	if @bailtest == "mod"
		dontbail = (|#z| <= @bailout)
	elseif @bailtest == "real"
		dontbail = (sqr(real(#z)) <= @bailout)
	elseif @bailtest == "imag"
		dontbail = (sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "and"
		dontbail = (sqr(real(#z)) <= @bailout && sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "or"
		dontbail = (sqr(real(#z)) <= @bailout || sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "eor"
		if sqr(real(#z)) <= @bailout
			dontbail = (sqr(imag(#z)) > @bailout)
		else
			dontbail = (sqr(imag(#z)) <= @bailout)
		endif ; sqr()
	elseif @bailtest == "manh"
		dontbail = (sqr(abs(real(#z)) + abs(imag(#z))) <= @bailout)
	elseif @bailtest == "manr"
		dontbail = (sqr(real(#z) + imag(#z)) <= @bailout)
	elseif @bailtest == "real 2"
		dontbail = (abs(real(#z)) <= @bailout)
	elseif @bailtest == "imag 2"
		dontbail = (abs(imag(#z)) <= @bailout)
	elseif @bailtest == "sum"
		dontbail = (abs(real(#z) + imag(#z)) <= @bailout)
	elseif @bailtest == "sum 2"
		dontbail = (abs(real(#z)) + abs(imag(#z)) <= @bailout)
	elseif @bailtest == "product"
		dontbail = (abs(real(#z) * imag(#z)) <= @bailout)
	elseif @bailtest == "difference"
		dontbail = (abs(real(#z)) - abs(imag(#z)) <= @bailout)
	elseif @bailtest == "difference 2"
		dontbail = (abs(real(#z) - imag(#z)) <= @bailout)
	elseif @bailtest == "difference 3"
		dontbail = (abs(imag(#z)) - abs(real(#z)) <= @bailout)
	elseif @bailtest == "quotient"
		dontbail = (abs(real(#z)) / abs(imag(#z)) <= @bailout)
	elseif @bailtest == "quotient 2"
		dontbail = (abs(imag(#z)) / abs(real(#z)) <= @bailout)
	endif ; @bailtest

	if @heatmap ; encode the eq1/eq2 ration in #z
		currentz = #z
		#z = equation1 + flip(equation2)
	endif ; @heatmap

bailout:
	dontbail

default:
	title = "Barnsley - Functions"
	center = (0,0)
	maxiter = 500
	method = multipass
	periodicity = 0
	magn = 0.75

param functionmode
	caption = "Function Mode"
	enum = "cabs" "real" "imag" "real 2" "imag 2" "sum" "sum 2" "sum 3" \
		"product" "product 2" "product 3" "difference" "difference 2" "difference 3"
	default = 0
	hint = "This setting determines the input argument to the test function."
endparam
param testfunction
	caption = "Test Function"
	enum = "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-n)" "exp(1/n)" \
		"exp(-1/n)" "exp(n^2)" "exp(-n^2)" "exp(1/n^2)" "exp(-1/n^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-n)" "log(1/n)" "log(-1/n)" "1/n" "absolute value" \
		"ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(n^2)" "log(-n^2)" "log(1/n^2)" "log(-1/n^2)" "log log" \
		"exp(exp)" "n^n" "n^n^n" "constant^n" "constant^n^n"
	default = 0
	hint = "This setting selects which function is applied in the Barnsley comparison."
endparam
param testpower
	caption = "Test Exponent"
	default = 3.0
	hint = "If the 'Test Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@testfunction == "power")
endparam
param testbase
	caption = "Test Base"
	default = 4.0
	hint = "If the 'Test Function' is set to 'constant^n' or 'constant^n^n', \
		then this is the constant that is used."
	visible = ((@testfunction == "constant^n")  || (@testfunction == "constant^n^n"))
endparam
param testadjustment
	caption = "Test Adjustment"
	default = 0.0
	hint = "This value is added to the result of the Test Function."
endparam
param barnsleymode
	caption = "Barnsley Mode"
	enum = "cabs" "real" "imag" "real 2" "imag 2" "sum" "sum 2" "sum 3" \
		"product" "product 2" "product 3" "difference" "difference 2" "difference 3" \
		"test constant"
	default = 1
	hint = "This setting determines what is compared to the test function."
endparam
param barntestconst
	caption = "Barnsley Test Constant"
	default = 0.3
	hint = "If parameter 'Barnsley Mode' is set to 'test constant', \
			then this is the constant used to test the 'Function Mode'/ \
			'Test Function' result.  If the function result <= the 'test constant' \
			value, Barnley equation 1 is executed; otherwise, equation 2 is \
			executed."
	visible = @barnsleymode == "test constant"
endparam
param barnsleytype
	caption = "Barnsley Type"
	enum = "1" "2" "3" "4" "5" "6" "7" "8"
	hint = "This setting determines which set of equations is used."
endparam
param barnconst1
	caption = "1st Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 1st Barnsley equation."
endparam
param barnconst2
	caption = "2nd Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 2nd Barnsley equation."
endparam
param bailtest
	caption = "Bailout Test"
	enum = "mod" "real" "imag" "and" "or" "eor" "manh" "manr" "real 2" "imag 2" \
		"sum" "sum 2" "product" "difference" "difference 2" "difference 3" \
		"quotient" "quotient 2"
	default = 0
endparam
param bailout 
	caption = "Bailout Value"
	default = 4.0
	min = 0.001
endparam
param heatmap
	caption = "Heat Map?"
	default = FALSE
	hint = "If enabled, #z encodes the ratio of the number of times that Barnsley equation \
		#1 is used to that of Barnsley equation #2, i.e., real(#z) = number \
		of uses of equation 1, and imag(#z) = number of uses of equation 2. \
		This value can be used with the 'Heat Map' coloring in jam2.ucl \
		to determine how often each Barnsley equation is chosen."
endparam
param jconstant 
	caption = "Seed/Perturbation"
	default = (0,0)
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
	type = "jam-FunctionBarnsley"
	functionmode = functionmode
	testfunction = testfunction
	testpower = testpower
	testbase = testbase
	testadjustment = testadjustment
	barnsleymode = barnsleymode
	barntestconst = barntestconst
	barnsleytype = barnsleytype
	barnconst1 = barnconst1
	barnconst2 = barnconst2
	bailtest = bailtest
	bailout = bailout
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-3functionsV2 { ; jam 181229
  ; 2 or 3 different Mandelbrot/Julia style formulas are executed
  ; and combined in a user-specified manner, either each iteration
  ; or every N iterations.

  init:
	complex jc = (0,0)
  int iterations = 0
  complex zblend = (0,0)
  complex zextra = complex ztemp = (0,0) ; temp/spare scratch variable
  complex zf1 = complex zf2 = complex zf3 = (0,0)
  bool bail = FALSE

	if @mandy
		#z = #pixel, jc = #pixel
	else ; Julia
		#z = #pixel, jc = @jconstant
	endif

  ; Pixel/constant initialization section
  if @pixelformula != 0
    if @pixelformula == 1
      jc = jc * jc
    elseif  @pixelformula == 2
      jc = jc * jc * jc
    elseif  @pixelformula == 3
      zextra = jc * jc
      jc = zextra * zextra
    elseif  @pixelformula == 4
      jc = jc ^ @ppower
    elseif  @pixelformula == 5
      jc = 1/jc
    elseif  @pixelformula == 6
      jc = sqrt(jc)
    elseif  @pixelformula == 7
      jc = 1 / ( jc * jc )
    elseif  @pixelformula == 8
      jc = log(jc)
    elseif  @pixelformula == 9
      jc = exp( jc)
    elseif  @pixelformula == 10
      jc = jc^jc
    elseif  @pixelformula == 11
      jc = sin( jc )
    elseif  @pixelformula == 12
      jc = cos( jc )
    elseif  @pixelformula == 13
      jc = tan( jc )
    elseif  @pixelformula == 14
      jc = asin( jc )
    elseif  @pixelformula == 15
      jc = acos( jc )
    elseif  @pixelformula == 16
      jc = atan( jc )
    elseif  @pixelformula == 17
      jc = sinh( jc )
    elseif  @pixelformula == 18
      jc = cosh( jc )
    elseif  @pixelformula == 19
      jc = tanh( jc )
    elseif  @pixelformula == 20
      jc = asinh( jc )
    elseif  @pixelformula == 21
      jc = acosh( jc )
    elseif  @pixelformula == 22
      jc = atanh( jc )
    elseif  @pixelformula == 23
      jc = log( 1/jc )
    elseif  @pixelformula == 24
      jc = log( log( jc ))
    elseif  @pixelformula == 25
      jc = exp( -jc )
    elseif  @pixelformula == 26
      jc = exp( 1/jc )
    elseif  @pixelformula == 27
      jc = jc^(-jc)
    elseif  @pixelformula == 28
      zextra = sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 29
      zextra = cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 30
      zextra = tan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 31
      jc = cotan( jc )
    elseif  @pixelformula == 32
      jc = 1/cos( jc )
    elseif  @pixelformula == 33
      jc = 1/sin( jc )
    elseif  @pixelformula == 34
      zextra = cotan( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 35
      zextra = 1/cos( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 36
      zextra = 1/sin( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 37
      zextra = jc^(jc)
      jc = jc^zextra
    elseif  @pixelformula == 38
      zextra = jc^(jc)
      jc = 1/( jc^zextra )
    elseif  @pixelformula == 39
      jc = log(-jc)
    elseif  @pixelformula == 40
      jc = 1/log( jc )
    elseif  @pixelformula == 41
      jc = jc * log( jc )
    elseif  @pixelformula == 42
      jc = sin( jc ) / jc
    elseif  @pixelformula == 43
      jc = cos( jc ) / jc
    elseif  @pixelformula == 44
      jc = sin( jc ) * cos( jc )
    elseif  @pixelformula == 45
      jc = sin( jc^2 )
    elseif  @pixelformula == 46
      jc = exp( -1/jc )
    elseif  @pixelformula == 47
      jc = jc * exp( jc )
    elseif  @pixelformula == 48
      jc = jc * exp( -jc )
    elseif  @pixelformula == 49
      jc = jc * exp( 1/jc )
    elseif  @pixelformula == 50
      jc = jc * exp( -1/jc )
    elseif  @pixelformula == 51
      jc = jc * jc * jc
    elseif  @pixelformula == 52
      jc = 1 / ( jc * jc * jc )
    elseif  @pixelformula == 53
      jc = atan( 1 / jc )
    elseif  @pixelformula == 54
      jc = acos( 1 / jc )
    elseif  @pixelformula == 55
      jc = asin( 1 / jc )
    elseif  @pixelformula == 56
      jc = tan( jc ) / jc
    elseif  @pixelformula == 57
      jc = cotan( jc ) / jc
    elseif  @pixelformula == 58
      jc = 1 / ( jc * cos( jc ))
    elseif  @pixelformula == 59
      jc = 1 / ( jc * sin( jc ))
    elseif  @pixelformula == 60
      jc = jc * sin( jc )
    elseif  @pixelformula == 61
      jc = jc * cos( jc )
    elseif  @pixelformula == 62
      jc = jc * tan( jc )
    elseif  @pixelformula == 63
      jc = jc * cotan( jc )
    elseif  @pixelformula == 64
      jc = jc/cos( jc )
    elseif  @pixelformula == 65
      jc = jc/sin( jc )
    elseif  @pixelformula == 66
      jc = sin( 1/jc )
    elseif  @pixelformula == 67
      jc = cos( 1/jc )
    elseif  @pixelformula == 68
      jc = tan( 1/jc )
    elseif  @pixelformula == 69
      jc = cotan( 1/jc )
    elseif  @pixelformula == 70
      jc = 1/cos( 1/jc )
    elseif  @pixelformula == 71
      jc = 1/sin( 1/jc )
    elseif  @pixelformula == 72
      jc = cotanh( jc )
    elseif  @pixelformula == 73
      jc = 1/cosh( jc )
    elseif  @pixelformula == 74
      jc = 1/sinh( jc )
    elseif  @pixelformula == 75
      jc = atanh( 1/jc )
    elseif  @pixelformula == 76
      jc = acosh( 1/jc )
    elseif  @pixelformula == 77
      jc = asinh( 1/jc )
    elseif @pixelformula == 78
      jc = @coeffpa * jc^@exponentpa + @coeffpb * jc^@exponentpb + \
          @coeffpc * jc^@exponentpc
    elseif  @pixelformula == 79
      zextra = sinh(#z)
      jc = zextra * zextra
    elseif  @pixelformula == 80
      zextra = cosh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 81
      zextra = tanh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 82
      zextra = cotanh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 83
      zextra = (1,0)/cosh(jc)
      jc = zextra * zextra
    elseif  @pixelformula == 84
      zextra = (1,0) / sinh( jc )
      jc = zextra * zextra
    elseif  @pixelformula == 85
      jc = sinh(1/jc)
    elseif  @pixelformula == 86
      jc = cosh(1/jc)
    elseif  @pixelformula == 87
      jc = tanh(1/jc)
    elseif  @pixelformula == 88
      jc = cotanh(1/jc)
    elseif  @pixelformula == 89
      jc = (1,0)/cosh(1/jc)
    elseif  @pixelformula == 90
      jc = (1,0)/sinh(1/jc)
    elseif  @pixelformula == 91
      jc = sin( jc ) * tan(jc)
    elseif  @pixelformula == 92
      jc = sinh(jc) * tanh(jc)
    elseif  @pixelformula == 93
      jc = sinh(jc) * cosh(jc)
    elseif  @pixelformula == 94
      ztemp = sinh(jc), zextra = cosh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 95
      ztemp = sin(jc), zextra = cos(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 96
      zextra = 1/jc
      jc = sin(zextra)*cos(zextra)
    elseif  @pixelformula == 97
      zextra = sin( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 98
      jc = sin(jc) * cos(1/jc)
    elseif  @pixelformula == 99
      jc = sin(jc) * sin(1/jc)
    elseif  @pixelformula == 100
      zextra = log(jc)
      jc = zextra*zextra
    elseif  @pixelformula == 101
      jc = sin(jc) * sin(2*jc)
    elseif @pixelformula == 102
      jc = exp(2*jc)
    elseif  @pixelformula == 103
      jc = exp(-2*jc)
    elseif  @pixelformula == 104
      zextra = 1/jc
      jc = sinh(zextra)*cosh(zextra)
    elseif  @pixelformula == 105
      zextra = sinh( 1/jc )
      jc = zextra*zextra
    elseif  @pixelformula == 106
      jc = sinh(jc) * cosh(1/jc)
    elseif  @pixelformula == 107
      jc = sinh(jc) * sinh(1/jc)
    elseif  @pixelformula == 108
      jc = sin(jc) * sinh(jc)
    elseif  @pixelformula == 109
      jc = sin(jc) * cosh(jc)
    elseif  @pixelformula == 110
      zextra = sin(jc), ztemp = sinh(jc)
      jc = ztemp*ztemp*zextra*zextra
    elseif  @pixelformula == 111
      jc = sin(jc)*exp(jc)
    elseif  @pixelformula == 112
      jc = cos(jc)*exp(jc)
    elseif  @pixelformula == 113
      jc = sinh(jc)*exp(jc)
    elseif  @pixelformula == 114
      jc = cosh(jc)*exp(jc)
    elseif  @pixelformula == 115
      jc = sin(jc)*log(jc)
    elseif  @pixelformula == 116
      jc = cos(jc)*log(jc)
    elseif  @pixelformula == 117
      jc = sinh(jc)*log(jc)
    else ; @pixelformula == 118
      jc = cosh(jc)*log(jc)
    endif ; @pixelformula = 1
  endif ; @pixelformula != 0

  loop:
  if @pmode != 0
    z = z + jc
  endif ; pmode

  zblend = z
  iterations = iterations + 1

  if @formula1 == "z^2"
    zf1 = sqr(z)
  elseif  @formula1 == "z^3"
    zf1 = z * sqr(z)
  elseif  @formula1 == "z^4"
    zf1 = sqr(sqr(z))
  elseif  @formula1 == "z^power"
    zf1 = z ^ @power1
  elseif  @formula1 == "1/z"
    zf1 = 1/z
  elseif  @formula1 == "sqrt"
    zf1 = sqrt(z)
  elseif  @formula1 == "1/z^2"
    zf1 = 1 / (sqr(z))
  elseif  @formula1 == "log"
    zf1 = log(@premult1a*z)
  elseif  @formula1 == "e^z"
    zf1 = exp(@premult1a*z)
  elseif  @formula1 == "z^z"
    zf1 = z^(@premult1a*z)
  elseif  @formula1 == "sin"
    zf1 = sin(@premult1a*z )
  elseif  @formula1 == "cos"
    zf1 = cos(@premult1a*z )
  elseif  @formula1 == "tan"
    zf1 = tan(@premult1a*z )
  elseif  @formula1 == "asin"
    zf1 = asin(@premult1a*z )
  elseif  @formula1 == "acos"
    zf1 = acos( @premult1a*z )
  elseif  @formula1 == "atan"
    zf1 = atan( @premult1a*z )
  elseif  @formula1 == "sinh"
    zf1 = sinh( @premult1a*z )
  elseif  @formula1 == "cosh"
    zf1 = cosh( @premult1a*z )
  elseif  @formula1 == "tanh"
    zf1 = tanh( @premult1a*z )
  elseif  @formula1 == "asinh"
    zf1 = asinh( @premult1a*z )
  elseif @formula1 == "acosh"
    zf1 = acosh( @premult1a*z )
  elseif  @formula1 == "atanh"
    zf1 = atanh( @premult1a*z )
  elseif  @formula1 == "log(1/z)"
    zf1 = log( 1/(@premult1a*z) )
  elseif  @formula1 == "log(log)"
    zf1 = log(@premult1b* log( @premult1a*z ))
  elseif  @formula1 == "e^-z"
    zf1 = exp( -z )
  elseif  @formula1 == "e^(1/z)"
    zf1 = exp( @premult1a/z )
  elseif  @formula1 == "z^-z"
    zf1 = z^(-@premult1a*z)
  elseif  @formula1 == "sin^2"
    zextra = sin( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "cos^2"
    zextra = cos( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "tan^2"
    zextra = tan( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "cot"
    zf1 = cotan( @premult1a*z )
  elseif  @formula1 == "sec"
    zf1 = 1/cos( @premult1a*z )
  elseif  @formula1 == "csc"
    zf1 = 1/sin( @premult1a*z )
  elseif  @formula1 == "cot^2"
    zextra = cotan( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "sec^2"
    zextra = 1/cos( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "csc^2"
    zextra = 1/sin( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "z^z^z"
    zextra = z^(@premult1a*z)
    zf1 = z^zextra
  elseif  @formula1 == "1/z^z^z"
    zextra = z^(@premult1a*z)
    zf1 = 1/( z^zextra )
  elseif  @formula1 == "log(-z)"
    zf1 = log(-@premult1a*z)
  elseif  @formula1 == "1/log"
    zf1 = 1/log( @premult1a*z )
  elseif  @formula1 == "zlog"
    zf1 = z * log( @premult1a*z )
  elseif  @formula1 == "sin(z)/z"
    zf1 = sin( @premult1a*z ) / z
  elseif  @formula1 == "cos(z)/z"
    zf1 = cos( @premult1a*z ) / z
  elseif  @formula1 == "sin*cos"
    zf1 = sin( @premult1a*z ) * cos( @premult1b*z )
  elseif  @formula1 == "sin(z^2)"
    zf1 = sin( @premult1a*z^2 )
  elseif  @formula1 == "e^(-1/z)"
    zf1 = exp( -@premult1a/z )
  elseif  @formula1 == "ze^z"
    zf1 = z * exp( @premult1a*z )
  elseif  @formula1 == "ze^-z"
    zf1 = z * exp( -z )
  elseif  @formula1 == "ze^(1/z)"
    zf1 = z * exp( @premult1a/z )
  elseif  @formula1 == "ze^(-1/z)"
    zf1 = z * exp( -1/z )
  elseif  @formula1 == "1/z^3"
    zf1 = 1 / ( z * sqr(z) )
  elseif  @formula1 == "acot"
    zf1 = atan( 1 / @premult1a*z )
  elseif  @formula1 == "asec"
    zf1 = acos( 1 / @premult1a*z )
  elseif  @formula1 == "acsc"
    zf1 = asin( 1 / @premult1a*z )
  elseif  @formula1 == "tan(z)/z"
    zf1 = tan( @premult1a*z ) / z
  elseif  @formula1 == "cot(z)/z"
    zf1 = cotan( @premult1a*z ) / z
  elseif  @formula1 == "sec(z)/z"
    zf1 = 1 / ( z * cos( @premult1a*z ))
  elseif  @formula1 == "csc(z)/z"
    zf1 = 1 / ( z * sin( @premult1a*z ))
  elseif  @formula1 == "zsin"
    zf1 = z * sin( @premult1a*z )
  elseif  @formula1 == "zcos"
    zf1 = z * cos( @premult1a*z )
  elseif  @formula1 == "ztan"
    zf1 = z * tan( @premult1a*z )
  elseif  @formula1 == "zcot"
    zf1 = z * cotan( @premult1a*z )
  elseif  @formula1 == "zsec"
    zf1 = z/cos( @premult1a*z )
  elseif  @formula1 == "zcsc"
    zf1 = z/sin( @premult1a*z )
  elseif  @formula1 == "sin(1/z)"
    zf1 = sin( @premult1a/z )
  elseif  @formula1 == "cos(1/z)"
    zf1 = cos( @premult1a/z )
  elseif  @formula1 == "tan(1/z)"
    zf1 = tan( @premult1a/z )
  elseif  @formula1 == "cot(1/z)"
    zf1 = cotan( @premult1a/z )
  elseif  @formula1 == "sec(1/z)"
    zf1 = 1/cos( @premult1a/z )
  elseif  @formula1 == "csc(1/z)"
    zf1 = 1/sin( @premult1a/z )
  elseif  @formula1 == "cotanh"
    zf1 = cotanh( @premult1a*z )
  elseif  @formula1 == "sech"
    zf1 = 1/cosh( @premult1a*z )
  elseif  @formula1 == "cosech"
    zf1 = 1/sinh( @premult1a*z )
  elseif  @formula1 == "acoth"
    zf1 = atanh( 1/(@premult1a*z) )
  elseif  @formula1 == "asech"
    zf1 = acosh( 1/(@premult1a*z) )
  elseif  @formula1 == "acosech"
    zf1 = asinh( 1/(@premult1a*z) )
  elseif @formula1 == "3-term polynomial"
    zf1 = @coeff1a * z^@exponent1a + @coeff1b * z^@exponent1b + \
          @coeff1c * z^@exponent1c
  elseif  @formula1 == "sinh^2"
    zextra = sinh(@premult1a*z)
    zf1 = zextra * zextra
  elseif  @formula1 == "cosh^2"
    zextra = cosh( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "tanh^2"
    zextra = tanh(@premult1a*z)
    zf1 = zextra * zextra
  elseif  @formula1 == "cotanh^2"
    zextra = cotanh( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "sech^2"
    zextra = (1,0)/cosh(@premult1a*z)
    zf1 = zextra * zextra
  elseif  @formula1 == "cosech^2"
    zextra = (1,0) / sinh( @premult1a*z )
    zf1 = zextra * zextra
  elseif  @formula1 == "sinh(1/z)"
    zf1 = sinh(@premult1a/z)
  elseif  @formula1 == "cosh(1/z)"
    zf1 = cosh(@premult1a/z)
  elseif  @formula1 == "tanh(1/z)"
    zf1 = tanh(@premult1a/z)
  elseif  @formula1 == "cotanh(1/z)"
    zf1 = cotanh(@premult1a/z)
  elseif  @formula1 == "sech(1/z)"
    zf1 = (1,0)/cosh(@premult1a/z)
  elseif  @formula1 == "cosech(1/z)"
    zf1 = (1,0)/sinh(@premult1a/z)
  elseif  @formula1 == "sin*tan"
    zf1 = sin( @premult1a*z ) * tan(@premult1b*z)
  elseif  @formula1 == "sinh*tanh"
    zf1 = sinh(@premult1a*z) * tanh(@premult1b*z)
  elseif  @formula1 == "sinh*cosh"
    zf1 = sinh(@premult1a*z) * cosh(@premult1b*z)
  elseif  @formula1 == "sinh^2*cosh^2"
    ztemp = sinh(@premult1a*z), zextra = cosh(@premult1b*z)
    zf1 = ztemp*ztemp*zextra*zextra
  elseif  @formula1 == "sin^2*cos^2"
    ztemp = sin(@premult1a*z), zextra = cos(@premult1b*z)
    zf1 = ztemp*ztemp*zextra*zextra
  elseif  @formula1 == "sin(1/z)*cos(1/z)"
    zextra = 1/(@premult1a*z), ztemp = 1/(@premult1b*z)
    zf1 = sin(zextra)*cos(ztemp)
  elseif  @formula1 == "sin(1/z)^2"
    zextra = sin( @premult1a/z )
    zf1 = zextra*zextra
  elseif  @formula1 == "sin(z)*cos(1/z)"
    zf1 = sin(@premult1a*z) * cos(@premult1b/z)
  elseif  @formula1 == "sin(z)*sin(1/z)"
    zf1 = sin(@premult1a*z) * sin(@premult1b/z)
  elseif  @formula1 == "log^2"
    zextra = log(@premult1a*z)
    zf1 = zextra*zextra
  elseif  @formula1 == "sin(mz)*sin(nz)"
    zf1 = sin(@premult1a*z) * sin(@premult1b*z)
  elseif  @formula1 == "sinh(1/z)*cosh(1/z)"
    zextra = @premult1a/z, ztemp = @premult1b/z
    zf1 = sinh(zextra)*cosh(ztemp)
  elseif  @formula1 == "sinh(1/z)^2"
    zextra = sinh( @premult1a/z )
    zf1 = zextra*zextra
  elseif  @formula1 == "sinh*cosh(1/z)"
    zf1 = sinh(@premult1a*z) * cosh(@premult1b/z)
  elseif  @formula1 == "sinh*sinh(1/z)"
    zf1 = sinh(@premult1a*z) * sinh(@premult1b/z)
  elseif  @formula1 == "sin*sinh"
    zf1 = sin(@premult1a*z) * sinh(@premult1b*z)
  elseif  @formula1 == "sin*cosh"
    zf1 = sin(@premult1a*z) * cosh(@premult1b*z)
  elseif  @formula1 == "sin^2*sinh^2"
    zextra = sin(@premult1a*z), ztemp = sinh(@premult1b*z)
    zf1 = ztemp*ztemp*zextra*zextra
  elseif  @formula1 == "sin*e^z"
    zf1 = sin(@premult1a*z)*exp(@premult1b*z)
  elseif  @formula1 == "cos*e^z"
    zf1 = cos(@premult1a*z)*exp(@premult1b*z)
  elseif  @formula1 == "sinh*e^z"
    zf1 = sinh(@premult1a*z)*exp(@premult1b*z)
  elseif  @formula1 == "cosh*e^z"
    zf1 = cosh(@premult1a*z)*exp(@premult1b*z)
  elseif  @formula1 == "sin*log"
    zf1 = sin(@premult1a*z)*log(@premult1b*z)
  elseif  @formula1 == "cos*log"
    zf1 = cos(@premult1a*z)*log(@premult1b*z)
  elseif  @formula1 == "sinh*log"
    zf1 = sinh(@premult1a*z)*log(@premult1b*z)
  elseif @formula1 == "cosh*log"
    zf1 = cosh(@premult1a*z)*log(@premult1b*z)
  elseif @formula1 == "e^(z^2)"
    zf1 = exp(@premult1a*z*z)
  elseif @formula1 == "e^(-(z^2))"
    zf1 = exp(-(z*z))
  elseif @formula1 == "e^(1/z^2)"
    zf1 = exp(@premult1a/(z*z))
  elseif @formula1 == "e^(-1/z^2)"
    zf1 = exp(-1/(z*z))
  elseif @formula1 == "ver" ; versine
	zf1 = 1 - cos(@premult1a*z)
  elseif @formula1 == "vcs" ; vercosine
	zf1 = 1 + cos(@premult1a*z)
  elseif @formula1 == "cvs" ; coversine
	zf1 = 1 - sin(@premult1a*z)
  elseif @formula1 == "cvc" ; covercosine
	zf1 = 1 + sin(@premult1a*z)
  elseif @formula1 == "exs" ; exsecant
	zf1 = 1/cos(@premult1a*z) - 1
  elseif @formula1 == "exc" ; excosecant
	zf1 = 1/sin(@premult1a*z) - 1
  elseif @formula1 == "crd" ; chord
	zf1 = 2 * sin(@premult1a*z/2)
  elseif @formula1 == "aver" ; arcversine
	zf1 = acos(1 - @premult1a*z)
  elseif @formula1 == "avcs" ; arcvercosine
	zf1 = acos(1 + @premult1a*z)
  elseif @formula1 == "acvs" ; arccoversine
	zf1 = asin(1 - @premult1a*z)
  elseif @formula1 == "acvc" ; arccovercosine
	zf1 = asin(1 + @premult1a*z)
  elseif @formula1 == "aexs" ; arcexsecant
	zf1 = acos( (1/(@premult1a*(z+1))))
  elseif @formula1 == "aexc" ; arcexcosecant
	zf1 = asin( (1/(@premult1a*(z+1))))
  elseif @formula1 == "acrd" ; arcchord
	zf1 = 2 * asin( @premult1a*z/2 )
  elseif @formula1 == "abs"
	zf1 = abs( @premult1a*z )
  elseif @formula1 == "conj"
	zf1 = conj( @premult1a*z )
  elseif @formula1 == "flip"
	zf1 = flip( @premult1a*z )
  elseif @formula1 == "ceiling"
	zf1 = ceil( @premult1a*z )
  elseif @formula1 == "floor"
	zf1 = floor( @premult1a*z )
  elseif @formula1 == "truncation"
	zf1 = trunc( @premult1a*z )
  elseif @formula1 == "round"
	zf1 = round( @premult1a*z )
  elseif @formula1 == "atan2"
	zf1 = atan2( @premult1a*z )
  elseif @formula1 == "e^e^z"
	zf1 = exp(@premult1b*exp( @premult1a*z ))
  elseif @formula1 == "constant^z"
	zf1 = @base1^( @premult1a*z )
  elseif @formula1 == "constant^z^z"
	zf1 = @base1^(@premult1b*z^( @premult1a*z ))
  elseif @formula1 == "real"
	zf1 = real(z) + flip(0)
  elseif @formula1 == "imag"
	zf1 = (0,0) + flip(imag(z))
  elseif @formula1 == "conj(flip)"
	zf1 = conj(@premult1b*flip( @premult1a*z ))
  elseif @formula1 == "flip(conj)"
	zf1 = flip(@premult1b* conj(@premult1a*z ))
  elseif @formula1 == "z"
	zf1 = @premult1a*z
  endif ; @formula1

	zf1 = @funcmult1 * zf1

  if iterations % @frequency == 0 ; execute other formulas and combine
    zf1 = @weight1*zf1
    if ( @combo == 3 ) || ( @combo == 9 )
      z = zf1
    endif ; @combo
	  if @formula2 == "z^2"
		zf2 = sqr(z)
	  elseif  @formula2 == "z^3"
		zf2 = z * sqr(z)
	  elseif  @formula2 == "z^4"
		zf2 = sqr(sqr(z))
	  elseif  @formula2 == "z^power"
		zf2 = z ^ @power2
	  elseif  @formula2 == "1/z"
		zf2 = 1/z
	  elseif  @formula2 == "sqrt"
		zf2 = sqrt(z)
	  elseif  @formula2 == "1/z^2"
		zf2 = 1 / (sqr(z))
	  elseif  @formula2 == "log"
		zf2 = log(@premult2a*z)
	  elseif  @formula2 == "e^z"
		zf2 = exp(@premult2a*z)
	  elseif  @formula2 == "z^z"
		zf2 = z^(@premult2a*z)
	  elseif  @formula2 == "sin"
		zf2 = sin(@premult2a*z )
	  elseif  @formula2 == "cos"
		zf2 = cos(@premult2a*z )
	  elseif  @formula2 == "tan"
		zf2 = tan(@premult2a*z )
	  elseif  @formula2 == "asin"
		zf2 = asin(@premult2a*z )
	  elseif  @formula2 == "acos"
		zf2 = acos( @premult2a*z )
	  elseif  @formula2 == "atan"
		zf2 = atan( @premult2a*z )
	  elseif  @formula2 == "sinh"
		zf2 = sinh( @premult2a*z )
	  elseif  @formula2 == "cosh"
		zf2 = cosh( @premult2a*z )
	  elseif  @formula2 == "tanh"
		zf2 = tanh( @premult2a*z )
	  elseif  @formula2 == "asinh"
		zf2 = asinh( @premult2a*z )
	  elseif @formula2 == "acosh"
		zf2 = acosh( @premult2a*z )
	  elseif  @formula2 == "atanh"
		zf2 = atanh( @premult2a*z )
	  elseif  @formula2 == "log(1/z)"
		zf2 = log( 1/(@premult2a*z) )
	  elseif  @formula2 == "log(log)"
		zf2 = log(@premult2b* log( @premult2a*z ))
	  elseif  @formula2 == "e^-z"
		zf2 = exp( -z )
	  elseif  @formula2 == "e^(1/z)"
		zf2 = exp( @premult2a/z )
	  elseif  @formula2 == "z^-z"
		zf2 = z^(-@premult2a*z)
	  elseif  @formula2 == "sin^2"
		zextra = sin( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "cos^2"
		zextra = cos( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "tan^2"
		zextra = tan( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "cot"
		zf2 = cotan( @premult2a*z )
	  elseif  @formula2 == "sec"
		zf2 = 1/cos( @premult2a*z )
	  elseif  @formula2 == "csc"
		zf2 = 1/sin( @premult2a*z )
	  elseif  @formula2 == "cot^2"
		zextra = cotan( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "sec^2"
		zextra = 1/cos( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "csc^2"
		zextra = 1/sin( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "z^z^z"
		zextra = z^(@premult2a*z)
		zf2 = z^zextra
	  elseif  @formula2 == "1/z^z^z"
		zextra = z^(@premult2a*z)
		zf2 = 1/( z^zextra )
	  elseif  @formula2 == "log(-z)"
		zf2 = log(-@premult2a*z)
	  elseif  @formula2 == "1/log"
		zf2 = 1/log( @premult2a*z )
	  elseif  @formula2 == "zlog"
		zf2 = z * log( @premult2a*z )
	  elseif  @formula2 == "sin(z)/z"
		zf2 = sin( @premult2a*z ) / z
	  elseif  @formula2 == "cos(z)/z"
		zf2 = cos( @premult2a*z ) / z
	  elseif  @formula2 == "sin*cos"
		zf2 = sin( @premult2a*z ) * cos( @premult2b*z )
	  elseif  @formula2 == "sin(z^2)"
		zf2 = sin( @premult2a*z^2 )
	  elseif  @formula2 == "e^(-1/z)"
		zf2 = exp( -@premult2a/z )
	  elseif  @formula2 == "ze^z"
		zf2 = z * exp( @premult2a*z )
	  elseif  @formula2 == "ze^-z"
		zf2 = z * exp( -z )
	  elseif  @formula2 == "ze^(1/z)"
		zf2 = z * exp( @premult2a/z )
	  elseif  @formula2 == "ze^(-1/z)"
		zf2 = z * exp( -1/z )
	  elseif  @formula2 == "1/z^3"
		zf2 = 1 / ( z * sqr(z) )
	  elseif  @formula2 == "acot"
		zf2 = atan( 1 / @premult2a*z )
	  elseif  @formula2 == "asec"
		zf2 = acos( 1 / @premult2a*z )
	  elseif  @formula2 == "acsc"
		zf2 = asin( 1 / @premult2a*z )
	  elseif  @formula2 == "tan(z)/z"
		zf2 = tan( @premult2a*z ) / z
	  elseif  @formula2 == "cot(z)/z"
		zf2 = cotan( @premult2a*z ) / z
	  elseif  @formula2 == "sec(z)/z"
		zf2 = 1 / ( z * cos( @premult2a*z ))
	  elseif  @formula2 == "csc(z)/z"
		zf2 = 1 / ( z * sin( @premult2a*z ))
	  elseif  @formula2 == "zsin"
		zf2 = z * sin( @premult2a*z )
	  elseif  @formula2 == "zcos"
		zf2 = z * cos( @premult2a*z )
	  elseif  @formula2 == "ztan"
		zf2 = z * tan( @premult2a*z )
	  elseif  @formula2 == "zcot"
		zf2 = z * cotan( @premult2a*z )
	  elseif  @formula2 == "zsec"
		zf2 = z/cos( @premult2a*z )
	  elseif  @formula2 == "zcsc"
		zf2 = z/sin( @premult2a*z )
	  elseif  @formula2 == "sin(1/z)"
		zf2 = sin( @premult2a/z )
	  elseif  @formula2 == "cos(1/z)"
		zf2 = cos( @premult2a/z )
	  elseif  @formula2 == "tan(1/z)"
		zf2 = tan( @premult2a/z )
	  elseif  @formula2 == "cot(1/z)"
		zf2 = cotan( @premult2a/z )
	  elseif  @formula2 == "sec(1/z)"
		zf2 = 1/cos( @premult2a/z )
	  elseif  @formula2 == "csc(1/z)"
		zf2 = 1/sin( @premult2a/z )
	  elseif  @formula2 == "cotanh"
		zf2 = cotanh( @premult2a*z )
	  elseif  @formula2 == "sech"
		zf2 = 1/cosh( @premult2a*z )
	  elseif  @formula2 == "cosech"
		zf2 = 1/sinh( @premult2a*z )
	  elseif  @formula2 == "acoth"
		zf2 = atanh( 1/(@premult2a*z) )
	  elseif  @formula2 == "asech"
		zf2 = acosh( 1/(@premult2a*z) )
	  elseif  @formula2 == "acosech"
		zf2 = asinh( 1/(@premult2a*z) )
	  elseif @formula2 == "3-term polynomial"
		zf2 = @coeff2a * z^@exponent2a + @coeff2b * z^@exponent2b + \
			  @coeff2c * z^@exponent2c
	  elseif  @formula2 == "sinh^2"
		zextra = sinh(@premult2a*z)
		zf2 = zextra * zextra
	  elseif  @formula2 == "cosh^2"
		zextra = cosh( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "tanh^2"
		zextra = tanh(@premult2a*z)
		zf2 = zextra * zextra
	  elseif  @formula2 == "cotanh^2"
		zextra = cotanh( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "sech^2"
		zextra = (1,0)/cosh(@premult2a*z)
		zf2 = zextra * zextra
	  elseif  @formula2 == "cosech^2"
		zextra = (1,0) / sinh( @premult2a*z )
		zf2 = zextra * zextra
	  elseif  @formula2 == "sinh(1/z)"
		zf2 = sinh(@premult2a/z)
	  elseif  @formula2 == "cosh(1/z)"
		zf2 = cosh(@premult2a/z)
	  elseif  @formula2 == "tanh(1/z)"
		zf2 = tanh(@premult2a/z)
	  elseif  @formula2 == "cotanh(1/z)"
		zf2 = cotanh(@premult2a/z)
	  elseif  @formula2 == "sech(1/z)"
		zf2 = (1,0)/cosh(@premult2a/z)
	  elseif  @formula2 == "cosech(1/z)"
		zf2 = (1,0)/sinh(@premult2a/z)
	  elseif  @formula2 == "sin*tan"
		zf2 = sin( @premult2a*z ) * tan(@premult2b*z)
	  elseif  @formula2 == "sinh*tanh"
		zf2 = sinh(@premult2a*z) * tanh(@premult2b*z)
	  elseif  @formula2 == "sinh*cosh"
		zf2 = sinh(@premult2a*z) * cosh(@premult2b*z)
	  elseif  @formula2 == "sinh^2*cosh^2"
		ztemp = sinh(@premult2a*z), zextra = cosh(@premult2b*z)
		zf2 = ztemp*ztemp*zextra*zextra
	  elseif  @formula2 == "sin^2*cos^2"
		ztemp = sin(@premult2a*z), zextra = cos(@premult2b*z)
		zf2 = ztemp*ztemp*zextra*zextra
	  elseif  @formula2 == "sin(1/z)*cos(1/z)"
		zextra = 1/(@premult2a*z), ztemp = 1/(@premult2b*z)
		zf2 = sin(zextra)*cos(ztemp)
	  elseif  @formula2 == "sin(1/z)^2"
		zextra = sin( @premult2a/z )
		zf2 = zextra*zextra
	  elseif  @formula2 == "sin(z)*cos(1/z)"
		zf2 = sin(@premult2a*z) * cos(@premult2b/z)
	  elseif  @formula2 == "sin(z)*sin(1/z)"
		zf2 = sin(@premult2a*z) * sin(@premult2b/z)
	  elseif  @formula2 == "log^2"
		zextra = log(@premult2a*z)
		zf2 = zextra*zextra
	  elseif  @formula2 == "sin(mz)*sin(nz)"
		zf2 = sin(@premult2a*z) * sin(@premult2b*z)
	  elseif  @formula2 == "sinh(1/z)*cosh(1/z)"
		zextra = @premult2a/z, ztemp = @premult2b/z
		zf2 = sinh(zextra)*cosh(ztemp)
	  elseif  @formula2 == "sinh(1/z)^2"
		zextra = sinh( @premult2a/z )
		zf2 = zextra*zextra
	  elseif  @formula2 == "sinh*cosh(1/z)"
		zf2 = sinh(@premult2a*z) * cosh(@premult2b/z)
	  elseif  @formula2 == "sinh*sinh(1/z)"
		zf2 = sinh(@premult2a*z) * sinh(@premult2b/z)
	  elseif  @formula2 == "sin*sinh"
		zf2 = sin(@premult2a*z) * sinh(@premult2b*z)
	  elseif  @formula2 == "sin*cosh"
		zf2 = sin(@premult2a*z) * cosh(@premult2b*z)
	  elseif  @formula2 == "sin^2*sinh^2"
		zextra = sin(@premult2a*z), ztemp = sinh(@premult2b*z)
		zf2 = ztemp*ztemp*zextra*zextra
	  elseif  @formula2 == "sin*e^z"
		zf2 = sin(@premult2a*z)*exp(@premult2b*z)
	  elseif  @formula2 == "cos*e^z"
		zf2 = cos(@premult2a*z)*exp(@premult2b*z)
	  elseif  @formula2 == "sinh*e^z"
		zf2 = sinh(@premult2a*z)*exp(@premult2b*z)
	  elseif  @formula2 == "cosh*e^z"
		zf2 = cosh(@premult2a*z)*exp(@premult2b*z)
	  elseif  @formula2 == "sin*log"
		zf2 = sin(@premult2a*z)*log(@premult2b*z)
	  elseif  @formula2 == "cos*log"
		zf2 = cos(@premult2a*z)*log(@premult2b*z)
	  elseif  @formula2 == "sinh*log"
		zf2 = sinh(@premult2a*z)*log(@premult2b*z)
	  elseif @formula2 == "cosh*log"
		zf2 = cosh(@premult2a*z)*log(@premult2b*z)
	  elseif @formula2 == "e^(z^2)"
		zf2 = exp(@premult2a*z*z)
	  elseif @formula2 == "e^(-(z^2))"
		zf2 = exp(-(z*z))
	  elseif @formula2 == "e^(1/z^2)"
		zf2 = exp(@premult2a/(z*z))
	  elseif @formula2 == "e^(-1/z^2)"
		zf2 = exp(-1/(z*z))
	  elseif @formula2 == "ver" ; versine
		zf2 = 1 - cos(@premult2a*z)
	  elseif @formula2 == "vcs" ; vercosine
		zf2 = 1 + cos(@premult2a*z)
	  elseif @formula2 == "cvs" ; coversine
		zf2 = 1 - sin(@premult2a*z)
	  elseif @formula2 == "cvc" ; covercosine
		zf2 = 1 + sin(@premult2a*z)
	  elseif @formula2 == "exs" ; exsecant
		zf2 = 1/cos(@premult2a*z) - 1
	  elseif @formula2 == "exc" ; excosecant
		zf2 = 1/sin(@premult2a*z) - 1
	  elseif @formula2 == "crd" ; chord
		zf2 = 2 * sin(@premult2a*z/2)
	  elseif @formula2 == "aver" ; arcversine
		zf2 = acos(1 - @premult2a*z)
	  elseif @formula2 == "avcs" ; arcvercosine
		zf2 = acos(1 + @premult2a*z)
	  elseif @formula2 == "acvs" ; arccoversine
		zf2 = asin(1 - @premult2a*z)
	  elseif @formula2 == "acvc" ; arccovercosine
		zf2 = asin(1 + @premult2a*z)
	  elseif @formula2 == "aexs" ; arcexsecant
		zf2 = acos( (1/(@premult2a*(z+1))))
	  elseif @formula2 == "aexc" ; arcexcosecant
		zf2 = asin( (1/(@premult2a*(z+1))))
	  elseif @formula2 == "acrd" ; arcchord
		zf2 = 2 * asin( @premult2a*z/2 )
	  elseif @formula2 == "abs"
		zf2 = abs( @premult2a*z )
	  elseif @formula2 == "conj"
		zf2 = conj( @premult2a*z )
	  elseif @formula2 == "flip"
		zf2 = flip( @premult2a*z )
	  elseif @formula2 == "ceiling"
		zf2 = ceil( @premult2a*z )
	  elseif @formula2 == "floor"
		zf2 = floor( @premult2a*z )
	  elseif @formula2 == "truncation"
		zf2 = trunc( @premult2a*z )
	  elseif @formula2 == "round"
		zf2 = round( @premult2a*z )
	  elseif @formula2 == "atan2"
		zf2 = atan2( @premult2a*z )
	  elseif @formula2 == "e^e^z"
		zf2 = exp(@premult2b*exp( @premult2a*z ))
	  elseif @formula2 == "constant^z"
		zf2 = @base2^( @premult2a*z )
	  elseif @formula2 == "constant^z^z"
		zf2 = @base2^(@premult2b*z^( @premult2a*z ))
	  elseif @formula2 == "real"
		zf2 = real(z) + flip(0)
	  elseif @formula2 == "imag"
		zf2 = (0,0) + flip(imag(z))
	  elseif @formula2 == "conj(flip)"
		zf2 = conj(@premult2b*flip( @premult2a*z ))
	  elseif @formula2 == "flip(conj)"
		zf2 = flip(@premult2b* conj(@premult2a*z ))
	  elseif @formula2 == "z"
		zf2 = @premult2a*z
	  endif ; @formula2

	zf2 = @weight2 * @funcmult2 * zf2

    if @combo > 5 ; also need func 3 for these combinations
      if @combo == 9
        z = zf2
      elseif @combo == 17
        z = zf1 + zf2
      elseif @combo == 18
        z = zf1 * zf2
      elseif @combo == 19
        z = zf1 / zf2
      elseif @combo == 20
        z = zf1 ^ zf2
      elseif @combo == 21
        z = log(zf1)/log(zf2)
      endif; @combo

	  if @formula3 == "z^2"
		zf3 = sqr(z)
	  elseif  @formula3 == "z^3"
		zf3 = z * sqr(z)
	  elseif  @formula3 == "z^4"
		zf3 = sqr(sqr(z))
	  elseif  @formula3 == "z^power"
		zf3 = z ^ @power3
	  elseif  @formula3 == "1/z"
		zf3 = 1/z
	  elseif  @formula3 == "sqrt"
		zf3 = sqrt(z)
	  elseif  @formula3 == "1/z^2"
		zf3 = 1 / (sqr(z))
	  elseif  @formula3 == "log"
		zf3 = log(@premult3a*z)
	  elseif  @formula3 == "e^z"
		zf3 = exp(@premult3a*z)
	  elseif  @formula3 == "z^z"
		zf3 = z^(@premult3a*z)
	  elseif  @formula3 == "sin"
		zf3 = sin(@premult3a*z )
	  elseif  @formula3 == "cos"
		zf3 = cos(@premult3a*z )
	  elseif  @formula3 == "tan"
		zf3 = tan(@premult3a*z )
	  elseif  @formula3 == "asin"
		zf3 = asin(@premult3a*z )
	  elseif  @formula3 == "acos"
		zf3 = acos( @premult3a*z )
	  elseif  @formula3 == "atan"
		zf3 = atan( @premult3a*z )
	  elseif  @formula3 == "sinh"
		zf3 = sinh( @premult3a*z )
	  elseif  @formula3 == "cosh"
		zf3 = cosh( @premult3a*z )
	  elseif  @formula3 == "tanh"
		zf3 = tanh( @premult3a*z )
	  elseif  @formula3 == "asinh"
		zf3 = asinh( @premult3a*z )
	  elseif @formula3 == "acosh"
		zf3 = acosh( @premult3a*z )
	  elseif  @formula3 == "atanh"
		zf3 = atanh( @premult3a*z )
	  elseif  @formula3 == "log(1/z)"
		zf3 = log( 1/(@premult3a*z) )
	  elseif  @formula3 == "log(log)"
		zf3 = log(@premult3b* log( @premult3a*z ))
	  elseif  @formula3 == "e^-z"
		zf3 = exp( -z )
	  elseif  @formula3 == "e^(1/z)"
		zf3 = exp( @premult3a/z )
	  elseif  @formula3 == "z^-z"
		zf3 = z^(-@premult3a*z)
	  elseif  @formula3 == "sin^2"
		zextra = sin( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "cos^2"
		zextra = cos( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "tan^2"
		zextra = tan( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "cot"
		zf3 = cotan( @premult3a*z )
	  elseif  @formula3 == "sec"
		zf3 = 1/cos( @premult3a*z )
	  elseif  @formula3 == "csc"
		zf3 = 1/sin( @premult3a*z )
	  elseif  @formula3 == "cot^2"
		zextra = cotan( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "sec^2"
		zextra = 1/cos( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "csc^2"
		zextra = 1/sin( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "z^z^z"
		zextra = z^(@premult3a*z)
		zf3 = z^zextra
	  elseif  @formula3 == "1/z^z^z"
		zextra = z^(@premult3a*z)
		zf3 = 1/( z^zextra )
	  elseif  @formula3 == "log(-z)"
		zf3 = log(-@premult3a*z)
	  elseif  @formula3 == "1/log"
		zf3 = 1/log( @premult3a*z )
	  elseif  @formula3 == "zlog"
		zf3 = z * log( @premult3a*z )
	  elseif  @formula3 == "sin(z)/z"
		zf3 = sin( @premult3a*z ) / z
	  elseif  @formula3 == "cos(z)/z"
		zf3 = cos( @premult3a*z ) / z
	  elseif  @formula3 == "sin*cos"
		zf3 = sin( @premult3a*z ) * cos( @premult3b*z )
	  elseif  @formula3 == "sin(z^2)"
		zf3 = sin( @premult3a*z^2 )
	  elseif  @formula3 == "e^(-1/z)"
		zf3 = exp( -@premult3a/z )
	  elseif  @formula3 == "ze^z"
		zf3 = z * exp( @premult3a*z )
	  elseif  @formula3 == "ze^-z"
		zf3 = z * exp( -z )
	  elseif  @formula3 == "ze^(1/z)"
		zf3 = z * exp( @premult3a/z )
	  elseif  @formula3 == "ze^(-1/z)"
		zf3 = z * exp( -1/z )
	  elseif  @formula3 == "1/z^3"
		zf3 = 1 / ( z * sqr(z) )
	  elseif  @formula3 == "acot"
		zf3 = atan( 1 / @premult3a*z )
	  elseif  @formula3 == "asec"
		zf3 = acos( 1 / @premult3a*z )
	  elseif  @formula3 == "acsc"
		zf3 = asin( 1 / @premult3a*z )
	  elseif  @formula3 == "tan(z)/z"
		zf3 = tan( @premult3a*z ) / z
	  elseif  @formula3 == "cot(z)/z"
		zf3 = cotan( @premult3a*z ) / z
	  elseif  @formula3 == "sec(z)/z"
		zf3 = 1 / ( z * cos( @premult3a*z ))
	  elseif  @formula3 == "csc(z)/z"
		zf3 = 1 / ( z * sin( @premult3a*z ))
	  elseif  @formula3 == "zsin"
		zf3 = z * sin( @premult3a*z )
	  elseif  @formula3 == "zcos"
		zf3 = z * cos( @premult3a*z )
	  elseif  @formula3 == "ztan"
		zf3 = z * tan( @premult3a*z )
	  elseif  @formula3 == "zcot"
		zf3 = z * cotan( @premult3a*z )
	  elseif  @formula3 == "zsec"
		zf3 = z/cos( @premult3a*z )
	  elseif  @formula3 == "zcsc"
		zf3 = z/sin( @premult3a*z )
	  elseif  @formula3 == "sin(1/z)"
		zf3 = sin( @premult3a/z )
	  elseif  @formula3 == "cos(1/z)"
		zf3 = cos( @premult3a/z )
	  elseif  @formula3 == "tan(1/z)"
		zf3 = tan( @premult3a/z )
	  elseif  @formula3 == "cot(1/z)"
		zf3 = cotan( @premult3a/z )
	  elseif  @formula3 == "sec(1/z)"
		zf3 = 1/cos( @premult3a/z )
	  elseif  @formula3 == "csc(1/z)"
		zf3 = 1/sin( @premult3a/z )
	  elseif  @formula3 == "cotanh"
		zf3 = cotanh( @premult3a*z )
	  elseif  @formula3 == "sech"
		zf3 = 1/cosh( @premult3a*z )
	  elseif  @formula3 == "cosech"
		zf3 = 1/sinh( @premult3a*z )
	  elseif  @formula3 == "acoth"
		zf3 = atanh( 1/(@premult3a*z) )
	  elseif  @formula3 == "asech"
		zf3 = acosh( 1/(@premult3a*z) )
	  elseif  @formula3 == "acosech"
		zf3 = asinh( 1/(@premult3a*z) )
	  elseif @formula3 == "3-term polynomial"
		zf3 = @coeff3a * z^@exponent3a + @coeff3b * z^@exponent3b + \
			  @coeff3c * z^@exponent3c
	  elseif  @formula3 == "sinh^2"
		zextra = sinh(@premult3a*z)
		zf3 = zextra * zextra
	  elseif  @formula3 == "cosh^2"
		zextra = cosh( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "tanh^2"
		zextra = tanh(@premult3a*z)
		zf3 = zextra * zextra
	  elseif  @formula3 == "cotanh^2"
		zextra = cotanh( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "sech^2"
		zextra = (1,0)/cosh(@premult3a*z)
		zf3 = zextra * zextra
	  elseif  @formula3 == "cosech^2"
		zextra = (1,0) / sinh( @premult3a*z )
		zf3 = zextra * zextra
	  elseif  @formula3 == "sinh(1/z)"
		zf3 = sinh(@premult3a/z)
	  elseif  @formula3 == "cosh(1/z)"
		zf3 = cosh(@premult3a/z)
	  elseif  @formula3 == "tanh(1/z)"
		zf3 = tanh(@premult3a/z)
	  elseif  @formula3 == "cotanh(1/z)"
		zf3 = cotanh(@premult3a/z)
	  elseif  @formula3 == "sech(1/z)"
		zf3 = (1,0)/cosh(@premult3a/z)
	  elseif  @formula3 == "cosech(1/z)"
		zf3 = (1,0)/sinh(@premult3a/z)
	  elseif  @formula3 == "sin*tan"
		zf3 = sin( @premult3a*z ) * tan(@premult3b*z)
	  elseif  @formula3 == "sinh*tanh"
		zf3 = sinh(@premult3a*z) * tanh(@premult3b*z)
	  elseif  @formula3 == "sinh*cosh"
		zf3 = sinh(@premult3a*z) * cosh(@premult3b*z)
	  elseif  @formula3 == "sinh^2*cosh^2"
		ztemp = sinh(@premult3a*z), zextra = cosh(@premult3b*z)
		zf3 = ztemp*ztemp*zextra*zextra
	  elseif  @formula3 == "sin^2*cos^2"
		ztemp = sin(@premult3a*z), zextra = cos(@premult3b*z)
		zf3 = ztemp*ztemp*zextra*zextra
	  elseif  @formula3 == "sin(1/z)*cos(1/z)"
		zextra = 1/(@premult3a*z), ztemp = 1/(@premult3b*z)
		zf3 = sin(zextra)*cos(ztemp)
	  elseif  @formula3 == "sin(1/z)^2"
		zextra = sin( @premult3a/z )
		zf3 = zextra*zextra
	  elseif  @formula3 == "sin(z)*cos(1/z)"
		zf3 = sin(@premult3a*z) * cos(@premult3b/z)
	  elseif  @formula3 == "sin(z)*sin(1/z)"
		zf3 = sin(@premult3a*z) * sin(@premult3b/z)
	  elseif  @formula3 == "log^2"
		zextra = log(@premult3a*z)
		zf3 = zextra*zextra
	  elseif  @formula3 == "sin(mz)*sin(nz)"
		zf3 = sin(@premult3a*z) * sin(@premult3b*z)
	  elseif  @formula3 == "sinh(1/z)*cosh(1/z)"
		zextra = @premult3a/z, ztemp = @premult3b/z
		zf3 = sinh(zextra)*cosh(ztemp)
	  elseif  @formula3 == "sinh(1/z)^2"
		zextra = sinh( @premult3a/z )
		zf3 = zextra*zextra
	  elseif  @formula3 == "sinh*cosh(1/z)"
		zf3 = sinh(@premult3a*z) * cosh(@premult3b/z)
	  elseif  @formula3 == "sinh*sinh(1/z)"
		zf3 = sinh(@premult3a*z) * sinh(@premult3b/z)
	  elseif  @formula3 == "sin*sinh"
		zf3 = sin(@premult3a*z) * sinh(@premult3b*z)
	  elseif  @formula3 == "sin*cosh"
		zf3 = sin(@premult3a*z) * cosh(@premult3b*z)
	  elseif  @formula3 == "sin^2*sinh^2"
		zextra = sin(@premult3a*z), ztemp = sinh(@premult3b*z)
		zf3 = ztemp*ztemp*zextra*zextra
	  elseif  @formula3 == "sin*e^z"
		zf3 = sin(@premult3a*z)*exp(@premult3b*z)
	  elseif  @formula3 == "cos*e^z"
		zf3 = cos(@premult3a*z)*exp(@premult3b*z)
	  elseif  @formula3 == "sinh*e^z"
		zf3 = sinh(@premult3a*z)*exp(@premult3b*z)
	  elseif  @formula3 == "cosh*e^z"
		zf3 = cosh(@premult3a*z)*exp(@premult3b*z)
	  elseif  @formula3 == "sin*log"
		zf3 = sin(@premult3a*z)*log(@premult3b*z)
	  elseif  @formula3 == "cos*log"
		zf3 = cos(@premult3a*z)*log(@premult3b*z)
	  elseif  @formula3 == "sinh*log"
		zf3 = sinh(@premult3a*z)*log(@premult3b*z)
	  elseif @formula3 == "cosh*log"
		zf3 = cosh(@premult3a*z)*log(@premult3b*z)
	  elseif @formula3 == "e^(z^2)"
		zf3 = exp(@premult3a*z*z)
	  elseif @formula3 == "e^(-(z^2))"
		zf3 = exp(-(z*z))
	  elseif @formula3 == "e^(1/z^2)"
		zf3 = exp(@premult3a/(z*z))
	  elseif @formula3 == "e^(-1/z^2)"
		zf3 = exp(-1/(z*z))
	  elseif @formula3 == "ver" ; versine
		zf3 = 1 - cos(@premult3a*z)
	  elseif @formula3 == "vcs" ; vercosine
		zf3 = 1 + cos(@premult3a*z)
	  elseif @formula3 == "cvs" ; coversine
		zf3 = 1 - sin(@premult3a*z)
	  elseif @formula3 == "cvc" ; covercosine
		zf3 = 1 + sin(@premult3a*z)
	  elseif @formula3 == "exs" ; exsecant
		zf3 = 1/cos(@premult3a*z) - 1
	  elseif @formula3 == "exc" ; excosecant
		zf3 = 1/sin(@premult3a*z) - 1
	  elseif @formula3 == "crd" ; chord
		zf3 = 2 * sin(@premult3a*z/2)
	  elseif @formula3 == "aver" ; arcversine
		zf3 = acos(1 - @premult3a*z)
	  elseif @formula3 == "avcs" ; arcvercosine
		zf3 = acos(1 + @premult3a*z)
	  elseif @formula3 == "acvs" ; arccoversine
		zf3 = asin(1 - @premult3a*z)
	  elseif @formula3 == "acvc" ; arccovercosine
		zf3 = asin(1 + @premult3a*z)
	  elseif @formula3 == "aexs" ; arcexsecant
		zf3 = acos( (1/(@premult3a*(z+1))))
	  elseif @formula3 == "aexc" ; arcexcosecant
		zf3 = asin( (1/(@premult3a*(z+1))))
	  elseif @formula3 == "acrd" ; arcchord
		zf3 = 2 * asin( @premult3a*z/2 )
	  elseif @formula3 == "abs"
		zf3 = abs( @premult3a*z )
	  elseif @formula3 == "conj"
		zf3 = conj( @premult3a*z )
	  elseif @formula3 == "flip"
		zf3 = flip( @premult3a*z )
	  elseif @formula3 == "ceiling"
		zf3 = ceil( @premult3a*z )
	  elseif @formula3 == "floor"
		zf3 = floor( @premult3a*z )
	  elseif @formula3 == "truncation"
		zf3 = trunc( @premult3a*z )
	  elseif @formula3 == "round"
		zf3 = round( @premult3a*z )
	  elseif @formula3 == "atan2"
		zf3 = atan2( @premult3a*z )
	  elseif @formula3 == "e^e^z"
		zf3 = exp(@premult3b*exp( @premult3a*z ))
	  elseif @formula3 == "constant^z"
		zf3 = @base3^( @premult3a*z )
	  elseif @formula3 == "constant^z^z"
		zf3 = @base3^(@premult3b*z^( @premult3a*z ))
	  elseif @formula3 == "real"
		zf3 = real(z) + flip(0)
	  elseif @formula3 == "imag"
		zf3 = (0,0) + flip(imag(z))
	  elseif @formula3 == "conj(flip)"
		zf3 = conj(@premult3b*flip( @premult3a*z ))
	  elseif @formula3 == "flip(conj)"
		zf3 = flip(@premult3b* conj(@premult3a*z ))
	  elseif @formula3 == "z"
		zf3 = @premult3a*z
	  endif ; @formula3

		zf3 = @weight3 * @funcmult3 * zf3

    endif ; @combo

    if @combo == 0
      z = zf1 + zf2
    elseif @combo == 1
      z = zf1 * zf2
    elseif @combo == 2
      z = zf1 / zf2
    elseif @combo == 3
      z = zf2
    elseif @combo == 4
      z = zf1 ^ zf2
    elseif @combo == 5
      z = log(zf1)/log(zf2)
    elseif @combo == 6
      z = zf1 + zf2 + zf3
    elseif @combo == 7
      z = zf1 * zf2 * zf3
    elseif @combo == 8
      z = zf1 ^ ( zf2 ^ zf3 )
    elseif @combo == 9
      z = zf3
    elseif @combo == 10
      z = log(log(zf1)/log(zf2))/log(zf3)
    elseif @combo == 11
      z = zf1 * ( zf2 + zf3 )
    elseif @combo == 12
      z = zf1 + ( zf2 * zf3 )
    elseif @combo == 13
      z = zf1 + ( zf2 / zf3 )
    elseif @combo == 14
      z = ( zf1 + zf2 ) / zf3
    elseif @combo == 15
      z = zf1 / ( zf2 + zf3 )
    elseif @combo == 16
      z = ( zf1 * zf2 ) / zf3
    elseif @combo == 17
      z = zf3
    elseif @combo == 18
      z = zf3
    elseif @combo == 19
      z = zf3
    elseif @combo == 20
      z = zf3
    elseif @combo == 21
      z = zf3
    elseif @combo == 22
      z = zf1 + ( zf2 ^ zf3 )
    elseif @combo == 23
      z = zf1 * ( zf2 ^ zf3 )
    elseif @combo == 24
      z = zf1 / ( zf2 ^ zf3 )
    elseif @combo == 25
      z = ( zf1 ^ zf2 ) / zf3
    elseif @combo == 26
      z = zf3 + (log(zf1)/log(zf2))
    elseif @combo == 27
      z = zf3 * (log(zf1)/log(zf2))
    elseif @combo == 28
      z = zf3 / (log(zf1)/log(zf2))
    elseif @combo == 29
      z = (log(zf1)/log(zf2)) / zf3
    else ; @combo == 30
      z = zf3 ^ (log(zf1)/log(zf2))
    endif ; @combo
  else
    z = zf1
  endif ; iterations

  if @blend
    z = @weightzfn * z + @weightzpwr * zblend^@zpower
  endif ; @blend

  if @pmode != 1
    z = z + jc
  endif ; pmode

  if @biomorph
  	if @biomorphtype == "real + imag"
	  	bail = (abs(real(z)) < @biomorphtest) || (abs(imag(z)) < @biomorphtest)
  	elseif @biomorphtype == "real + imag + cabs"
	  	bail = (abs(real(z)) < @biomorphtest) || (abs(imag(z)) < @biomorphtest) || (cabs(z) < sqr(@biomorphtest))
  	elseif @biomorphtype == "real"
	  	bail = abs(real(z)) < @biomorphtest
  	elseif @biomorphtype == "imag"
	  	bail = abs(imag(z)) < @biomorphtest
  	elseif @biomorphtype == "cabs"
	  	bail = cabs(z) < sqr(@biomorphtest)
	endif ; @biomorphtype
  else
		bail = |z| < @bail
  endif ; @biomorph

  bailout:
  	bail

  default:
  title = "oz3 Functions Mk II"
  center = (0,0)
  maxiter = 250
  method = multipass
  periodicity = 0
  magn = 0.75

  param frequency
    caption = "Cycle Length"
    default = 1
    min = 1
    hint = "This is the frequency that Formulas G and H are executed (Formula \
          F is executed every iteration). If 'Cycle length' = 1, then Formulas \
          G and H are also executed every iter, else every N iters"
  endparam
  param combo
    caption = "Func Combo"
    enum = "f[z]+g[z]" "f[z]*g[z]" "f/g" "g[f[z]]" "f^g" "logg[f[z]]" \
          "f[z]+g[z]+h[z]" "f*g*h" "f^(g^h)" "h[g[f[z]]]" "logh[logg[f[z]]]" \
          "f*(g+h)" "f+(g*h)" "f+(g/h)" "(f+g)/h" "f/(g+h)" "(f*g)/h" \
          "h[f[z]+g[z]]" "h[f*g]" "h[f/g]" "h[f^g]" "h[logg[f]]" "f+(g^h)" \
          "f*(g^h)" "f/(g^h)" "(f^g)/h" "h+logg[f]" "h*logg[f]" "h/logg[f]" \
          "logg[f]/h" "h^(logg[f])"
    default = 0
    min = 0
    hint = "Selects the number of functions and how they will be \
        combined. 'Formula H' is unused in the 2-function options. 'logg(f)' \
        means the logarithm of f to the base g; similarly for the other log \
        options"
  endparam
  param formula1
    caption = "Formula F"
    enum = "z^2" "z^3" "z^4" "z^power" "1/z" "sqrt" "1/z^2" "log" "e^z" "z^z" \
          "sin" "cos" "tan" "asin" "acos" "atan" "sinh" "cosh" "tanh" \
          "asinh" "acosh" "atanh" "log(1/z)" "log(log)" "e^-z" \
          "e^(1/z)" "z^-z" "sin^2" "cos^2" "tan^2" "cot" "sec" \
          "csc" "cot^2" "sec^2" "csc^2" "z^z^z" "1/z^z^z" "log(-z)" \
          "1/log" "zlog" "sin(z)/z" "cos(z)/z" "sin*cos" "sin(z^2)" \
          "e^(-1/z)" "ze^z" "ze^-z" "ze^(1/z)" "ze^(-1/z)" "1/z^3" \
          "acot" "asec" "acsc" "tan(z)/z" "cot(z)/z" "sec(z)/z" \
          "csc(z)/z" "zsin" "zcos" "ztan" "zcot" "zsec" "zcsc" \
          "sin(1/z)" "cos(1/z)" "tan(1/z)" "cot(1/z)" "sec(1/z)" "csc(1/z)" \
          "cotanh" "sech" "cosech" "acoth" "asech" "acosech" \
          "3-term polynomial" "sinh^2" "cosh^2" "tanh^2" "cotanh^2" \
          "sech^2" "cosech^2" "sinh(1/z)" "cosh(1/z)" "tanh(1/z)" \
          "cotanh(1/z)" "sech(1/z)" "cosech(1/z)" "sin*tan" "sinh*tanh" \
          "sinh*cosh" "sinh^2*cosh^2" "sin^2*cos^2" \
          "sin(1/z)*cos(1/z)" "sin(1/z)^2" "sin(z)*cos(1/z)" "sin(z)*sin(1/z)" \
          "log^2" "sin(mz)*sin(nz)" "sinh(1/z)*cosh(1/z)" \
          "sinh(1/z)^2" "sinh*cosh(1/z)" "sinh*sinh(1/z)" "sin*sinh" \
          "sin*cosh" "sin^2*sinh^2" "sin*e^z" "cos*e^z" \
          "sinh*e^z" "cosh*e^z" "sin*log" "cos*log" "sinh*log" \
          "cosh*log" "e^(z^2)" "e^(-(z^2))" "e^(1/z^2)" "e^(-1/z^2)" "ver" \
          "vcs" "cvs" "cvc" "exs" "exc" "crd" "aver" "avcs" "acvs" "acvc" "aexs" \
          "aexc" "acrd" "abs" "conj" "flip" \
          "ceiling" "floor" "truncation" "round" "atan2" "e^e^z" \
          "constant^z" "constant^z^z" "real" "imag" "conj(flip)" "flip(conj)" "z"
    default = 0
    hint = "Default formula, executed each iteration. For 'z^power', set \
          parameter 'Power F'. For '3-term polynomial' set \
          6 params 'Coefficient' & 'Exponent' FA, FB, and FC"
  endparam
  param premult1a
    caption = "Premultiplier F1"
    default = (1,0)
    hint = "This constant is multiplied by z before its use as the \
    	argument of some of the functions (e.g., sin(n*z))."
    visible = @weight1 != 0.0
  endparam
  param premult1b
    caption = "Premultiplier F2"
    default = (1,0)
    hint = "This constant is multiplied by z before its use as the \
    	argument of some of the two-function options (e.g. sin(n*z)*cos(m*z))."
    visible = @weight1 != 0.0
  endparam
  param base1
    caption = "Base Constant F"
    default = (2,0)
    hint = "If function f is set to 'constant^z' or 'constant^z^z', \
    	then this parameter sets the constant"
    visible = (@formula1 == "constant^z") || (@formula1 == "constant^z^z")
  endparam
  param funcmult1
    caption = "Postmultiplier F"
    default = (1,0)
    hint = "This parameter is multiplied by the output of function f \
    	before combining with functions g and h"
  endparam
  param power1
    caption = "Power F"
    default = (5,0)
    hint = "This is the power used for the first formula series if parameter \
        'Formula F' is set to 'z^power'"
    visible = @formula1 == "z^power"
  endparam
  param coeff1a
    caption = "Coefficient FA"
    default = (1,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the coefficient \
          of the 1st term"
    visible = @formula1 == "3-term polynomial"
  endparam
  param exponent1a
    caption = "Exponent FA"
    default = (6,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the exponent \
          of the 1st term"
    visible = @formula1 == "3-term polynomial"
  endparam
  param coeff1b
    caption = "Coefficient FB"
    default = (-1,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the coefficient \
          of the 2nd term"
    visible = @formula1 == "3-term polynomial"
  endparam
  param exponent1b
    caption = "Exponent FB"
    default = (4,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the exponent \
          of the 2nd term"
    visible = @formula1 == "3-term polynomial"
  endparam
  param coeff1c
    caption = "Coefficient FC"
    default = (1,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the coefficient \
          of the 3rd term"
    visible = @formula1 == "3-term polynomial"
  endparam
  param exponent1c
    caption = "Exponent FC"
    default = (2,0)
    hint = "If 'Formula F' is set to '3-term polynomial', this is the exponent \
          of the 3rd term"
    visible = @formula1 == "3-term polynomial"
  endparam
  param formula2
    caption = "Formula G"
    enum = "z^2" "z^3" "z^4" "z^power" "1/z" "sqrt" "1/z^2" "log" "e^z" "z^z" \
          "sin" "cos" "tan" "asin" "acos" "atan" "sinh" "cosh" "tanh" \
          "asinh" "acosh" "atanh" "log(1/z)" "log(log)" "e^-z" \
          "e^(1/z)" "z^-z" "sin^2" "cos^2" "tan^2" "cot" "sec" \
          "csc" "cot^2" "sec^2" "csc^2" "z^z^z" "1/z^z^z" "log(-z)" \
          "1/log" "zlog" "sin(z)/z" "cos(z)/z" "sin*cos" "sin(z^2)" \
          "e^(-1/z)" "ze^z" "ze^-z" "ze^(1/z)" "ze^(-1/z)" "1/z^3" \
          "acot" "asec" "acsc" "tan(z)/z" "cot(z)/z" "sec(z)/z" \
          "csc(z)/z" "zsin" "zcos" "ztan" "zcot" "zsec" "zcsc" \
          "sin(1/z)" "cos(1/z)" "tan(1/z)" "cot(1/z)" "sec(1/z)" "csc(1/z)" \
          "cotanh" "sech" "cosech" "acoth" "asech" "acosech" \
          "3-term polynomial" "sinh^2" "cosh^2" "tanh^2" "cotanh^2" \
          "sech^2" "cosech^2" "sinh(1/z)" "cosh(1/z)" "tanh(1/z)" \
          "cotanh(1/z)" "sech(1/z)" "cosech(1/z)" "sin*tan" "sinh*tanh" \
          "sinh*cosh" "sinh^2*cosh^2" "sin^2*cos^2" \
          "sin(1/z)*cos(1/z)" "sin(1/z)^2" "sin(z)*cos(1/z)" "sin(z)*sin(1/z)" \
          "log^2" "sin(mz)*sin(nz)" "sinh(1/z)*cosh(1/z)" \
          "sinh(1/z)^2" "sinh*cosh(1/z)" "sinh*sinh(1/z)" "sin*sinh" \
          "sin*cosh" "sin^2*sinh^2" "sin*e^z" "cos*e^z" \
          "sinh*e^z" "cosh*e^z" "sin*log" "cos*log" "sinh*log" \
          "cosh*log" "e^(z^2)" "e^(-(z^2))" "e^(1/z^2)" "e^(-1/z^2)" "ver" \
          "vcs" "cvs" "cvc" "exs" "exc" "crd" "aver" "avcs" "acvs" "acvc" "aexs" \
          "aexc" "acrd" "abs" "conj" "flip" \
          "ceiling" "floor" "truncation" "round" "atan2" "e^e^z" \
          "constant^z" "constant^z^z" "real" "imag" "conj(flip)" "flip(conj)" "z"
    default = 1
    hint = "Formula g, executed every N iterations, where N is set \
          by param 'Cycle Length'. For 'z^power', set param 'Power G'. For \
          '3-term polynomial' set 6 params 'Coefficient' & 'Exponent' GA, GB, \
          and GC"
  endparam
  param premult2a
    caption = "Premultiplier G1"
    default = (1,0)
    hint = "This constant is multiplied by z before its use as the \
    	argument of some of the functions (e.g., sin(n*z))."
    visible = @weight2 != 0.0
  endparam
  param premult2b
    caption = "Premultiplier G2"
    default = (1,0)
    hint = "This constant is multiplied by z before its use as the \
    	argument of some of the two-function options (e.g. sin(n*z)*cos(m*z))."
    visible = @weight2 != 0.0
  endparam
  param base2
    caption = "Base Constant G"
    default = (2,0)
    hint = "If function g is set to 'constant^z' or 'constant^z^z', \
    	then this parameter sets the constant"
    visible = (@formula2 == "constant^z") || (@formula2 == "constant^z^z")
  endparam
  param funcmult2
    caption = "Postmultiplier G"
    default = (1,0)
    hint = "This parameter is multiplied by the output of function g \
    	before combining with functions f and h"
  endparam
  param power2
    caption = "Power G"
    default = (6,0)
    hint = "This is the power used for the second formula series if parameter \
        'Formula G' is set to 'z^power'"
    visible = @formula2 == "z^power"
  endparam
  param coeff2a
    caption = "Coefficient GA"
    default = (1,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the coefficient \
          of the 1st term"
    visible = @formula2 == "3-term polynomial"
  endparam
  param exponent2a
    caption = "Exponent GA"
    default = (6,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the exponent \
          of the 1st term"
    visible = @formula2 == "3-term polynomial"
  endparam
  param coeff2b
    caption = "Coefficient GB"
    default = (-1,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the coefficient \
          of the 2nd term"
    visible = @formula2 == "3-term polynomial"
  endparam
  param exponent2b
    caption = "Exponent GB"
    default = (4,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the exponent \
          of the 2nd term"
    visible = @formula2 == "3-term polynomial"
  endparam
  param coeff2c
    caption = "Coefficient GC"
    default = (1,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the coefficient \
          of the 3rd term"
    visible = @formula2 == "3-term polynomial"
  endparam
  param exponent2c
    caption = "Exponent GC"
    default = (2,0)
    hint = "If 'Formula G' is set to '3-term polynomial', this is the exponent \
          of the 3rd term"
    visible = @formula2 == "3-term polynomial"
  endparam
  param coeff3a
    caption = "Coefficient HA"
    default = (1,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the coefficient \
          of the 1st term"
    visible = @formula3 == "3-term polynomial"
  endparam
  param exponent3a
    caption = "Exponent HA"
    default = (6,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the exponent \
          of the 1st term"
    visible = @formula3 == "3-term polynomial"
  endparam
  param coeff3b
    caption = "Coefficient HB"
    default = (-1,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the coefficient \
          of the 2nd term"
    visible = @formula3 == "3-term polynomial"
  endparam
  param exponent3b
    caption = "Exponent HB"
    default = (4,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the exponent \
          of the 2nd term"
    visible = @formula3 == "3-term polynomial"
  endparam
  param coeff3c
    caption = "Coefficient HC"
    default = (1,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the coefficient \
          of the 3rd term"
    visible = @formula3 == "3-term polynomial"
  endparam
  param exponent3c
    caption = "Exponent HC"
    default = (2,0)
    hint = "If 'Formula H' is set to '3-term polynomial', this is the exponent \
          of the 3rd term"
    visible = @formula3 == "3-term polynomial"
  endparam
  param formula3
    caption = "Formula H"
    enum = "z^2" "z^3" "z^4" "z^power" "1/z" "sqrt" "1/z^2" "log" "e^z" "z^z" \
          "sin" "cos" "tan" "asin" "acos" "atan" "sinh" "cosh" "tanh" \
          "asinh" "acosh" "atanh" "log(1/z)" "log(log)" "e^-z" \
          "e^(1/z)" "z^-z" "sin^2" "cos^2" "tan^2" "cot" "sec" \
          "csc" "cot^2" "sec^2" "csc^2" "z^z^z" "1/z^z^z" "log(-z)" \
          "1/log" "zlog" "sin(z)/z" "cos(z)/z" "sin*cos" "sin(z^2)" \
          "e^(-1/z)" "ze^z" "ze^-z" "ze^(1/z)" "ze^(-1/z)" "1/z^3" \
          "acot" "asec" "acsc" "tan(z)/z" "cot(z)/z" "sec(z)/z" \
          "csc(z)/z" "zsin" "zcos" "ztan" "zcot" "zsec" "zcsc" \
          "sin(1/z)" "cos(1/z)" "tan(1/z)" "cot(1/z)" "sec(1/z)" "csc(1/z)" \
          "cotanh" "sech" "cosech" "acoth" "asech" "acosech" \
          "3-term polynomial" "sinh^2" "cosh^2" "tanh^2" "cotanh^2" \
          "sech^2" "cosech^2" "sinh(1/z)" "cosh(1/z)" "tanh(1/z)" \
          "cotanh(1/z)" "sech(1/z)" "cosech(1/z)" "sin*tan" "sinh*tanh" \
          "sinh*cosh" "sinh^2*cosh^2" "sin^2*cos^2" \
          "sin(1/z)*cos(1/z)" "sin(1/z)^2" "sin(z)*cos(1/z)" "sin(z)*sin(1/z)" \
          "log^2" "sin(mz)*sin(nz)" "sinh(1/z)*cosh(1/z)" \
          "sinh(1/z)^2" "sinh*cosh(1/z)" "sinh*sinh(1/z)" "sin*sinh" \
          "sin*cosh" "sin^2*sinh^2" "sin*e^z" "cos*e^z" \
          "sinh*e^z" "cosh*e^z" "sin*log" "cos*log" "sinh*log" \
          "cosh*log" "e^(z^2)" "e^(-(z^2))" "e^(1/z^2)" "e^(-1/z^2)" "ver" \
          "vcs" "cvs" "cvc" "exs" "exc" "crd" "aver" "avcs" "acvs" "acvc" "aexs" \
          "aexc" "acrd" "abs" "conj" "flip" \
          "ceiling" "floor" "truncation" "round" "atan2" "e^e^z" \
          "constant^z" "constant^z^z" "real" "imag" "conj(flip)" "flip(conj)" "z"
    default = 2
    hint = "Formula h, executed every N iterations if param 'Func Combo' \
          requires func h. N is set by param 'Cycle Length'. For 'z^power', \
          set param 'Power H'. For '3-term polynomial' set 6 params 'Coefficient' \
          & 'Exponent' HA, HB, and HC"
  endparam
  param premult3a
    caption = "Premultiplier H1"
    default = (1,0)
    hint = "This constant is multiplied by z before its use as the \
    	argument of some of the functions (e.g., sin(n*z))."
    visible = @weight3 != 0.0
  endparam
  param premult3b
    caption = "Premultiplier H2"
    default = (1,0)
    hint = "This constant is multiplied by z before its use as the \
    	argument of some of the two-function options (e.g. sin(n*z)*cos(m*z))."
    visible = @weight3 != 0.0
  endparam
  param base3
    caption = "Base Constant H"
    default = (2,0)
    hint = "If function h is set to 'constant^z' or 'constant^z^z', \
    	then this parameter sets the constant"
    visible = (@formula3 == "constant^z") || (@formula3 == "constant^z^z")
  endparam
  param funcmult3
  	caption = "Postmultiplier H"
    default = (1,0)
    hint = "This parameter is multiplied by the output of function h \
    	before combining with functions f and g"
  endparam
  param power3
    caption = "Power H"
    default = (6,0)
    hint = "This is the power used for the third formula series if parameter \
        'Formula H' is set to 'z^power'"
    visible = @formula3 == "z^power"
  endparam
  param weight1
    caption = "Formula F Weight"
    default = 1.0
    hint = "This is the relative proportion of Formula F that is combined with \
        the other formulas every N iterations"
  endparam
  param weight2
    caption = "Formula G Weight"
    default = 1.0
    hint = "This is the relative proportion of Formula G that is combined with \
        the other formulas every N iterations"
  endparam
  param weight3
    caption = "Formula H Weight"
    default = 1.0
    hint = "This is the relative proportion of Formula H that is combined with \
        the other formulas every N iterations"
  endparam
  param blend
    caption = "Blend Z^Power?"
    default = FALSE
    hint = "If enabled, the iterated function can be blended into a normal \
          z^power Mandelbrot function; set parameter 'Z Power' to fix exponent, \
          and 'Z Weight' and 'Function Weight' to fix blend proportions"
  endparam
  param weightzfn
    caption = "Function Weight"
    default = -0.1
    hint = "If 'Blend Z^Power' is enabled, then this is the fraction of the \
          function that is blended in with the normal z^power Mandelbrot"
    visible = @blend == TRUE
  endparam
  param weightzpwr
    caption = "Z^Power Weight"
    default = 1.0
    hint = "If 'Blend Z^Power' is enabled, then this is the fraction of the \
          normal z^power Mandelbrot that is blended in with the function"
    visible = @blend == TRUE
  endparam
  param zpower
    caption = "Z Power"
    default = (2,0)
    hint = "If 'Blend Z^Power' is enabled, then this is the exponent for the \
          normal z^power Mandelbrot"
    visible = @blend == TRUE
  endparam
  param pixelformula
    caption = "Pixel Formula"
    enum = "p" "p^2" "p^3" "p^4" "p^power" "1/p" "sqrt(p)" "1/p^2" "log(p)" "e^p" "p^p" \
          "sin(p)" "cos(p)" \
          "tan(p)" "asin(p)" "acos(p)" "atan(p)" "sinh(p)" "cosh(p)" "tanh(p)" \
          "asinh(p)" "acosh(p)" "atanh(p)" "log(1/p)" "log(log(p))" "e^-p" \
          "e^(1/p)" "p^-p" "sin(p)^2" "cos(p)^2" "tan(p)^2" "cot(p)" "sec(p)" \
          "csc(p)" "cot(p)^2" "sec(p)^2" "csc(p)^2" "p^p^p" "1/p^p^p" "log(-p)" \
          "1/log(p)" "plog(p)" "sin(p)/p" "cos(p)/p" "sin(p)*cos(p)" "sin(p^2)" \
          "e^(-1/p)" "pe^p" "pe^-p" "pe^(1/p)" "pe^(-1/p)" "p^3" "1/p^3" \
          "acot(p)" "asec(p)" "acsc(p)" "tan(p)/p" "cot(p)/p" "sec(p)/p" \
          "csc(p)/p" "psin(p)" "pcos(p)" "ptan(p)" "pcot(p)" "psec(p)" "pcsc(p)" \
          "sin(1/p)" "cos(1/p)" "tan(1/p)" "cot(1/p)" "sec(1/p)" "csc(1/p)" \
          "cotanh(p)" "sech(p)" "cosech(p)" "acoth(p)" "asech(p)" "acosech(p)" \
          "3-term polynomial" "sinh(p)^2" "cosh(p)^2" "tanh(p)^2" "cotanh(p)^2" \
          "sech(p)^2" "cosech(p)^2" "sinh(1/p)" "cosh(1/p)" "tanh(1/p)" \
          "cotanh(1/p)" "sech(1/p)" "cosech(1/p)" "sin(p)tan(p)" "sinh(p)tanh(p)" \
          "sinh(p)cosh(p)" "sinh(p)^2*cosh(p)^2" "sin(p)^2*cos(p)^2" \
          "sin(1/p)*cos(1/p)" "sin(1/p)^2" "sin(p)cos(1/p)" "sin(p)sin(1/p)" \
          "log(p)^2" "sin(p)sin(2p)" "e^2p" "e^-2p" "sinh(1/p)cosh(1/p)" \
          "sinh(1/p)^2" "sinh(p)cosh(1/p)" "sinh(p)sinh(1/p)" "sin(p)sinh(p)" \
          "sin(p)cosh(p)" "sin(p)^2*sinh(p)^2" "sin(p)e^p" "cos(p)e^p" \
          "sinh(p)e^p" "cosh(p)e^p" "sin(p)log(p)" "cos(p)log(p)" "sinh(p)log(p)" \
          "cosh(p)log(p)"
    default = 0
    hint = "Pixel value (Mand) or seed (Julia) can be initialized \
        before iterating. For 'p^power', set parameter 'Pixel Power'; \
        for '3-term polynomial', set 'Coeff Pa', 'Exponent Pa', 'Coeff Pb', \
        'Exponent Pb', 'Coeff Pc', 'Exponent Pc'. 'p' results in normal \
        initialization"
  endparam
  param ppower
    caption = "Pixel Power"
    default = (5,0)
    hint = "This is the power used if parameter \
        'Pixel Formula' is set to 'p^power'"
    visible = @pixelformula == "p^power"
  endparam
  param coeffpa
    caption = "Coeff Pa"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 1st term"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param exponentpa
    caption = "Exponent Pa"
    default = (6,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 1st term"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param coeffpb
    caption = "Coeff Pb"
    default = (-1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 2nd term"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param exponentpb
    caption = "Exponent Pb"
    default = (4,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 2nd term"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param coeffpc
    caption = "Coeff Pc"
    default = (1,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the coefficient \
        of the 3rd term"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param exponentpc
    caption = "Exponent Pc"
    default = (2,0)
    hint = "If 'Pixel Formula' is set to '3-term polynomial', this is the power \
        of the 3rd term"
    visible = @pixelformula == "3-term polynomial"
  endparam
  param pmode
    caption = "Pixel Mode"
    default = 0
    enum = "Post-add" "Pre-add" "Both"
    hint = "'Post-add' -- formula is executed, then pixel/constant is added to result; \
        'Pre-add' -- pixel is added to z, then formula executed; 'Both' -- pixel added, \
        formula executed, then pixel added again to result"
  endparam
  param jconstant
    caption = "Julia Constant"
    default = (0,0)
    hint = "Iteration constant"
  endparam
  param bail
    caption = "Bailout Value"
    default = 64.0
    hint = "Value needed to 'escape' to infinity"
    visible = !@biomorph
  endparam
  param biomorph
  	caption = "Biomorph Bailout?"
  	default = FALSE
  	hint = "Enabling this setting changes the bailout condition to match \
  		Pickover's 'biomorph' definition.  For coloring, consider using \
  		'Biomorph' in the public folder 'jam2.ucl'."
  endparam  		
  param biomorphtest
    caption = "Biomorph Bailout Test"
    default = 10.0
    hint = "The bailout value for the 'Biomorph' test."
    visible = @biomorph
  endparam
param biomorphtype
	caption = "Biomorph Type"
	enum = "real" "imag" "real + imag" "real + imag + cabs" "cabs"
	default = 3
	hint = "This determines the bailout condition for the Biomorph."
	visible = @biomorph
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

  switch:
  type = "jam-3functionsV2"
  jconstant = #pixel
  frequency = frequency
  combo = combo
  formula1 = formula1
  formula2 = formula2
  formula3 = formula3
  power1 = power1
  power2 = power2
  power3 = power3
  premult1a = premult1a
  premult1b = premult1b
  premult2a = premult2a
  premult2b = premult2b
  premult3a = premult3a
  premult3b = premult3b
  funcmult1 = funcmult1
  funcmult2 = funcmult2
  funcmult3 = funcmult3
  base1 = base1
  base2 = base2
  base3 = base3
  weight1 = weight1
  weight2 = weight2
  weight3 = weight3
  coeff1a = coeff1a
  exponent1a = exponent1a
  coeff1b = coeff1b
  exponent1b = exponent1b
  coeff1c = coeff1c
  exponent1c = exponent1c
  coeff2a = coeff2a
  exponent2a = exponent2a
  coeff2b = coeff2b
  exponent2b = exponent2b
  coeff2c = coeff2c
  exponent2c = exponent2c
  coeff3a = coeff3a
  exponent3a = exponent3a
  coeff3b = coeff3b
  exponent3b = exponent3b
  coeff3c = coeff3c
  exponent3c = exponent3c
  blend = blend
  weightzfn = weightzfn
  weightzpwr = weightzpwr
  zpower = zpower
  pixelformula = pixelformula
  ppower = ppower
  coeffpa = coeffpa
  exponentpa = exponentpa
  coeffpb = coeffpb
  exponentpb = exponentpb
  coeffpc = coeffpc
  exponentpc = exponentpc
  pmode = pmode
  bail = bail
  biomorph = biomorph
  biomorphtest = biomorphtest
  biomorphtype = biomorphtype
  mandy = julia
  julia = mandy
}

comment {
This file contains streamlined formulas for series representations of various
hypergeometric functions, pFq(a1,...,am; b1,...,bn; z).  The functions included
are 1F1, 1F2, 2F1, 2F2, 2F3, 3F0, 3F1, 3F2, 3F3.

Originally written by Joe Maddry beginning on 02 Jan 2022.
}

jam-hypergeometric-1F1 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 1F1(a; b; z), the confluent hypergeometric functions of the first kind,
;
; 1F1(a; b; z) = Sum[ ( a(n) / b(n) ) * (z^n)/n! ], n = 0 -> infinity, or
;
;                ___
; 1F1(a; b; z) = \     [ (a)n/(b)n  * z^n / n!] , where (a)n and (b)n are
;                /__
;                 n
;
; rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float b1denom[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
b1denom[0] = 1.0
b1denom[1] = @b1
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	b1denom[gindex] = b1denom[itemp] * (@b1 + itemp)
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = a1numer[gindex] * factorial[gindex] / b1denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 1F1(a; b; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 1F1(a; b; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a"
	default = 1.0
	hint = "This value is the numerator parameter 'a' in the series \
			representation of the hypergeometric function 1F1(a; b; z)."
endparam
param b1
	caption = "Fn Constant b"
	default = 2.0
	hint = "This value is the denominator parameter 'b' in the series \
			representation of the hypergeometric function 1F1(a; b; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 1F1(a; b; z). \
			The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-1F1"
	a1 = a1
	b1 = b1
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-hypergeometric-1F2 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 1F2(a; b1, b2; z):
;
; 1F2(a; b1, b2; z) = Sum[ ( a(n) / (b1(n)*b2(n)) ) * (z^n)/n! ], n = 0 ->
; infinity, or,
;
;                     ___
; 1F2(a; b1, b2; z) = \     [ (a)n/((b1)n * (b2)n)  * z^n / n!] , where (a)n and
;                     /__
;                      n
;
; the (bi)ns are rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float b1denom[@terms]
float b2denom[@terms]
float denom[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
b1denom[0] = 1.0
b1denom[1] = @b1
b2denom[0] = 1.0
b2denom[1] = @b2
denom[0] = 1.0
denom[1] = @b1 * @b2
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	b1denom[gindex] = b1denom[itemp] * (@b1 + itemp)
	b2denom[gindex] = b2denom[itemp] * (@b2 + itemp)
	denom[gindex] = b1denom[gindex] * b2denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = a1numer[gindex] * factorial[gindex] / denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 1F2(a; b1, b2; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 1F2(a; b1, b2; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a"
	default = -0.5
	hint = "This value is the numerator parameter 'a' in the series \
			representation of the hypergeometric function 1F2(a; b1, b2; z)."
endparam
param b1
	caption = "Fn Constant b1"
	default = 0.25
	hint = "This value is the denominator parameter 'b1' in the series \
			representation of the hypergeometric function 1F2(a; b1, b2; z)."
endparam
param b2
	caption = "Fn Constant b2"
	default = 1.0
	hint = "This value is the denominator parameter 'b2' in the series \
			representation of the hypergeometric function 1F2(a; b1, b2; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 1F2(a; b1, b2; z). \
			The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-1F2"
	a1 = a1
	b1 = b1
	b2 = b2
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-hypergeometric-2F1 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 2F1(a1, a2; b; z),
;
; 2F1(a1, a2; b; z) = Sum[ ( a1(n)*a2(n) / b(n) ) * (z^n)/n! ], n = 0 -> infinity, or
;
;                     ___
; 2F1(a1, a2; b; z) = \     [ (a1)n(a2)n/(b)n  * z^n / n!] , where
;                     /__
;                      n
;
;  the (ai)ns and (b)n are rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float a2numer[@terms]
float b1denom[@terms]
float numer[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
a2numer[0] = 1.0
a2numer[1] = @a2
b1denom[0] = 1.0
b1denom[1] = @b1
numer[0] = 1.0
numer[1] = @a1 * @a2
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	a2numer[gindex] = a2numer[itemp] * (@a2 + itemp)
	b1denom[gindex] = b1denom[itemp] * (@b1 + itemp)
	numer[gindex] = a1numer[gindex] * a2numer[gindex]
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = numer[gindex] * factorial[gindex] / b1denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 2F1(a1, a2; b; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 2F1(a1, a2; b; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a1"
	default = -0.5
	hint = "This value is the numerator parameter 'a1' in the series \
			representation of the hypergeometric function 2F1(a1, a2; b; z)."
endparam
param a2
	caption = "Fn Constant a2"
	default = 0.75
	hint = "This value is the numerator parameter 'a2' in the series \
			representation of the hypergeometric function 2F1(a1, a2; b; z)."
endparam
param b1
	caption = "Fn Constant b"
	default = 2.0
	hint = "This value is the denominator parameter 'b' in the series \
			representation of the hypergeometric function 2F1(a1, a2; b; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 2F1(a1, a2; b; z). \
			The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-2F1"
	a1 = a1
	a2 = a2
	b1 = b1
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-hypergeometric-2F2 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 2F2(a1, a2; b1, b2; z):
;
; 2F2(a1, a2; b1, b2; z) = Sum[ ( a1(n)*a2(n) / (b1(n)*b2(n)) ) * (z^n)/n! ],
; n = 0 -> infinity, or,
;
;                          ___
; 2F2(a1, a2; b1, b2; z) = \     [ (a1)n * (a2)n / ((b1)n * (b2)n)  * z^n / n!],
;                          /__
;                           n
;
; where the (ai)n and (bi)n are rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float a2numer[@terms]
float b1denom[@terms]
float b2denom[@terms]
float numer[@terms]
float denom[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
a2numer[0] = 1.0
a2numer[1] = @a2
b1denom[0] = 1.0
b1denom[1] = @b1
b2denom[0] = 1.0
b2denom[1] = @b2
numer[0] = 1.0
numer[1] = @a1 * @a2
denom[0] = 1.0
denom[1] = @b1 * @b2
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	a2numer[gindex] = a2numer[itemp] * (@a2 + itemp)
	b1denom[gindex] = b1denom[itemp] * (@b1 + itemp)
	b2denom[gindex] = b2denom[itemp] * (@b2 + itemp)
	numer[gindex] = a1numer[gindex] * a2numer[gindex]
	denom[gindex] = b1denom[gindex] * b2denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = numer[gindex] * factorial[gindex] / denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 2F2(a1, a2; b1, b2; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 2F2(a1, a2; b1, b2; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a1"
	default = -0.5
	hint = "This value is the numerator parameter 'a1' in the series \
			representation of the hypergeometric function \
			2F2(a1, a2; b1, b2; z)."
endparam
param a2
	caption = "Fn Constant a2"
	default = -0.333333333333333333333333333333
	hint = "This value is the numerator parameter 'a' in the series \
			representation of the hypergeometric function \
			2F2(a1, a2; b1, b2; z)."
endparam
param b1
	caption = "Fn Constant b1"
	default = 0.25
	hint = "This value is the denominator parameter 'b1' in the series \
			representation of the hypergeometric function \
			2F2(a1, a2; b1, b2; z)."
endparam
param b2
	caption = "Fn Constant b2"
	default = 2.0
	hint = "This value is the denominator parameter 'b2' in the series \
			representation of the hypergeometric function \
			2F2(a1, a2; b1, b2; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 2F2(a1, a2; b1, b2; z). \
			The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-2F2"
	a1 = a1
	a2 = a2
	b1 = b1
	b2 = b2
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-hypergeometric-2F3 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 2F3(a1, a2; b1, b2, b3; z):
;
; 2F3(a1, a2; b1, b2; z) = Sum[ ( a1(n)*a2(n) /( b1(n)*b2(n)*b3(n) ) * (z^n)/n!) ],
; n = 0 -> infinity, or,
;
;                          ___
; 2F3(a1, a2; b1, b2; z) = \     [ (a1)n * (a2)n / ((b1)n * (b2)n * b3(n))  * z^n / n!],
;                          /__
;                           n
;
; where the (ai)n and (bi)n are rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float a2numer[@terms]
float b1denom[@terms]
float b2denom[@terms]
float b3denom[@terms]
float numer[@terms]
float denom[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
a2numer[0] = 1.0
a2numer[1] = @a2
b1denom[0] = 1.0
b1denom[1] = @b1
b2denom[0] = 1.0
b2denom[1] = @b2
b3denom[0] = 1.0
b3denom[1] = @b3
numer[0] = 1.0
numer[1] = @a1 * @a2
denom[0] = 1.0
denom[1] = @b1 * @b2 * @b3
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	a2numer[gindex] = a2numer[itemp] * (@a2 + itemp)
	b1denom[gindex] = b1denom[itemp] * (@b1 + itemp)
	b2denom[gindex] = b2denom[itemp] * (@b2 + itemp)
	b3denom[gindex] = b3denom[itemp] * (@b3 + itemp)
	numer[gindex] = a1numer[gindex] * a2numer[gindex]
	denom[gindex] = b1denom[gindex] * b2denom[gindex] * b3denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = numer[gindex] * factorial[gindex] / denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 2F3(a1, a2; b1, b2, b3; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 2F3(a1, a2; b1, b2, b3; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a1"
	default = -0.25
	hint = "This value is the numerator parameter 'a1' in the series \
			representation of the hypergeometric function \
			2F3(a1, a2; b1, b2, b3; z)."
endparam
param a2
	caption = "Fn Constant a2"
	default = 0.375
	hint = "This value is the numerator parameter 'a' in the series \
			representation of the hypergeometric function \
			2F3(a1, a2; b1, b2, b3; z)."
endparam
param b1
	caption = "Fn Constant b1"
	default = 0.2
	hint = "This value is the denominator parameter 'b1' in the series \
			representation of the hypergeometric function \
			2F3(a1, a2; b1, b2, b3; z)."
endparam
param b2
	caption = "Fn Constant b2"
	default = 1.0
	hint = "This value is the denominator parameter 'b2' in the series \
			representation of the hypergeometric function \
			2F3(a1, a2; b1, b2, b3; z)."
endparam
param b3
	caption = "Fn Constant b3"
	default = 1.6
	hint = "This value is the denominator parameter 'b3' in the series \
			representation of the hypergeometric function \
			2F3(a1, a2; b1, b2, b3; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 2F3(a1, a2; b1, b2, b3; z). \
			The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-2F3"
	a1 = a1
	a2 = a2
	b1 = b1
	b2 = b2
	b3 = b3
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-hypergeometric-3F0 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 3F0(a1, a2, a3; ; z),
;
; 3F0(a1, a2, a3; ; z) = Sum[ ( a1(n)*a2(n)*a3(n) ) * (z^n)/n! ], n = 0 -> infinity, or
;
;                        ___
; 3F0(a1, a2, a3; ; z) = \     [ (a1)n(a2)n(a3)n  * z^n / n!] , where
;                        /__
;                         n
;
;  the (ai)ns are rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float a2numer[@terms]
float a3numer[@terms]
float numer[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
a2numer[0] = 1.0
a2numer[1] = @a2
a3numer[0] = 1.0
a3numer[1] = @a3
numer[0] = 1.0
numer[1] = @a1 * @a2 * @a3
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	a2numer[gindex] = a2numer[itemp] * (@a2 + itemp)
	a3numer[gindex] = a3numer[itemp] * (@a3 + itemp)
	numer[gindex] = a1numer[gindex] * a2numer[gindex] * a3numer[gindex]
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = numer[gindex] * factorial[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 3F0(a1, a2, a3; ; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 3F0(a1, a2, a3; ; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a1"
	default = -1.5
	hint = "This value is the numerator parameter 'a1' in the series \
			representation of the hypergeometric function 3F0(a1, a2, a3; ; z)."
endparam
param a2
	caption = "Fn Constant a2"
	default = -0.75
	hint = "This value is the numerator parameter 'a2' in the series \
			representation of the hypergeometric function 3F0(a1, a2, a3; ; z)."
endparam
param a3
	caption = "Fn Constant a3"
	default = 0.25
	hint = "This value is the numerator parameter 'a2' in the series \
			representation of the hypergeometric function 3F0(a1, a2, a3; ; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 3F0(a1, a2, a3; ; z). \
			The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-3F0"
	a1 = a1
	a2 = a2
	a3 = a3
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-hypergeometric-3F1 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 3F1(a1, a2, a3; b; z),
;
; 3F1(a1, a2, a3; b; z) = Sum[ ( a1(n)*a2(n)*a3(n) / b(n) ) * (z^n)/n! ], n = 0 ->
; infinity, or,
;
;                         ___
; 2F1(a1, a2, a3; b; z) = \     [ (a1)n(a2)n(a3)n/(b)n  * z^n / n!] , where
;                         /__
;                          n
;
;  the (ai)ns and (b)n are rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float a2numer[@terms]
float a3numer[@terms]
float b1denom[@terms]
float numer[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
a2numer[0] = 1.0
a2numer[1] = @a2
a3numer[0] = 1.0
a3numer[1] = @a3
b1denom[0] = 1.0
b1denom[1] = @b1
numer[0] = 1.0
numer[1] = @a1 * @a2 * @a3
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	a2numer[gindex] = a2numer[itemp] * (@a2 + itemp)
	a3numer[gindex] = a3numer[itemp] * (@a3 + itemp)
	b1denom[gindex] = b1denom[itemp] * (@b1 + itemp)
	numer[gindex] = a1numer[gindex] * a2numer[gindex] * a3numer[gindex]
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = numer[gindex] * factorial[gindex] / b1denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 3F1(a1, a2, a3; b; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 3F1(a1, a2, a3; b; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a1"
	default = -0.5
	hint = "This value is the numerator parameter 'a1' in the series \
			representation of the hypergeometric function 3F1(a1, a2, a3; b; z)."
endparam
param a2
	caption = "Fn Constant a2"
	default = 0.25
	hint = "This value is the numerator parameter 'a2' in the series \
			representation of the hypergeometric function 3F1(a1, a2, a3; b; z)."
endparam
param a3
	caption = "Fn Constant a3"
	default = 0.75
	hint = "This value is the numerator parameter 'a2' in the series \
			representation of the hypergeometric function 3F1(a1, a2, a3; b; z)."
endparam
param b1
	caption = "Fn Constant b"
	default = 0.66666666666666666666667
	hint = "This value is the denominator parameter 'b' in the series \
			representation of the hypergeometric function 3F1(a1, a2, a3; b; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 3F1(a1, a2, a3; b; z). \
			The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-3F1"
	a1 = a1
	a2 = a2
	a3 = a3
	b1 = b1
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-hypergeometric-3F2 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 3F2(a1, a2, a3; b1, b2; z):
;
; 3F2(a1, a2, a3; b1, b2; z) = Sum[ ( a1(n)*a2(n)*a3(n) / (b1(n)*b2(n)) ) * (z^n)/n! ],
; n = 0 -> infinity, or,
;
;                              ___
; 3F2(a1, a2, a3; b1, b2; z) = \     [ (a1)n * (a2)n * (a3)n / ((b1)n * (b2)n)  * z^n / n!],
;                              /__
;                               n
;
; where the (ai)n and (bi)n are rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float a2numer[@terms]
float a3numer[@terms]
float b1denom[@terms]
float b2denom[@terms]
float numer[@terms]
float denom[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
a2numer[0] = 1.0
a2numer[1] = @a2
a3numer[0] = 1.0
a3numer[1] = @a3
b1denom[0] = 1.0
b1denom[1] = @b1
b2denom[0] = 1.0
b2denom[1] = @b2
numer[0] = 1.0
numer[1] = @a1 * @a2 * @a3
denom[0] = 1.0
denom[1] = @b1 * @b2
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	a2numer[gindex] = a2numer[itemp] * (@a2 + itemp)
	a3numer[gindex] = a3numer[itemp] * (@a3 + itemp)
	b1denom[gindex] = b1denom[itemp] * (@b1 + itemp)
	b2denom[gindex] = b2denom[itemp] * (@b2 + itemp)
	numer[gindex] = a1numer[gindex] * a2numer[gindex] * a3numer[gindex]
	denom[gindex] = b1denom[gindex] * b2denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = numer[gindex] * factorial[gindex] / denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 3F2(a1, a2, a3; b1, b2; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 3F2(a1, a2, a3; b1, b2; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a1"
	default = -1.25
	hint = "This value is the numerator parameter 'a1' in the series \
			representation of the hypergeometric function \
			3F2(a1, a2, a3; b1, b2; z)."
endparam
param a2
	caption = "Fn Constant a2"
	default = -0.333333333333333333333333333333
	hint = "This value is the numerator parameter 'a' in the series \
			representation of the hypergeometric function \
			3F2(a1, a2, a3; b1, b2; z)."
endparam
param a3
	caption = "Fn Constant a3"
	default = 0.25
	hint = "This value is the numerator parameter 'a' in the series \
			representation of the hypergeometric function \
			3F2(a1, a2, a3; b1, b2; z)."
endparam
param b1
	caption = "Fn Constant b1"
	default = -0.5
	hint = "This value is the denominator parameter 'b1' in the series \
			representation of the hypergeometric function \
			3F2(a1, a2, a3; b1, b2; z)."
endparam
param b2
	caption = "Fn Constant b2"
	default = 1.0
	hint = "This value is the denominator parameter 'b2' in the series \
			representation of the hypergeometric function \
			3F2(a1, a2, a3; b1, b2; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 3F2(a1, a2, a3; b1, b2; z). \
			The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-3F2"
	a1 = a1
	a2 = a2
	a3 = a3
	b1 = b1
	b2 = b2
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-hypergeometric-3F3 {
; jam 220102

; This formula implements an optimized version of the generalized hypergeometric
; function 3F3(a1, a2, a3; b1, b2, b3; z):
;
; 3F3(a1, a2, a3; b1, b2, b3; z) = Sum[ ( a1(n)*a2(n)*a3(n) / (b1(n)*b2(n)*b3(n)) ) *
; (z^n)/n! ],
; n = 0 -> infinity, or,
;
;                                  ___
; 3F3(a1, a2, a3; b1, b2, b3; z) = \     [ (a1)n * (a2)n * (a3)n / ((b1)n * (b2)n *
;                                  /__
;                                   n
;
;											(b3)n)  * z^n / n!],
;
; where the (ai)n and (bi)n are rising Pochhammer symbols.

global:
; Declare arrays for various coefficient components
float a1numer[@terms]
float a2numer[@terms]
float a3numer[@terms]
float b1denom[@terms]
float b2denom[@terms]
float b3denom[@terms]
float numer[@terms]
float denom[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable

; Initialize the factorial array --- factorial[n] = 1/n!
factorial[0] = 1.0
factorial[1] = 1.0
gindex = 2
while gindex < @terms
	factorial[gindex] = factorial[gindex - 1] / gindex
	gindex = gindex + 1
endwhile ; gindex

; Initialize the numerator and denominator arrays
a1numer[0] = 1.0
a1numer[1] = @a1
a2numer[0] = 1.0
a2numer[1] = @a2
a3numer[0] = 1.0
a3numer[1] = @a3
b1denom[0] = 1.0
b1denom[1] = @b1
b2denom[0] = 1.0
b2denom[1] = @b2
b3denom[0] = 1.0
b3denom[1] = @b3
numer[0] = 1.0
numer[1] = @a1 * @a2 * @a3
denom[0] = 1.0
denom[1] = @b1 * @b2 * @b3
gindex = 2
while gindex < @terms
	itemp = gindex - 1
	a1numer[gindex] = a1numer[itemp] * (@a1 + itemp)
	a2numer[gindex] = a2numer[itemp] * (@a2 + itemp)
	a3numer[gindex] = a3numer[itemp] * (@a3 + itemp)
	b1denom[gindex] = b1denom[itemp] * (@b1 + itemp)
	b2denom[gindex] = b2denom[itemp] * (@b2 + itemp)
	b3denom[gindex] = b3denom[itemp] * (@b3 + itemp)
	numer[gindex] = a1numer[gindex] * a2numer[gindex] * a3numer[gindex]
	denom[gindex] = b1denom[gindex] * b2denom[gindex] * b3denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
while gindex < @terms
	coefficient[gindex] = numer[gindex] * factorial[gindex] / denom[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z
zpower[1] = #z
lindex = 2
while lindex < @terms
	zpower[lindex] = zpower[lindex - 1] * #z
	lindex = lindex + 1
endwhile ; lindex

; Calculate the new value of #z as z(n+1) = 3F3(a1, a2, a3; b1, b2, b3; z(n)) + jc
lindex = 0
#z = (0,0)
while lindex < @terms
	#z = #z + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = #z + jc

bailout:
|#z| < @bail

default:
title = "pFq 3F3(a1, a2, a3; b1, b2, b3; z)"
maxiter = 2000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.1
angle = 0.0

param a1
	caption = "Fn Constant a1"
	default = -2.5
	hint = "This value is the numerator parameter 'a1' in the series \
			representation of the hypergeometric function \
			3F3(a1, a2, a3; b1, b2, b3; z)."
endparam
param a2
	caption = "Fn Constant a2"
	default = -0.333333333333333333333333333333
	hint = "This value is the numerator parameter 'a' in the series \
			representation of the hypergeometric function \
			3F3(a1, a2, a3; b1, b2, b3; z)."
endparam
param a3
	caption = "Fn Constant a3"
	default = 0.5
	hint = "This value is the numerator parameter 'a' in the series \
			representation of the hypergeometric function \
			3F3(a1, a2, a3; b1, b2, b3; z)."
endparam
param b1
	caption = "Fn Constant b1"
	default = -0.25
	hint = "This value is the denominator parameter 'b1' in the series \
			representation of the hypergeometric function \
			3F3(a1, a2, a3; b1, b2, b3; z)."
endparam
param b2
	caption = "Fn Constant b2"
	default = 0.25
	hint = "This value is the denominator parameter 'b2' in the series \
			representation of the hypergeometric function \
			3F3(a1, a2, a3; b1, b2, b3; z)."
endparam
param b3
	caption = "Fn Constant b3"
	default = 3.0
	hint = "This value is the denominator parameter 'b2' in the series \
			representation of the hypergeometric function \
			3F3(a1, a2, a3; b1, b2, b3; z)."
endparam
param terms
	caption = "Number of Terms"
	default = 6
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the series \
			representation of the hypergeometric function 3F3(a1, a2, a3; b1, b2, b3; \
			z). The default is six terms; the range is 2-24."
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-hypergeometric-3F3"
	a1 = a1
	a2 = a2
	a3 = a3
	b1 = b1
	b2 = b2
	b3 = b3
	terms = terms
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

comment {
This file contains streamlined formulas for functions represented by factorial
series, including double factorials, triple factorials, etc.

Originally written by Joe Maddry beginning on 03 Jan 2022.
}

jam-04factorial {
; jam 220104

; This formula implements a streamlined version of the generalized order-4 multifactorial
; functions f(#z) as found in the earlier formula, 'Factorial Fun'.  The order-4, or
; quadruple, factorial, n!!!! or n!4, is defined as n * (n-4) * ... * (4, 3, 2, or 1,
; depending on n).
;
; f(z) = Sum[ c(n) * z^(an + b) / (an + b)!4 ], n = 0 -> infinity, or,
;
;        ___
; f(z) = \     [ c(n)  * z^(an+b) / (an+b)!4] , where the coefficient (c)n may
;        /__
;         n
;
; or may not alternate in sign, and the parameters a and b, as well as the
; number of terms in the series, are user specified.  For example, if a=1, b=0,
; the function evaluates to the series representation of the exponential function;
; a=2, b=0 is the cosine function, if the term signs alternate; a=2, b=1 represents
; the sine function; etc.
; For purposes of this formula, negative multifactorials are all assigned the value of 1.

global:
; Declare arrays for various coefficient components
float exponent[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable
float ftemp = 0.0 ; float scratch variable
int multiplier = int addend = 0
int factorialorder = 4

; Test that the addend is < the multiplier
multiplier = @amultiplier
addend = @baddend
if addend >= multiplier
	addend = 0 ; reset an incorrect addend to zero
endif ; addend

; Initialize the factorial and exponent arrays
gindex = 0
while gindex < @terms
	itemp = gindex * multiplier + addend
	exponent[gindex] = itemp
	if itemp <= 1 ; define negative factorials = 1
		factorial[gindex] = 1.0
	else ; calculate the appropriate positive factorial
		ftemp = 1.0
		while itemp > 1
			ftemp = ftemp * itemp
			itemp = itemp - factorialorder
		endwhile ; itemp
		factorial[gindex] = ftemp
	endif ; item
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
ftemp = 1.0
while gindex < @terms
	if @alternate ; alternate coefficient signs
		if @negate ; opposite the usual alternation pattern
			if gindex % 2 == 0
				ftemp = -1.0
			else
				ftemp = 1.0
			endif ; gindex
		else ; alternation not reversed
			if gindex % 2 == 1
				ftemp = -1.0
			else
				ftemp = 1.0
			endif ; gindex
		endif ; @reverse
	endif ; @alternate
	coefficient[gindex] = ftemp / factorial[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
complex ztemp = (0,0)
float tempexp = 0.0
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z, and the new #z value as z(n+1) = f(z(n)) + jc
zpower[1] = #z
lindex = 2
ztemp = coefficient[0] + coefficient[1] * #z
while lindex < @terms
	tempexp = exponent[lindex]
	zpower[lindex] = #z^tempexp
	ztemp = ztemp + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = ztemp + jc

bailout:
|#z| < @bail

default:
title = "Factorial Series 04"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.2
angle = 0.0

heading
caption = "Order-4 Multifactorial Series"
text = "This formula is identical to 'Factorial Series' except that the series \
		is evaluated using quadruple, rather than regular, factorials."
endheading

param amultiplier
	caption = "Fn Constant a"
	default = 1
	min = 1
	hint = "For each term in the series, n = 0, 1,..., i, the exponent \
			of #z and the factorial denominator are defined by the expression \
			a*n + b; this parameter is the multiplier, a, in that expression. \
			(a >= 1)"
endparam
param baddend
	caption = "Fn Constant b"
	default = 0
	hint = "For each term in the series, n = 0, 1,..., i, the exponent \
			of #z and the factorial denominator are defined by the expression \
			a*n + b; this parameter is the addend, b, in that expression. \
			(b < a)"
endparam
param terms
	caption = "Number of Terms"
	default = 8
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the factorial series. \
			The default is eight terms; the range is 2-24."
endparam
param alternate
	caption = "Alternate Signs?"
	default = FALSE
	hint = "If enabled, then the signs of the terms in the series alternate between \
			positive and negative."
endparam
param negate
	caption = "Reverse Signs?"
	default = FALSE
	hint = "If enabled, then the pattern of sign alternations is reversed."
	visible = @alternate
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-04factorial"
	amultiplier = amultiplier
	baddend = baddend
	terms = terms
	alternate = alternate
	negate = negate
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-03factorial {
; jam 220104

; This formula implements a streamlined version of the generalized triple factorial
; functions f(#z) as found in the earlier formula, 'Factorial Fun'.  The
; triple factorial, n!!! or n!3, is defined as n * (n-3) * ... * (3, 2, or 1,
; depending on n).
;
; f(z) = Sum[ c(n) * z^(an + b) / (an + b)!!! ], n = 0 -> infinity, or,
;
;        ___
; f(z) = \     [ c(n)  * z^(an+b) / (an+b)!!!] , where the coefficient (c)n may
;        /__
;         n
;
; or may not alternate in sign, and the parameters a and b, as well as the
; number of terms in the series, are user specified.  For example, if a=1, b=0,
; the function evaluates to the series representation of the exponential function;
; a=2, b=0 is the cosine function, if the term signs alternate; a=2, b=1 represents
; the sine function; etc.
; For purposes of this formula, negative factorials are all assigned the value of 1.

global:
; Declare arrays for various coefficient components
float exponent[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable
float ftemp = 0.0 ; float scratch variable
int multiplier = int addend = 0

; Test that the addend is < the multiplier
multiplier = @amultiplier
addend = @baddend
if addend >= multiplier
	addend = 0 ; reset an incorrect addend to zero
endif ; addend

; Initialize the factorial and exponent arrays
gindex = 0
while gindex < @terms
	itemp = gindex * multiplier + addend
	exponent[gindex] = itemp
	if itemp <= 1 ; define negative factorials = 1
		factorial[gindex] = 1.0
	else ; calculate the appropriate positive factorial
		ftemp = 1.0
		while itemp > 1
			ftemp = ftemp * itemp
			itemp = itemp - 3
		endwhile ; itemp
		factorial[gindex] = ftemp
	endif ; itemp
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
ftemp = 1.0
while gindex < @terms
	if @alternate ; alternate coefficient signs
		if @negate ; opposite the usual alternation pattern
			if gindex % 2 == 0
				ftemp = -1.0
			else
				ftemp = 1.0
			endif ; gindex
		else ; alternation not reversed
			if gindex % 2 == 1
				ftemp = -1.0
			else
				ftemp = 1.0
			endif ; gindex
		endif ; @reverse
	endif ; @alternate
	coefficient[gindex] = ftemp / factorial[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
complex ztemp = (0,0)
float tempexp = 0.0
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z, and the new #z value as z(n+1) = f(z(n)) + jc
zpower[1] = #z
lindex = 2
ztemp = coefficient[0] + coefficient[1] * #z
while lindex < @terms
	tempexp = exponent[lindex]
	zpower[lindex] = #z^tempexp
	ztemp = ztemp + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = ztemp + jc

bailout:
|#z| < @bail

default:
title = "Factorial Series 03"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.2
angle = 0.0

heading
caption = "Triple Factorial Series"
text = "This formula is identical to 'Factorial Series' except that the series \
		is evaluated using triple, rather than regular, factorials."
endheading

param amultiplier
	caption = "Fn Constant a"
	default = 1
	min = 1
	hint = "For each term in the series, n = 0, 1,..., i, the exponent \
			of #z and the factorial denominator are defined by the expression \
			a*n + b; this parameter is the multiplier, a, in that expression. \
			(a >= 1)"
endparam
param baddend
	caption = "Fn Constant b"
	default = 0
	hint = "For each term in the series, n = 0, 1,..., i, the exponent \
			of #z and the factorial denominator are defined by the expression \
			a*n + b; this parameter is the addend, b, in that expression. \
			(b < a)"
endparam
param terms
	caption = "Number of Terms"
	default = 8
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the factorial series. \
			The default is eight terms; the range is 2-24."
endparam
param alternate
	caption = "Alternate Signs?"
	default = FALSE
	hint = "If enabled, then the signs of the terms in the series alternate between \
			positive and negative."
endparam
param negate
	caption = "Reverse Signs?"
	default = FALSE
	hint = "If enabled, then the pattern of sign alternations is reversed."
	visible = @alternate
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-03factorial"
	amultiplier = amultiplier
	baddend = baddend
	terms = terms
	alternate = alternate
	negate = negate
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-factorial {
; jam 220103

; This formula implements a streamlined version of the generalized factorial
; functions f(#z) as found in the earlier formula, 'Factorial Fun'.
;
; f(z) = Sum[ c(n) * z^(an + b) / (an + b)! ], n = 0 -> infinity, or,
;
;        ___
; f(z) = \     [ c(n)  * z^(an+b) / (an+b)!] , where the coefficient (c)n may
;        /__
;         n
;
; or may not alternate in sign, and the parameters a and b, as well as the
; number of terms in the series, are user specified.  For example, if a=1, b=0,
; the function evaluates to the series representation of the exponential function;
; a=2, b=0 is the cosine function, if the term signs alternate; a=2, b=1 represents
; the sine function; etc.
; For purposes of this formula, negative factorials are all assigned the value of 1.

global:
; Declare arrays for various coefficient components
float exponent[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable
float ftemp = 0.0 ; float scratch variable
int multiplier = int addend = 0

; Test that the addend is < the multiplier
multiplier = @amultiplier
addend = @baddend
if addend >= multiplier
	addend = 0 ; reset an incorrect addend to zero
endif ; addend

; Initialize the factorial and exponent arrays
gindex = 0
while gindex < @terms
	itemp = gindex * multiplier + addend
	exponent[gindex] = itemp
	if itemp <= 1 ; define negative factorials = 1
		factorial[gindex] = 1.0
	else ; calculate the appropriate positive factorial
		ftemp = 1.0
		while itemp > 1
			ftemp = ftemp * itemp
			itemp = itemp - 1
		endwhile ; itemp
		factorial[gindex] = ftemp
	endif ; itemp
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
ftemp = 1.0
while gindex < @terms
	if @alternate ; alternate coefficient signs
		if @negate ; opposite the usual alternation pattern
			if gindex % 2 == 0
				ftemp = -1.0
			else
				ftemp = 1.0
			endif ; gindex
		else ; alternation not reversed
			if gindex % 2 == 1
				ftemp = -1.0
			else
				ftemp = 1.0
			endif ; gindex
		endif ; @reverse
	endif ; @alternate
	coefficient[gindex] = ftemp / factorial[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
complex ztemp = (0,0)
float tempexp = 0.0
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z, and the new #z value as z(n+1) = f(z(n)) + jc
zpower[1] = #z
lindex = 2
ztemp = coefficient[0] + coefficient[1] * #z
while lindex < @terms
	tempexp = exponent[lindex]
	zpower[lindex] = #z^tempexp
	ztemp = ztemp + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = ztemp + jc

bailout:
|#z| < @bail

default:
title = "Factorial Series"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.2
angle = 0.0

param amultiplier
	caption = "Fn Constant a"
	default = 1
	min = 1
	hint = "For each term in the series, n = 0, 1,..., i, the exponent \
			of #z and the factorial denominator are defined by the expression \
			a*n + b; this parameter is the multiplier, a, in that expression. \
			(a >= 1)"
endparam
param baddend
	caption = "Fn Constant b"
	default = 0
	hint = "For each term in the series, n = 0, 1,..., i, the exponent \
			of #z and the factorial denominator are defined by the expression \
			a*n + b; this parameter is the addend, b, in that expression. \
			(b < a)"
endparam
param terms
	caption = "Number of Terms"
	default = 8
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the factorial series. \
			The default is eight terms; the range is 2-24."
endparam
param alternate
	caption = "Alternate Signs?"
	default = FALSE
	hint = "If enabled, then the signs of the terms in the series alternate between \
			positive and negative."
endparam
param negate
	caption = "Reverse Signs?"
	default = FALSE
	hint = "If enabled, then the pattern of sign alternations is reversed."
	visible = @alternate
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-factorial"
	amultiplier = amultiplier
	baddend = baddend
	terms = terms
	alternate = alternate
	negate = negate
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-02factorial {
; jam 220104

; This formula implements a streamlined version of the generalized double factorial
; functions f(#z) as found in the earlier formula, 'Factorial Fun'.  The
; double factorial, n!!, is defined as n * (n-2) * ... * (2, if n is even, or 1, if n is odd).
;
; f(z) = Sum[ c(n) * z^(an + b) / (an + b)!! ], n = 0 -> infinity, or,
;
;        ___
; f(z) = \     [ c(n)  * z^(an+b) / (an+b)!!] , where the coefficient (c)n may
;        /__
;         n
;
; or may not alternate in sign, and the parameters a and b, as well as the
; number of terms in the series, are user specified.  For example, if a=1, b=0,
; the function evaluates to the series representation of the exponential function;
; a=2, b=0 is the cosine function, if the term signs alternate; a=2, b=1 represents
; the sine function; etc.
; For purposes of this formula, negative factorials are all assigned the value of 1.

global:
; Declare arrays for various coefficient components
float exponent[@terms]
float factorial[@terms] ; will actually hold the reciprocal factorials
float coefficient[@terms] ; the overall coefficient for each term

; Some useful variables for the global calculations
int gindex = 0 ; loop index
int itemp = 0 ; integer scratch variable
float ftemp = 0.0 ; float scratch variable
int multiplier = int addend = 0

; Test that the addend is < the multiplier
multiplier = @amultiplier
addend = @baddend
if addend >= multiplier
	addend = 0 ; reset an incorrect addend to zero
endif ; addend

; Initialize the factorial and exponent arrays
gindex = 0
while gindex < @terms
	itemp = gindex * multiplier + addend
	exponent[gindex] = itemp
	if itemp <= 1 ; define negative factorials = 1
		factorial[gindex] = 1.0
	else ; calculate the appropriate positive factorial
		ftemp = 1.0
		while itemp > 1
			ftemp = ftemp * itemp
			itemp = itemp - 2
		endwhile ; itemp
		factorial[gindex] = ftemp
	endif ; itemp
	gindex = gindex + 1
endwhile ; gindex

; Initialize the coefficient array
gindex = 0
ftemp = 1.0
while gindex < @terms
	if @alternate ; alternate coefficient signs
		if @negate ; opposite the usual alternation pattern
			if gindex % 2 == 0
				ftemp = -1.0
			else
				ftemp = 1.0
			endif ; gindex
		else ; alternation not reversed
			if gindex % 2 == 1
				ftemp = -1.0
			else
				ftemp = 1.0
			endif ; gindex
		endif ; @reverse
	endif ; @alternate
	coefficient[gindex] = ftemp / factorial[gindex]
	gindex = gindex + 1
endwhile ; gindex

init:
complex jc = (0,0)
if @mandy
	#z = #pixel, jc = #pixel
else ; Julia
	#z = #pixel, jc = @jconstant
endif

complex zpower[@terms] ; the variouis powers of #z needed for the series
zpower[0] = (1,0)
complex ztemp = (0,0)
float tempexp = 0.0
int lindex = 0 ; iteration loop index

loop:
; Compute the powers of the current #z, and the new #z value as z(n+1) = f(z(n)) + jc
zpower[1] = #z
lindex = 2
ztemp = coefficient[0] + coefficient[1] * #z
while lindex < @terms
	tempexp = exponent[lindex]
	zpower[lindex] = #z^tempexp
	ztemp = ztemp + coefficient[lindex] * zpower[lindex]
	lindex = lindex + 1
endwhile ; lindex
#z = ztemp + jc

bailout:
|#z| < @bail

default:
title = "Factorial Series 02"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 0.2
angle = 0.0

heading
caption = "Double Factorial Series"
text = "This formula is identical to 'Factorial Series' except that the series \
		is evaluated using double, rather than regular, factorials."
endheading

param amultiplier
	caption = "Fn Constant a"
	default = 1
	min = 1
	hint = "For each term in the series, n = 0, 1,..., i, the exponent \
			of #z and the factorial denominator are defined by the expression \
			a*n + b; this parameter is the multiplier, a, in that expression. \
			(a >= 1)"
endparam
param baddend
	caption = "Fn Constant b"
	default = 0
	hint = "For each term in the series, n = 0, 1,..., i, the exponent \
			of #z and the factorial denominator are defined by the expression \
			a*n + b; this parameter is the addend, b, in that expression. \
			(b < a)"
endparam
param terms
	caption = "Number of Terms"
	default = 8
	min = 2
	max = 24
	hint = "This value is the number of terms to compute in the factorial series. \
			The default is eight terms; the range is 2-24."
endparam
param alternate
	caption = "Alternate Signs?"
	default = FALSE
	hint = "If enabled, then the signs of the terms in the series alternate between \
			positive and negative."
endparam
param negate
	caption = "Reverse Signs?"
	default = FALSE
	hint = "If enabled, then the pattern of sign alternations is reversed."
	visible = @alternate
endparam
param bail
    caption = "Bailout Value"
    default = 1e6
    hint = "Value needed to 'escape' to infinity."
endparam
param jconstant
	caption = "Seed/Perturbation"
	default = (0,0)
	hint = "This is the seed constant for Julia-type fractals, or the initial \
		  perturbation for Mandelbrot-types."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching."
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching."
	visible = FALSE
endparam

switch:
	type = "jam-02factorial"
	amultiplier = amultiplier
	baddend = baddend
	terms = terms
	alternate = alternate
	negate = negate
	bail = bail
	jconstant = #pixel
	mandy = julia
	julia = mandy
}

jam-OrbitTrapBarnsley {

; jam 12/22/2018
; Based on variations of the traditional Barnsley formulas.
; Some ideas from Michèle Dessureault, Ed Algra, Sam Monnier, and many others.
; The various Barnsley equations are executed based on the distance #z and a point \
; on an orbit trap selected by the current #z value.
; January 2022 --- Major additions of new trap types, shapes, etc., plus bug fixes.

global:
	; Common constants
	float twopi = 2.0 * #pi
	float halfpi = #pi/2
	float degconversion = twopi/360
	float onehalf = 1.0/2
	float onethird = 1.0/3
	float onefourth = 1.0/4

	int numbervertices = 0 ; change to accomodate trap shape
	int cursality ; number of disjoint pieces for traps 1 & 2 -- change to accomodte trap shape
	int cincrement ; cursality increments
	float scratchfloat = 0.0
	float scratchfloat2 = float scratchfloat3 = float scratchfloat4 = 0.0
	int scratchint = int scratchint2 = 0
	int glindex = 0 ; for loops in the global section
	int glindex2 = 0 ; global outer loop index
	int glindex3 = 0 ; extra index
	int maxvertices = 402 ; maximum number of vertices for the trap
	complex vertex[402] ; maximum number of vertices for the trap
	float xcoord[402] ; x-coordinates of vertices
	float ycoord[402] ; y-coordinates vertices
	int traparray ; the selected trap shape
	float trapscales = @nscale1

	; variables specific for some of the 'lines & points' trap shapes
	int unityroots ; for 'roots of unity' option
	bool singleroot ; flag for 'roots of unity' option
	int whichroot ; for 'roots of unity' option
	int collinearspots ; for 'collinear spots' option
	int squaresize ; for 'square array' option
	int triarraysize ; for 'triangular array' and some other array options
	int spiralsize ; for the 'polygonal spiral' options
	float shrink2 = onehalf, float shrink3 = onethird
	float ellipseH ; for 'superellipse' option
	float ellipseW
	float ellipseX
	float hypotroA ; for 'hypotrochoid' and 'epitrochoid' options
	float hypotroB
	float hypotroH
	int granularity  = 100 ; for smoother curves
	int granularity2= 101
	float lissajdomain = 0.0 ; for 'lissajous 3' option
	int numbercircles ; for 'nested circles', 'osculant circles' options
	int dotnum ; for the 'dotted star' options
	int raynum
	int dashnum ; for the 'dashed star' options
	float cycloidamp
	float cycloidconst
	float cycloidlength
	float moritzamp
	float moritzfreqN
	float moritzfreqD
	float moritzconst

	; variables specific for some of the 'polar functions' trap shapes
	bool polarimplicit ; flag for marking some polar curves as defined implicitly rather than radially
	int rosepetals ; for the polar rose shape
	float folium ; folium shaping parameters
	float foliumperturb
	float cardioid ; cardioid shaping parameters
	float cardioidperturb
	float cissoidDioA ; cissoid of Diocles
	float cissoidDioB
	float cochleoid ; cochleoid
	float conchoidA ; various conchoid shaping parameters
	float conchoidB
	float conchoidC
	float cubicpA ; cubical parabola shaping parameters
	float cubicpB
	float cubicpC
	float majaxis
	float minaxis
	float epower
	float tanfreq
	float fosinfreq
	float focosfreq
	float sinfreq2
	float hyperbolic
	float kampfreq
	float kamppower
	float nodalfreq
	float lemfreq
	float lempower
	float limfreq
	float limamp
	float limoffset
	float litpower
	float logspiA
	float logspiB
	float parafreq
	float paraamp
	float paraoffset
	float paraspi
	float paraspioffset
	float semicubtanfreq
	float semicubcosfreq
	float semicubpower
	float archspioffset
	float strophcosfreqA
	float strophcosfreqB
	float polarfreqA
	float polarampA
	float trefoilcosamp
	float trefoilsinamp
	float trefoilcossym
	float trefoilsinsym
	float trefoilconst
	float trilimA
	float trilimB
	float trilimamp
	float trilimfreq
	float folioidamp
	float folioidfreqN
	float folioidfreqD
	float folioidconstA
	float folioidconstB

	; variables specific for the 'parametric functions' shapes
	int hyponumer ; hypocycloid shaping parameters
	int hypodenom ; hypocycloid shaping parameters
	float companC1
	float companC2
	float companfreq
	float cycampA
	float cycampB
	float cycxscale
	float cycyoffset
	float cycsinfreq
	float cyccosfreq
	float cycangle
	float epicycAN
	float epicycAD
	float epicycB
	float epicycC
	float nephconstA
	float nephconstB
	float nephsinfreq
	float nephcosfreq
	float parafreqA
	float parafreqB
	float paraconstA
	float paraconstB
	float wavysinfreq
	float wavysinamp
	float wavyradius
	float paraxaxis
	float parayaxis
	float epiradiusA
	float epiradiusB
	float epiradiusC

	; variables specific for the 'cartesian' trap shapes
	float cartxcoeff
	float cartycoeff
	float cartconst
	float cartconstB
	float cartconstC
	float cartexexp
	float carteyexp
	float coniceccent
	float conchmod
	
	; shaping variables for 'lines & points' traps
if @traptype == "lines & points"
		lissajdomain = #pi * @lissadomain
		unityroots = @unityroot1
		singleroot = @singleroot1
		whichroot = @whichroot1 - 1 ; indices should run from 0-(#roots-1)
		collinearspots = @collinearspot1
		squaresize = @squarespot1
		triarraysize = @triarray1
		spiralsize = @spiralorder1
		ellipseH = @ellipseheight1
		ellipseW = @ellipsewidth1
		ellipseX = @ellipseexponent1
		hypotroA = @hypotrochA1
		hypotroB = @hypotrochB1
		hypotroH = @hypotrochH1
		numbercircles = @circlenum1
		raynum = @raynumber
		dotnum = @dotnumber
		dashnum = @dashnumber
		cycloidamp = @cycloidamp1
		cycloidconst = @cycloidconst1
		cycloidlength = @cycloidlength1
		moritzamp = @moritzamp1
		moritzfreqN = @moritzfreqN1
		moritzfreqD = @moritzfreqD1
		moritzconst = @moritzconst1
endif ; @traptype

	; shaping variables for 'polar functions' traps
if @traptype == "polar functions"
	if @polarmode1 == "normal"
		polarimplicit = FALSE ; radial function, not implicit curve
	else ; polar implicit function
		polarimplicit = TRUE
		trapscales = recip(trapscales)
	endif ; @polarmode1

	rosepetals = @rose1
	folium = @folium1
	foliumperturb = @foliumperturb1
	cardioid = @cardioid1
	cardioidperturb = @cardioidperturb1
	cissoidDioA = @cissoidDioA1
	cissoidDioB = @cissoidDioB1
	cochleoid = @cochleoid1
	conchoidA = @conchoidA1
	conchoidB = @conchoidB1
	conchoidC = @conchoidC1
	conchoidA = @conchoidA1
	conchoidB = @conchoidB1
	conchoidC = @conchoidC1
	cubicpA = @cubicpA1
	cubicpB = @cubicpB1
	cubicpC = @cubicpC1
	majaxis = @majaxis1
	minaxis = @minaxis1
	epower = @epower1
	tanfreq = @tanfreq1
	fosinfreq = @fosinfreq1
	focosfreq = @focosfreq1
	sinfreq2 = @sinfreq21
	hyperbolic = @hyperbolic1
	kampfreq = @kampfreq1
	kamppower = @kamppower1
	nodalfreq = @nodalfreq1
	lemfreq = @lemfreq1
	lempower = @lempower1
	limfreq = @limfreq1
	limamp = @limamp1
	limoffset = @limoffset1
	litpower = @litpower1
	logspiA = @logspiA1
	logspiB = 0.2 * @logspiB1
	parafreq = @parafreq1
	paraamp = @paraamp1
	paraoffset = @paraoffset1
	paraspi = @paraspi1
	paraspioffset = @paraspioffset1
	semicubtanfreq = @semicubtanfreq1
	semicubcosfreq = @semicubcosfreq1
	semicubpower = @semicubpower1
	archspioffset = 3.0 * @archspioffset1
	strophcosfreqA = @strophcosfreqA1
	strophcosfreqB = @strophcosfreqB1
	polarfreqA = @polarfreqA1
	polarampA = @polarampA1
	trefoilcosamp = @trefoilcosamp1
	trefoilsinamp = @trefoilsinamp1
	trefoilcossym = @trefoilcossymmetry1
	trefoilsinsym = @trefoilsinsymmetry1
	trefoilconst = @trefoilconstant1
	trilimA = @trilimA1
	trilimB = @trilimB1
	trilimamp = @trilimamp1
	trilimfreq = @trilimfreq1
	folioidamp = @folioidamp1
	folioidfreqN = @folioidfreqN1
	folioidfreqD = @folioidfreqD1
	folioidconstA = @folioidconstA1
	folioidconstB = @folioidconstB1
endif ; @traptype

	; shaping variables for 'parametric functions' traps
if @traptype == "parametric functions"
	hyponumer = @hyponumerator1
	hypodenom = @hypodenom1
	companC1 = @companC11
	companC2 = @companC21
	companfreq = @companfreq1
	cycampA = @cycampA1
	cycampB = @cycampB1
	cycxscale = @cycxscale1
	cycyoffset = @cycyoffset1
	cycsinfreq = @cycsinfreq1
	cyccosfreq = @cyccosfreq1
	cycangle = @cycangle1
	epicycAN = @epicycAN1
	epicycAD = @epicycAD1
	epicycB = @epicycB1
	epicycC= @epicycC1
	nephsinfreq = @nephsinfreq1
	nephcosfreq = @nephcosfreq1
	nephconstA = @nephconstA1
	nephconstB = @nephconstB1
	parafreqA = @parafreqA1
	parafreqB = @parafreqB1
	paraconstA = @paraconstA1
	paraconstB = @paraconstB1
	wavysinfreq = @wavysinfreq1
	wavysinamp = @wavysinamp1
	wavyradius = @wavyradius1
	paraxaxis = @paraxaxis1
	parayaxis = @parayaxis1	
	epiradiusA = @epiradiusA1
	epiradiusB = @epiradiusB1
	epiradiusC = @epiradiusC1
endif ; @traptype

if @traptype == "cartesian"
	trapscales = 1/trapscales
	cartxcoeff = @cartxcoeff1
	cartycoeff = @cartycoeff1
	cartconst = @cartconstant1
	cartconstB = @cartconstantB1
	cartconstC = @cartconstantC1
	cartexexp = @cartexexp1
	carteyexp = @carteyexp1
	coniceccent = @coniceccent1
	conchmod = @conchmod1
endif ; @traptype

if @traptype == "lines & points"
	if @trapshape == "line"
		traparray = 0
	elseif @trapshape == "triangle"
		traparray = 1
	elseif @trapshape == "isosceles"
		traparray = 2
	elseif @trapshape == "3-asterisk"
		traparray = 3
	elseif @trapshape == "3-star"
		traparray = 4
	elseif @trapshape == "polytriangle"
		traparray = 5
	elseif @trapshape == "trigram"
		traparray = 6
	elseif @trapshape == "nested triangles"
		traparray = 7
	elseif @trapshape == "nested triangle 2"
		traparray = 8
	elseif @trapshape == "twisted triangles"
		traparray = 9
	elseif @trapshape == "twisted triangle 2"
		traparray = 10
	elseif @trapshape == "square"
		traparray = 11
	elseif @trapshape == "square 2"
		traparray = 12
	elseif @trapshape == "rhombus"
		traparray = 13
	elseif @trapshape == "kite"
		traparray = 14
	elseif @trapshape == "dart"
		traparray = 15
	elseif @trapshape == "rectangle"
		traparray = 214
	elseif @trapshape == "4-asterisk"
		traparray = 16
	elseif @trapshape == "4-star"
		traparray = 17
	elseif @trapshape == "flat 4-star"
		traparray = 18
	elseif @trapshape == "bowtie"
		traparray = 19
	elseif @trapshape == "windowpane"
		traparray = 20
	elseif @trapshape == "tetragram"
		traparray = 21
	elseif @trapshape == "nested squares"
		traparray = 22
	elseif @trapshape == "nested square 2"
		traparray = 23
	elseif @trapshape == "twisted squares"
		traparray = 24
	elseif @trapshape == "twisted square 2"
		traparray = 25
	elseif @trapshape == "windmill"
		traparray = 26
	elseif @trapshape == "windmill 2"
		traparray = 27
	elseif @trapshape == "pentagon"
		traparray = 28
	elseif @trapshape == "pentagon 2"
		traparray = 29
	elseif @trapshape == "pentagram"
		traparray = 30
	elseif @trapshape == "pentagram 2"
		traparray = 31
	elseif @trapshape == "pentagram 3"
		traparray = 32
	elseif @trapshape == "pentagram 4"
		traparray = 33
	elseif @trapshape == "5-asterisk"
		traparray = 34
	elseif @trapshape == "5-star"
		traparray = 35
	elseif @trapshape == "nested pentagons"
		traparray = 36
	elseif @trapshape == "nested pentagon 2"
		traparray = 37
	elseif @trapshape == "twisted pentagons"
		traparray = 38
	elseif @trapshape == "twisted pentagon 2"
		traparray = 39
	elseif @trapshape == "hexagon"
		traparray = 40
	elseif @trapshape == "hexagon 2"
		traparray = 41
	elseif @trapshape == "hexagram"
		traparray = 42
	elseif @trapshape == "hexagram 2"
		traparray = 43
	elseif @trapshape == "hexagram 3"
		traparray = 44
	elseif @trapshape == "hexagram 4"
		traparray = 45
	elseif @trapshape == "hexagram 5"
		traparray = 46
	elseif @trapshape == "hexagram 6"
		traparray = 47
	elseif @trapshape == "hexagram 7"
		traparray = 48
	elseif @trapshape == "6-asterisk"
		traparray = 49
	elseif @trapshape == "6-star"
		traparray = 50
	elseif @trapshape == "nested hexagons"
		traparray = 51
	elseif @trapshape == "nested hexagon 2"
		traparray = 52
	elseif @trapshape == "twisted hexagons"
		traparray = 53
	elseif @trapshape == "twisted hexagon 2"
		traparray = 54
	elseif @trapshape == "hand"
		traparray = 55
	elseif @trapshape == "zigzag-3"
		traparray = 56
	elseif @trapshape == "zigzag-4"
		traparray = 57
	elseif @trapshape == "zigzag-5"
		traparray = 58
	elseif @trapshape == "zigzag-6"
		traparray = 59
	elseif @trapshape == "zigzag-7"
		traparray = 60
	elseif @trapshape == "sawtooth-1"
		traparray = 61
	elseif @trapshape == "sawtooth-2"
		traparray = 62
	elseif @trapshape == "sawtooth-3"
		traparray = 63
	elseif @trapshape == "sawtooth-4"
		traparray = 64
	elseif @trapshape == "5-star 2"
		traparray = 65
	elseif @trapshape == "3-star 2"
		traparray = 66
	elseif @trapshape == "tetragram 2"
		traparray = 67
	elseif @trapshape == "pentagram 5"
		traparray = 68
	elseif @trapshape == "4-star 2"
		traparray = 69
	elseif @trapshape == "5-star 3"
		traparray = 70
	elseif @trapshape == "6-star 2"
		traparray = 71
	elseif @trapshape == "6-star 3"
		traparray = 72
	elseif @trapshape == "square-1"
		traparray = 73
	elseif @trapshape == "square-2"
		traparray = 74
	elseif @trapshape == "square-3"
		traparray = 75
	elseif @trapshape == "square-4"
		traparray = 76
	elseif @trapshape == "heptagon"
		traparray = 77
	elseif @trapshape == "heptagon 2"
		traparray = 78
	elseif @trapshape == "heptagram"
		traparray = 79
	elseif @trapshape == "heptagram 2"
		traparray = 80
	elseif @trapshape == "heptagram 3"
		traparray = 81
	elseif @trapshape == "heptagram 4"
		traparray = 82
	elseif @trapshape == "heptagram 5"
		traparray = 83
	elseif @trapshape == "heptagram 6"
		traparray = 84
	elseif @trapshape == "heptagram 7"
		traparray = 85
	elseif @trapshape == "7-asterisk"
		traparray = 86
	elseif @trapshape == "7-star"
		traparray = 87
	elseif @trapshape == "7-star 2"
		traparray = 88
	elseif @trapshape == "nested heptagons"
		traparray = 89
	elseif @trapshape == "nested heptagon 2"
		traparray = 90
	elseif @trapshape == "twisted heptagons"
		traparray = 91
	elseif @trapshape == "twisted heptagon 2"
		traparray = 92
	elseif @trapshape == "peano curve"
		traparray = 93
	elseif @trapshape == "octagon"
		traparray = 94
	elseif @trapshape == "octagon 2"
		traparray = 95
	elseif @trapshape == "octagram"
		traparray = 96
	elseif @trapshape == "octagram 2"
		traparray = 97
	elseif @trapshape == "octagram 3"
		traparray = 98
	elseif @trapshape == "octagram 4"
		traparray = 99
	elseif @trapshape == "octagram 5"
		traparray = 100
	elseif @trapshape == "octagram 6"
		traparray = 101
	elseif @trapshape == "octagram 7"
		traparray = 102
	elseif @trapshape == "8-asterisk"
		traparray = 103
	elseif @trapshape == "8-star"
		traparray = 104
	elseif @trapshape == "8-star 2"
		traparray = 105
	elseif @trapshape == "octagram 8"
		traparray = 106
	elseif @trapshape == "octagram 9"
		traparray = 107
	elseif @trapshape == "octagram 10"
		traparray = 108
	elseif @trapshape == "roots of unity"
		traparray = 109
	elseif @trapshape == "7-star 3"
		traparray = 110
	elseif @trapshape == "lissajous 1"
		traparray = 111
	elseif @trapshape == "nonagon"
		traparray = 112
	elseif @trapshape == "nonagram"
		traparray = 113
	elseif @trapshape == "nonagram 2"
		traparray = 114
	elseif @trapshape == "nonagram 3"
		traparray = 115
	elseif @trapshape == "nonagram 4"
		traparray = 116
	elseif @trapshape == "nonagram 5"
		traparray = 117
	elseif @trapshape == "nonagram 6"
		traparray = 118
	elseif @trapshape == "9-star"
		traparray = 119
	elseif @trapshape == "9-asterisk"
		traparray = 120
	elseif @trapshape == "9-star 2"
		traparray = 121
	elseif @trapshape == "9-star 3"
		traparray = 122
	elseif @trapshape == "decagon"
		traparray = 123
	elseif @trapshape == "10-asterisk"
		traparray = 124
	elseif @trapshape == "decagram"
		traparray = 125
	elseif @trapshape == "decagram 2"
		traparray = 126
	elseif @trapshape == "decagram 3"
		traparray = 127
	elseif @trapshape == "decagram 4"
		traparray = 128
	elseif @trapshape == "10-star"
		traparray = 129
	elseif @trapshape == "10-star 2"
		traparray = 130
	elseif @trapshape == "10-star 3"
		traparray = 131
	elseif @trapshape == "decagram 5"
		traparray = 132
	elseif @trapshape == "lissajous 2"
		traparray = 133
	elseif @trapshape == "collinear spots"
		traparray = 134
	elseif @trapshape == "square array"
		traparray = 135
	elseif @trapshape == "triangular array"
		traparray = 136
	elseif @trapshape == "triangular spiral"
		traparray = 137
	elseif @trapshape == "square spiral"
		traparray = 138
	elseif @trapshape == "pentagonal array"
		traparray = 139
	elseif @trapshape == "hexagonal array"
		traparray = 140
	elseif @trapshape == "pentagonal spiral"
		traparray = 141
	elseif @trapshape == "hexagonal spiral"
		traparray = 142
	elseif @trapshape == "octagonal spiral"
		traparray = 143
	elseif @trapshape == "superellipse"
		traparray = 144
	elseif @trapshape == "hypotrochoid"
		traparray = 145
	elseif @trapshape == "epitrochoid"
		traparray = 146
	elseif @trapshape == "lissajous 3"
		traparray = 147
	elseif @trapshape == "honeycomb"
		traparray = 148
	elseif @trapshape == "nested circles"
		traparray = 149
	elseif @trapshape == "osculant circles"
		traparray = 150
	elseif @trapshape == "nonagram 7"
		traparray = 151
	elseif @trapshape == "more polygons"
		if @morepolygons1 == "11-gon"
			traparray = 152
		elseif @morepolygons1 == "11-gram 1"
			traparray = 153
		elseif @morepolygons1 == "11-gram 2"
			traparray = 154
		elseif @morepolygons1 == "11-gram 3"
			traparray = 155
		elseif @morepolygons1 == "11-gram 4"
			traparray = 156
		elseif @morepolygons1 == "11-star"
			traparray = 163
		elseif @morepolygons1 == "11-star 2"
			traparray = 165
		elseif @morepolygons1 == "11-asterisk"
			traparray = 164
		elseif @morepolygons1 == "12-gon"
			traparray = 157
		elseif @morepolygons1 == "12-gram 1"
			traparray = 158
		elseif @morepolygons1 == "12-gram 2"
			traparray = 159
		elseif @morepolygons1 == "12-gram 3"
			traparray = 160
		elseif @morepolygons1 == "12-gram 4"
			traparray = 161
		elseif @morepolygons1 == "12-gram 5"
			traparray = 162
		elseif @morepolygons1 == "12-star"
			traparray = 166
		elseif @morepolygons1 == "12-star 2"
			traparray = 167
		elseif @morepolygons1 == "12-asterisk"
			traparray = 168
		elseif @morepolygons1 == "13-gon"
			traparray = 189
		elseif @morepolygons1 == "14-gon"
			traparray = 190
		elseif @morepolygons1 == "15-gon"
			traparray = 191
		elseif @morepolygons1 == "16-gon"
			traparray = 192
		elseif @morepolygons1 == "13-asterisk"
			traparray = 193
		elseif @morepolygons1 == "14-asterisk"
			traparray = 194
		elseif @morepolygons1 == "15-asterisk"
			traparray = 195
		elseif @morepolygons1 == "16-asterisk"
			traparray = 196
		elseif @morepolygons1 == "13-star"
			traparray = 197
		elseif @morepolygons1 == "14-star"
			traparray = 198
		elseif @morepolygons1 == "15-star"
			traparray = 199
		elseif @morepolygons1 == "16-star"
			traparray = 200
		elseif @morepolygons1 == "11-rhombstar"
			traparray = 208
		elseif @morepolygons1 == "12-rhombstar"
			traparray = 209
		elseif @morepolygons1 == "13-rhombstar"
			traparray = 210
		elseif @morepolygons1 == "14-rhombstar"
			traparray = 211
		elseif @morepolygons1 == "15-rhombstar"
			traparray = 212
		elseif @morepolygons1 == "16-rhombstar"
			traparray = 213
		endif ; @morepolygons1
	elseif @trapshape == "more spirolaterals"
		if @morespirolaterals1 == "1,1,1,2,3;1/2"
			traparray = 169
		elseif @morespirolaterals1 ==  "1,1,2,1,3;1/2"
			traparray = 170
		elseif @morespirolaterals1 ==  "1,1,2,2,4;1/2"
			traparray = 171
		elseif @morespirolaterals1 ==  "1,1,4,5,4;1/2"
			traparray = 172
		elseif @morespirolaterals1 ==  "1,2,2,2,5;1/2"
			traparray = 173
		elseif @morespirolaterals1 ==  "1,2,5,3,5;1/2"
			traparray = 174
		elseif @morespirolaterals1 ==  "2,2,1,4,3;1/2"
			traparray = 175
		elseif @morespirolaterals1 ==  "2,2,4,4,3;1/2"
			traparray = 176
		elseif @morespirolaterals1 ==  "2,3,5,3,2;1/2"
			traparray = 177
		elseif @morespirolaterals1 ==  "1,6,6,6;1/4,1/4,-5/6"
			traparray = 178
		elseif @morespirolaterals1 ==  "1,6,6,2;3/4,-1/4,-1/6"
			traparray = 179
		elseif @morespirolaterals1 ==  "1,2,1,3;-4/5"
			traparray = 180
		elseif @morespirolaterals1 ==  "1,2,1,3;-4/5,-4/5,0"
			traparray = 181
		elseif @morespirolaterals1 ==  "1,2,1,3;-4/5,-1/5,-4/5"
			traparray = 182
		elseif @morespirolaterals1 ==  "1,3;1/5,3/5,-1/5"
			traparray = 183
		elseif @morespirolaterals1 ==  "1,2,3,3,2,1;5/6,1/6,1/6"
			traparray = 184
		elseif @morespirolaterals1 ==  "1,1,3,1;-5/6,-1/6,3/7"
			traparray = 185
		elseif @morespirolaterals1 ==  "1,1,3,1;-1/6,1/6,-3/7"
			traparray = 186
		elseif @morespirolaterals1 ==  "1,1,3,1;5/6,1/6,4/7"
			traparray = 187
		elseif @morespirolaterals1 ==  "1,3,1,4,2;-1/2,1/6"
			traparray = 188
		endif ; @morespirolaterals1
	elseif @trapshape == "3-rhombstar"
		traparray = 201
	elseif @trapshape == "5-rhombstar"
		traparray = 202
	elseif @trapshape == "6-rhombstar"
		traparray = 203
	elseif @trapshape == "7-rhombstar"
		traparray = 204
	elseif @trapshape == "8-rhombstar"
		traparray = 205
	elseif @trapshape == "9-rhombstar"
		traparray = 206
	elseif @trapshape == "10-rhombstar"
		traparray = 207
	elseif @trapshape == "dotted star"
		traparray = 215
	elseif @trapshape == "dashed star"
		traparray = 216
	elseif @trapshape == "more curves"
		if @morecurves1 == "rhodonea"
			traparray = 217
		elseif @morecurves1 == "cycloid"
			traparray = 218
		elseif @morecurves1 == "parabolic lissajous"
			traparray = 219
		elseif @morecurves1 == "polar lissajous"
			traparray = 220
		elseif @morecurves1 == "Moritz cyclic harmonic"
			traparray = 221
		elseif @morecurves1 == "elliptic lissajous"
			traparray = 222
		elseif @morecurves1 == "bipolar lissajous"
			traparray = 223
		endif ; @morecurves
	endif ; @trapshape

elseif @traptype == "polar functions"
		if @polarshape1 == "rose"
			traparray = 0
		elseif @polarshape1 == "folium"
			traparray = 1
		elseif @polarshape1 == "cardioid"
			traparray = 2
		elseif @polarshape1 == "circle"
			traparray = 3
		elseif @polarshape1 == "cissoid of Diocles"
			traparray = 4
		elseif @polarshape1 == "cochleoid"
			traparray = 5
		elseif @polarshape1 == "conchoid of De Sluze"
			traparray = 7
		elseif @polarshape1 == "conchoid of Nicomedes"
			traparray = 8
		elseif @polarshape1 == "cubical parabola"
			traparray = 9
		elseif @polarshape1 == "ellipse"
			traparray = 10
		elseif @polarshape1 == "folium of Descartes"
			traparray = 11
		elseif @polarshape1 == "hyperbolic spiral"
			traparray = 12
		elseif @polarshape1 == "kampyle of Eudoxus"
			traparray = 13
		elseif @polarshape1 == "kappa"
			traparray = 14
		elseif @polarshape1 == "lemniscate of Bernoulli"
			traparray = 15
		elseif @polarshape1 == "limacon of Pascal"
			traparray = 16
		elseif @polarshape1 == "lituus"
			traparray = 17
		elseif @polarshape1 == "logarithmic spiral"
			traparray = 18
		elseif @polarshape1 == "parabola"
			traparray = 19
		elseif @polarshape1 == "parabolic spiral"
			traparray = 20
		elseif @polarshape1 == "semicubical parabola"
			traparray = 21
		elseif @polarshape1 == "spiral of Archimedes"
			traparray = 22
		elseif @polarshape1 == "strophoid"
			traparray = 23
		elseif @polarshape1 == "Cayley's sextic"
			traparray = 24
		elseif @polarshape1 == "trisectrix limacon"
			traparray = 25
		elseif @polarshape1 == "trefoil of Habenicht"
			traparray = 27
		elseif @polarshape1 == "Cayley's sextic 2"
			traparray = 28
		elseif @polarshape1 == "lituus 2"
			traparray = 29
			litpower = recip(litpower)
		elseif @polarshape1 == "hippopede"
			traparray = 30
		elseif @polarshape1 == "folioid"
			traparray = 31
		endif ; @polarshape1
elseif @traptype == "parametric functions"
		if @parashape1 == "hypocycloid"
			traparray = 0
		elseif @parashape1 == "companion of cycloid"
			traparray = 1
		elseif @parashape1 == "cycloid"
			traparray = 2
		elseif @parashape1 == "cycloid variant"
			traparray = 3
		elseif @parashape1 == "epicycloid"
			traparray = 4
		elseif @parashape1 == "nephroid"
			traparray = 5
		elseif @parashape1 == "hyperbola"
			traparray = 6
		elseif @parashape1 == "tractrix"
			traparray = 7
		elseif @parashape1 == "wavy circle"
			traparray = 8
		elseif @parashape1 == "ellipse"
			traparray = 9
		elseif @parashape1 == "serpentine"
			traparray = 10
		elseif @parashape1 == "witch of Agnesi"
			traparray = 11
		elseif @parashape1 == "Abdank quadratrix"
			traparray = 12
		elseif @parashape1 == "cornoid"
			traparray = 13
		elseif @parashape1 == "epicycloid 2"
			traparray = 14
		elseif @parashape1 == "epitrochoid"
			traparray = 15
		endif ; @parashape1

	elseif @traptype == "cartesian"
		if @xyshape1 == "ampersand"
			traparray = 0
		elseif @xyshape1 == "Alain's curve"
			traparray = 1
		elseif @xyshape1 == "arcs of Samothrace"
			traparray = 2
		elseif @xyshape1 == "astroid"
			traparray = 3
		elseif @xyshape1 == "atriphthaloid"
			traparray = 4
		elseif @xyshape1 == "bean curve 1"
			traparray = 5
		elseif @xyshape1 == "bean curve 2"
			traparray = 6
		elseif @xyshape1 == "beetle curve"
			traparray = 7
		elseif @xyshape1 == "bicorn"
			traparray = 8
		elseif @xyshape1 == "bicuspid"
			traparray = 9
		elseif @xyshape1 == "biquartic of Sacre"
			traparray = 10
		elseif @xyshape1 == "cubic egg"
			traparray = 11
		elseif @xyshape1 == "Bolza curve"
			traparray = 12
		elseif @xyshape1 == "bow curve"
			traparray = 13
		elseif @xyshape1 == "bullet nose curve"
			traparray = 14
		elseif @xyshape1 == "butterfly sextic"
			traparray = 15
		elseif @xyshape1 == "butterfly 2"
			traparray = 16
		elseif @xyshape1 == "cardioid"
			traparray = 17
		elseif @xyshape1 == "Cartesian oval"
			traparray = 18
		elseif @xyshape1 == "Cassini oval"
			traparray = 19
		elseif @xyshape1 == "catenary"
			traparray = 20
		elseif @xyshape1 == "Cayley's sextic"
			traparray = 21
		elseif @xyshape1 == "Ceva's trisectrix"
			traparray = 22
		elseif @xyshape1 == "Chasles cubic"
			traparray = 23
		elseif @xyshape1 == "circle"
			traparray = 24
		elseif @xyshape1 == "circular cubic"
			traparray = 25
		elseif @xyshape1 == "cissoid of Diocles"
			traparray = 26
		elseif @xyshape1 == "clinoid"
			traparray = 27
		elseif @xyshape1 == "cochleoid"
			traparray = 28
		elseif @xyshape1 == "conchoid of circle"
			traparray = 29
		elseif @xyshape1 == "conchoid of Nicomedes"
			traparray = 30
		elseif @xyshape1 == "conchoid of de Sluze"
			traparray = 31
		elseif @xyshape1 == "cornoid"
			traparray = 32
		elseif @xyshape1 == "cross curve"
			traparray = 33
		elseif @xyshape1 == "cubic of Apollonius"
			traparray = 34
		elseif @xyshape1 == "cranoid"
			traparray = 35
		elseif @xyshape1 == "Jerabek curve"
			traparray = 36
		elseif @xyshape1 == "Rosillo curve"
			traparray = 37
		elseif @xyshape1 == "deltoid"
			traparray = 38
		elseif @xyshape1 == "devil's curve"
			traparray = 39
		elseif @xyshape1 == "dipole curve"
			traparray = 40
		elseif @xyshape1 == "double egg"
			traparray = 41
		elseif @xyshape1 == "double folium"
			traparray = 42
		elseif @xyshape1 == "double U curve"
			traparray = 43
		elseif @xyshape1 == "dumbbell curve"
			traparray = 44
		elseif @xyshape1 == "cubic duplicatrix"
			traparray = 45
		elseif @xyshape1 == "Durer's conchoid"
			traparray = 46
		elseif @xyshape1 == "Sillke's egg of Columbus"
			traparray = 47
		elseif @xyshape1 == "Granville's egg"
			traparray = 48
		elseif @xyshape1 == "Kepler's egg"
			traparray = 49
		elseif @xyshape1 == "eight curve"
			traparray = 50
		elseif @xyshape1 == "ellipse"
			traparray = 51
		elseif @xyshape1 == "superellipse"
			traparray = 52
		elseif @xyshape1 == "fish quartic"
			traparray = 53
		elseif @xyshape1 == "conic focal conchoid"
			traparray = 54
		elseif @xyshape1 == "folium 1"
			traparray = 55
		elseif @xyshape1 == "folium 2"
			traparray = 56
		elseif @xyshape1 == "folium of Descartes"
			traparray = 57
		elseif @xyshape1 == "Durer's folium"
			traparray = 58
		elseif @xyshape1 == "Gaussian curve"
			traparray = 59
		elseif @xyshape1 == "Beutel heart"
			traparray = 60
		elseif @xyshape1 == "Proclus hippopede"
			traparray = 61
		elseif @xyshape1 == "Hoerl curve"
			traparray = 62
		elseif @xyshape1 == "Humbert cubic"
			traparray = 63
		elseif @xyshape1 == "hyperbola"
			traparray = 64
		elseif @xyshape1 == "hyperbola 2"
			traparray = 65
		elseif @xyshape1 == "illumination curve"
			traparray = 66
		elseif @xyshape1 == "kampyle of Eudoxus"
			traparray = 67
		elseif @xyshape1 == "kappa curve"
			traparray = 68
		elseif @xyshape1 == "Kiepert's curve"
			traparray = 69
		elseif @xyshape1 == "kieroid"
			traparray = 70
		elseif @xyshape1 == "kiss curve"
			traparray = 71
		elseif @xyshape1 == "Klein quartic"
			traparray = 72
		elseif @xyshape1 == "Kulp quartic"
			traparray = 73
		elseif @xyshape1 == "limacon of Pascal"
			traparray = 74
		elseif @xyshape1 == "links curve"
			traparray = 75
		elseif @xyshape1 == "Lissajous sextic"
			traparray = 76
		elseif @xyshape1 == "Lissajous quartic"
			traparray = 77
		elseif @xyshape1 == "logistic curve"
			traparray = 78
		elseif @xyshape1 == "Maltese cross"
			traparray = 79
		elseif @xyshape1 == "semicubical parabola"
			traparray = 80
		elseif @xyshape1 == "diverging parabola"
			traparray = 81
		elseif @xyshape1 == "nephroid"
			traparray = 82
		elseif @xyshape1 == "Freeth's nephroid"
			traparray = 83
		elseif @xyshape1 == "nodal curve"
			traparray = 84
		elseif @xyshape1 == "strophoid"
			traparray = 85
		elseif @xyshape1 == "ophiuride"
			traparray = 86
		elseif @xyshape1 == "parabola"
			traparray = 87
		elseif @xyshape1 == "parabola 2"
			traparray = 88
		elseif @xyshape1 == "parabolic trifolium"
			traparray = 89
		elseif @xyshape1 == "piriform"
			traparray = 90
		elseif @xyshape1 == "pearls of de Sluze"
			traparray = 91
		elseif @xyshape1 == "pursuit curve"
			traparray = 92
		elseif @xyshape1 == "quadratrix"
			traparray = 93
		elseif @xyshape1 == "quadrafolium"
			traparray = 94
		elseif @xyshape1 == "trifolium"
			traparray = 95
		elseif @xyshape1 == "right strophoid"
			traparray = 96
		elseif @xyshape1 == "scarabaeus"
			traparray = 97
		elseif @xyshape1 == "scyphoid"
			traparray = 98
		elseif @xyshape1 == "anguinea"
			traparray = 99
		elseif @xyshape1 == "damped sine"
			traparray = 100
		elseif @xyshape1 == "catastrophic sine"
			traparray = 101
		elseif @xyshape1 == "plane spiric"
			traparray = 102
		elseif @xyshape1 == "spiric of Perseus"
			traparray = 103
		elseif @xyshape1 == "svastika"
			traparray = 104
		elseif @xyshape1 == "syntractrix"
			traparray = 105
		elseif @xyshape1 == "tetracuspid"
			traparray = 106
		elseif @xyshape1 == "siluroid"
			traparray = 107
		elseif @xyshape1 == "trisectrix of Longchamps"
			traparray = 108
		elseif @xyshape1 == "trident"
			traparray = 109
		elseif @xyshape1 == "trisectrix of Delanges"
			traparray = 110
		elseif @xyshape1 == "trisectrix of Maclaurin"
			traparray = 111
		elseif @xyshape1 == "Trott curve"
			traparray = 112
		elseif @xyshape1 == "Tschirnhausen's cubic"
			traparray = 113
		elseif @xyshape1 == "visiera"
			traparray = 114
		elseif @xyshape1 == "resonance curve"
			traparray = 115
		elseif @xyshape1 == "Watt's curve"
			traparray = 116
		elseif @xyshape1 == "witch of Agnesi"
			traparray = 117
		endif ; @xyshape1
endif ; @traptype

if @traptype == 0 ; "lines & points"
	if traparray == 0 ; "line"
		cursality = 1
		numbervertices = 2 ; not a closed curve
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.5,-0.5)
		vertex[1] = @nscale1 * (0.5,0.5)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 1 ; "triangle"
		cursality = 1
		numbervertices = 4 ; n + cursality for a closed curve
		cincrement = 4 ; numbervertices/cursality
		scratchfloat = sqrt(3)/2 ; for some vertext coordinates
		; initialize arrays
		vertex[0] = @nscale1 * (0,1)
		vertex[1] = @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[2] = @nscale1 * (scratchfloat + flip(-0.5))
		vertex[3] = @nscale1 * (0,1)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 2 ; "isosceles"
		cursality = 1
		numbervertices = 4 ; n + cursality for a closed curve
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @isocwidth * @nscale1 * (0.35,-1)
		vertex[1] = @isocheight * @nscale1 * (1,0)
		vertex[2] = @isocwidth * @nscale1 * (-0.35,-1)
		vertex[3] = @isocwidth * @nscale1 * (0.35,-1)
		if @fixisosceles
			vertex[1] = flip(vertex[1])
		endif ; @fixisosceles
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 3 ; "3-asterisk"
		cursality = 3
		numbervertices = 6 ; n + cursality for a closed curve
		cincrement = 2 ; numbervertices/cursality
		scratchfloat = sqrt(3)/2 ; for some vertext coordinates
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @leafAlength * @nscale1 * (0,1)
		vertex[2] = @nscale1 * (0,0)
		vertex[3] = @leafBlength * @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[4] = @nscale1 * (0,0)
		vertex[5] = @leafClength * @nscale1 * (scratchfloat + flip(-0.5))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 4 ; "3-star"
		cursality = 1
		numbervertices = 7 ; n + cursality for a closed curve
		cincrement = 7 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.33333333,0)
		vertex[1] = @starspikiness * @nscale1 * (0.75,1.29904)
		vertex[2] = @nscale1 * (-0.16666667,0.288675)
		vertex[3] = @starspikiness * @nscale1 * (-1.5,0)
		vertex[4] = @nscale1 * (-0.16666667,-0.288675)
		vertex[5] = @starspikiness * @nscale1 * (0.75,-1.29904)
		vertex[6] = @nscale1 * (0.33333333,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 66 ; "3-star 2"
		cursality = 1
		numbervertices = 7 ; n + cursality for a closed curve
		cincrement = 7 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.289778, 0.0776457)
		vertex[2] = @nscale1 * (-0.5,0.866025)
		vertex[3] = @nscale1 * (-0.212132, 0.212132)
		vertex[4] = @nscale1 * (-0.5, -0.866025)
		vertex[5] = @nscale1 * (-0.0776457, -0.289778)
		vertex[6] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 5 ; "polytriangle"
		cursality = 2
		numbervertices = 8 ; n + cursality for a closed curve
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5, 0)
		vertex[1] = @nscale1 * (-0.25, 0.433013)
		vertex[2] = @nscale1 * (-0.25, -0.433013)
		vertex[3] = @nscale1 * (0.5,0)
		vertex[4] = @nscale1 * (0.5, 0.866025)
		vertex[5] = @nscale1 * (-1,0)
		vertex[6] = @nscale1 * (0.5, -0.866025)
		vertex[7] = @nscale1 * (0.5, 0.866025)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 6 ; "trigram"
		cursality = 1
		numbervertices = 7 ; n + cursality for a closed curve
		cincrement = 7 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.7, 0)
		vertex[1] = @nscale1 * (-0.34368,-1.55104)
		vertex[2] = @nscale1 * (-0.35,0.69282)
		vertex[3] = @nscale1 * (1.34718,0.435366)
		vertex[4] = @nscale1 * (-0.35,-0.69282)
		vertex[5] = @nscale1 * (-1.0035,1.11567)
		vertex[6] = @nscale1 * (0.7,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 7 ; "nested triangles"
		cursality = 2
		numbervertices = 8 ; n + cursality for closed curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.625, 1.08253)
		vertex[1] = @nscale1 * (-1.25, 0)
		vertex[2] = @nscale1 * (0.625, -1.08253)
		vertex[3] = @nscale1 * (0.625,1.08253)
		vertex[4] = @innerscale * @nscale1 * (0.1875,0.324755)
		vertex[5] = @innerscale * @nscale1 * (-0.375,0)
		vertex[6] = @innerscale * @nscale1 * (0.1875,-0.324755)
		vertex[7] = @innerscale * @nscale1 * (0.1875,0.324755)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 8 ; "nested triangle 2"
		cursality = 2
		numbervertices = 8 ; n + cursality for closed curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.625, 1.08253)
		vertex[1] = @nscale1 * (-1.25, 0)
		vertex[2] = @nscale1 * (0.625, -1.08253)
		vertex[3] = @nscale1 * (0.625,1.08253)
		vertex[4] = @innerscale * @nscale1 * (-0.118125,-0.24356625)
		vertex[5] = @innerscale * @nscale1 * (0.28125,0)
		vertex[6] = @innerscale * @nscale1 * (-0.118125,0.24356625)
		vertex[7] = @innerscale * @nscale1 * (-0.118125,-0.24356625)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 9 ; "twisted triangles"
		cursality = 4
		numbervertices = 16 ; n + cursality for closed curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.5,0.866025)
		vertex[2] = @nscale1 * (-0.5,-0.866025)
		vertex[3] = @nscale1 * (1,0)
		vertex[4] = @nscale1 * (-0.113341,0.642788)
		vertex[5] = @nscale1 * (-0.5,-0.41955)
		vertex[6] = @nscale1 * (0.613341,-0.223238)
		vertex[7] = @nscale1 * (-0.113341,0.642788)
		vertex[8] = @nscale1 * (-0.40033,-0.145708)
		vertex[9] = @nscale1 * (0.326352,-0.273842)
		vertex[10] = @nscale1 * (0.073978,0.41955)
		vertex[11] = @nscale1 * (-0.40033,-0.145708)
		vertex[12] = @nscale1 * (0.139033,-0.240812)
		vertex[13] = @nscale1 * (0.139033,0.240812)
		vertex[14] = @nscale1 * (-0.278066,0)
		vertex[15] = @nscale1 * (0.139033,-0.240812)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 10 ; "twisted triangle 2"
		cursality = 3
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.5,0.866025)
		vertex[2] = @nscale1 * (-0.5,-0.866025)
		vertex[3] = @nscale1 * (1,0)
		vertex[4] = @nscale1 * (-0.0646021,0.614648)
		vertex[5] = @nscale1 * (-0.5,-0.363271)
		vertex[6] = @nscale1 * (0.564602,-0.251377)
		vertex[7] = @nscale1 * (-0.0646021,0.614648)
		vertex[8] = @nscale1 * (-0.373619,-0.0794152)
		vertex[9] = @nscale1 * (0.255585,-0.283856)
		vertex[10] = @nscale1 * (0.118034,0.363271)
		vertex[11] = @nscale1 * (-0.373619,-0.0794152)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 11 ; "square"
		cursality = 1
		numbervertices = 5 ; n + cursality
		cincrement = 5 ; numbervertices/cursality
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0,1)
		vertex[2] = @nscale1 * (-1,0)
		vertex[3] = @nscale1 * (0,-1)
		vertex[4] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 12 ; "square 2"
		cursality = 6
		numbervertices = 12
		cincrement = 2 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.5,0.5)
		vertex[1] = @nscale1 * (-0.5,0.5)
		vertex[2] = @nscale1 * (-0.5,0.5)
		vertex[3] = @nscale1 * (-0.5,-0.5)
		vertex[4] = @nscale1 * (-0.5,-0.5)
		vertex[5] = @nscale1 * (0.5,-0.5)
		vertex[6] = @nscale1 * (0.5,-0.5)
		vertex[7] = @nscale1 * (0.5,0.5)
		vertex[8] = @nscale1 * (0.5,0.5)
		vertex[9] = @nscale1 * (-0.5,-0.5)
		vertex[10] = @nscale1 * (-0.5,0.5)
		vertex[11] = @nscale1 * (0.5,-0.5)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 13 ; "rhombus"
		cursality = 1
		numbervertices = 5 ; n + cursality
		cincrement = 5 ; numbervertices/cursality
		vertex[0] = @rhombheight * @nscale1 * (-1.5,0)
		vertex[1] = @rhombwidth * @nscale1 * (0,0.5)
		vertex[2] = @rhombheight * @nscale1 * (1.5,0)
		vertex[3] = @rhombwidth * @nscale1 * (0,-0.5)
		vertex[4] = @rhombheight * @nscale1 * (-1.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 14 ; "kite"
		cursality = 1
		numbervertices = 5 ; n + cursality
		cincrement = 5 ; numbervertices/cursality
		vertex[0] = @kiteheight * @nscale1 * (0,1.25)
		vertex[1] = @kitewidth * @nscale1 * (-0.5,0.75)
		vertex[2] = @kiteheight * @nscale1 * (0,-1.25)
		vertex[3] = @kitewidth * @nscale1 * (0.5,0.75)
		vertex[4] = @kiteheight * @nscale1 * (0,1.25)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 15 ; "dart"
		cursality = 1
		numbervertices = 5 ; n + cursality
		cincrement = 5 ; numbervertices/cursality
		vertex[0] = @dartheight * @nscale1 * (0,0.5)
		vertex[1] = @dartwidth * @nscale1 * (-0.5,1)
		vertex[2] = @dartheight * @nscale1 * (0,-1)
		vertex[3] = @dartwidth * @nscale1 * (0.5,1)
		vertex[4] = @dartheight * @nscale1 * (0,0.5)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 214 ; "rectangle"
		cursality = 1
		numbervertices = 5 ; n + cursality
		cincrement = 5 ; numbervertices/cursality
		scratchfloat = @rectlength * 0.5 ; x-coordinate of rectangle vertex
		scratchfloat2 = @rectwidth * 0.5 ; y-coordinate
		vertex[0] = @nscale1 * (scratchfloat + flip(scratchfloat2))
		vertex[1] = @nscale1 * (-scratchfloat + flip(scratchfloat2))
		vertex[2] = @nscale1 * (-scratchfloat + flip(-scratchfloat2))
		vertex[3] = @nscale1 * (scratchfloat + flip(-scratchfloat2))
		vertex[4] = @nscale1 * (scratchfloat + flip(scratchfloat2))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 16 ; "4-asterisk"
		cursality = 4
		numbervertices = 8 ; n + cursality
		cincrement = 2 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @leafAlength * @nscale1 * (1,0)
		vertex[2] = @nscale1 * (0,0)
		vertex[3] = @leafBlength * @nscale1 * (0,1)
		vertex[4] = @nscale1 * (0,0)
		vertex[5] = @leafClength * @nscale1 * (-1,0)
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @leafDlength * @nscale1 * (0,-1)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 17 ; "4-star"
		cursality = 1
		numbervertices = 9 ; n + cursality
		cincrement = 9 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @starspikiness * @nscale1 * (1.06066, 1.06066)
		vertex[2] = @nscale1 * (0, 0.5)
		vertex[3] = @starspikiness * @nscale1 * (-1.06066, 1.06066)
		vertex[4] = @nscale1 * (-0.5, 0)
		vertex[5] = @starspikiness * @nscale1 * (-1.06066, -1.06066)
		vertex[6] = @nscale1 * (0, -0.5)
		vertex[7] = @starspikiness * @nscale1 * (1.06066, -1.06066)
		vertex[8] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 18 ; "flat 4-star"
		cursality = 1
		numbervertices = 9 ; n + cursality
		cincrement = 9 ; numbervertices/cursality
		vertex[0] = @flat4height * @nscale1 * (0.5,0)
		vertex[1] = @flat4width * @nscale1 * (1.06066, 0.53033)
		vertex[2] = @flat4height * @nscale1 * (0, 0.25)
		vertex[3] = @flat4width * @nscale1 * (-1.06066, 0.53033)
		vertex[4] = @flat4height * @nscale1 * (-0.5, 0)
		vertex[5] = @flat4width * @nscale1 * (-1.06066, -0.53033)
		vertex[6] = @flat4height * @nscale1 * (0, -0.25)
		vertex[7] = @flat4width * @nscale1 * (1.06066, -0.53033)
		vertex[8] = @flat4height * @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 69 ; "4-star 2"
		cursality = 1
		numbervertices = 9 ; n + cursality
		cincrement = 9 ; numbervertices/cursality
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.289778, 0.0776457)
		vertex[2] = @nscale1 * (0, 1)
		vertex[3] = @nscale1 * (-0.0776457, 0.289778)
		vertex[4] = @nscale1 * (-1, 0)
		vertex[5] = @nscale1 * (-0.289778, -0.0776457)
		vertex[6] = @nscale1 * (0, -1)
		vertex[7] = @nscale1 * (0.0776457, -0.289778)
		vertex[8] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 19 ; "bowtie"
		cursality = 1
		numbervertices = 5 ; n + cursality
		cincrement = 5 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.5,0.5)
		vertex[1] = @nscale1 * (-0.5,-0.5)
		vertex[2] = @nscale1 * (-0.5,0.5)
		vertex[3] = @nscale1 * (0.5,-0.5)
		vertex[4] = @nscale1 * (0.5,0.5)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 20 ; "windowpane"
		cursality = 6
		numbervertices = 12 ; open figures (line segments)
		cincrement = 2 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.5,0.5)
		vertex[1] = @nscale1 * (-0.5,0.5)
		vertex[2] = @nscale1 * (0.5,0)
		vertex[3] = @nscale1 * (-0.5,0)
		vertex[4] = @nscale1 * (0.5,-0.5)
		vertex[5] = @nscale1 * (-0.5,-0.5)
		vertex[6] = @nscale1 * (0.5,0.5)
		vertex[7] = @nscale1 * (0.5,-0.5)
		vertex[8] = @nscale1 * (0,0.5)
		vertex[9] = @nscale1 * (0,-0.5)
		vertex[10] = @nscale1 * (-0.5,0.5)
		vertex[11] = @nscale1 * (-0.5,-0.5)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 21 ; "tetragram"
		cursality = 1
		numbervertices = 9 ; n + cursality for a closed curve
		cincrement = 9 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.7, 0)
		vertex[1] = @nscale1 * (0.573427,-1.27718)
		vertex[2] = @nscale1 * (0,0.7)
		vertex[3] = @nscale1 * (-1.27718,-0.573427)
		vertex[4] = @nscale1 * (0.7,0)
		vertex[5] = @nscale1 * (-0.573427,1.27718)
		vertex[6] = @nscale1 * (0,-0.7)
		vertex[7] = @nscale1 * (1.27718,0.573427)
		vertex[8] = @nscale1 * (-0.7, 0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 67 ; "tetragram 2"
		cursality = 2
		numbervertices = 10 ; n + cursality for a closed curve
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.207912, -0.978148)
		vertex[2] = @nscale1 * (-0.978148, -0.207912)
		vertex[3] = @nscale1 * (0.207912, 0.978148)
		vertex[4] = @nscale1 * (0.978148, 0.207912)
		vertex[5] = @nscale1 * (-0.207912, 0.978148)
		vertex[6] = @nscale1 * (0.978148, -0.207912)
		vertex[7] = @nscale1 * (0.207912, -0.978148)
		vertex[8] = @nscale1 * (-0.978148, 0.207912)
		vertex[9] = @nscale1 * (-0.207912, 0.978148)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 22 ; "nested squares"
		cursality = 2
		numbervertices = 10 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1.2, 0)
		vertex[1] = @nscale1 * (0,1.2)
		vertex[2] = @nscale1 * (-1.2,0)
		vertex[3] = @nscale1 * (0,-1.2)
		vertex[4] = @nscale1 * (1.2,0)
		vertex[5] = @innerscale * @nscale1 * (0.75,0)
		vertex[6] = @innerscale * @nscale1 * (0,0.75)
		vertex[7] = @innerscale * @nscale1 * (-0.75,0)
		vertex[8] = @innerscale * @nscale1 * (0,-0.75)
		vertex[9] = @innerscale * @nscale1 * (0.75,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 23 ; "nested square 2"
		cursality = 2
		numbervertices = 10 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1.2, 0)
		vertex[1] = @nscale1 * (0,1.2)
		vertex[2] = @nscale1 * (-1.2,0)
		vertex[3] = @nscale1 * (0,-1.2)
		vertex[4] = @nscale1 * (1.2,0)
		vertex[5] = @innerscale * @nscale1 * (0.35,0.35)
		vertex[6] = @innerscale * @nscale1 * (-0.35,0.35)
		vertex[7] = @innerscale * @nscale1 * (-0.35,-0.35)
		vertex[8] = @innerscale * @nscale1 * (0.35,-0.35)
		vertex[9] = @innerscale * @nscale1 * (0.35,0.35)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 24 ; "twisted squares"
		cursality = 3
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1, 0)
		vertex[1] = @nscale1 * (0,1)
		vertex[2] = @nscale1 * (-1,0)
		vertex[3] = @nscale1 * (0,-1)
		vertex[4] = @nscale1 * (1,0)
		vertex[5] = @nscale1 * (0.266846,0.733154)
		vertex[6] = @nscale1 * (-0.733154,0.266846)
		vertex[7] = @nscale1 * (-0.266846,-0.733154)
		vertex[8] = @nscale1 * (0.733154,-0.266846)
		vertex[9] = @nscale1 * (0.266846,0.733154)
		vertex[10] = @nscale1 * (-0.466308,0.391279)
		vertex[11] = @nscale1 * (-0.391279,-0.466308)
		vertex[12] = @nscale1 * (0.466308,-0.391279)
		vertex[13] = @nscale1 * (0.391279,0.466308)
		vertex[14] = @nscale1 * (-0.466308,0.391279)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 25 ; "twisted square 2"
		cursality = 4
		numbervertices = 20 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1, 0)
		vertex[1] = @nscale1 * (0,1)
		vertex[2] = @nscale1 * (-1,0)
		vertex[3] = @nscale1 * (0,-1)
		vertex[4] = @nscale1 * (1,0)
		vertex[5] = @nscale1 * (0.366025,0.633975)
		vertex[6] = @nscale1 * (-0.633975,0.366025)
		vertex[7] = @nscale1 * (-0.366025,-0.633975)
		vertex[8] = @nscale1 * (0.633975,-0.366025)
		vertex[9] = @nscale1 * (0.366025,0.633975)
		vertex[10] = @nscale1 * (-0.267949,0.464102)
		vertex[11] = @nscale1 * (-0.464102,-0.267949)
		vertex[12] = @nscale1 * (0.267949,-0.464102)
		vertex[13] = @nscale1 * (0.464102,0.267949)
		vertex[14] = @nscale1 * (-0.267949,0.464102)
		vertex[15] = @nscale1 * (-0.392305, 0)
		vertex[16] = @nscale1 * (0,-0.392305)
		vertex[17] = @nscale1 * (0.392305,0)
		vertex[18] = @nscale1 * (0,0.392305)
		vertex[19] = @nscale1 * (-0.392305,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 26 ; "windmill"
		cursality = 2
		numbervertices = 10 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.965926, 0.258819)
		vertex[1] = @nscale1 * (-0.965926, 0.258819)
		vertex[2] = @nscale1 * (-0.965926, -0.258819)
		vertex[3] = @nscale1 * (0.965926, -0.258819)
		vertex[4] = @nscale1 * (0.965926, 0.258819)
		vertex[5] = @nscale1 * ((@windwidth * -0.258819) + flip(@windheight * 0.965926))
		vertex[6] = @nscale1 * ((@windwidth * -0.258819) + flip(@windheight * -0.965926))
		vertex[7] = @nscale1 * ((@windwidth * 0.258819) + flip(@windheight * -0.965926))
		vertex[8] = @nscale1 * ((@windwidth * 0.258819) + flip(@windheight * 0.965926))
		vertex[9] = @nscale1 * ((@windwidth * -0.258819) + flip(@windheight * 0.965926))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 27 ; "windmill 2"
		cursality = 2
		numbervertices = 10 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.965926, 0.258819)
		vertex[1] = @nscale1 * (-0.965926, -0.258819)
		vertex[2] = @nscale1 * (-0.965926, 0.258819)
		vertex[3] = @nscale1 * (0.965926, -0.258819)
		vertex[4] = @nscale1 * (0.965926, 0.258819)
		vertex[5] = @nscale1 * ((@windwidth * -0.258819) + flip(@windheight * 0.965926))
		vertex[6] = @nscale1 * ((@windwidth * 0.258819) + flip(@windheight * -0.965926))
		vertex[7] = @nscale1 * ((@windwidth * -0.258819) + flip(@windheight * -0.965926))
		vertex[8] = @nscale1 * ((@windwidth * 0.258819) + flip(@windheight * 0.965926))
		vertex[9] = @nscale1 * ((@windwidth * -0.258819) + flip(@windheight * 0.965926))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 28 ; "pentagon"
		cursality = 1
		numbervertices = 6 ; n + cursality
		cincrement = 6 ; numbervertices/cursality
		scratchfloat = 0.951056516295153572
		scratchfloat2 = -0.809016994374947424
		scratchfloat3 = 0.587785252292473129
		scratchfloat4 = 0.309016994374947424
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (scratchfloat4 + flip(scratchfloat))
		vertex[2] = @nscale1 * (scratchfloat2 + flip(scratchfloat3))
		vertex[3] = @nscale1 * (scratchfloat2 + flip(-scratchfloat3))
		vertex[4] = @nscale1 * (scratchfloat4 + flip(-scratchfloat))
		vertex[5] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 29 ; "pentagon 2"
		cursality = 5
		numbervertices = 15 ; open pieces
		cincrement = 3 ; numbervertices/cursality
		scratchfloat = 0.951056516295153572
		scratchfloat2 = -0.809016994374947424
		scratchfloat3 = 0.587785252292473129
		scratchfloat4 = 0.309016994374947424
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @nscale1 * (1,0)
		vertex[2] = @nscale1 * (scratchfloat4 + flip(scratchfloat))
		vertex[3] = @nscale1 * (0,0)
		vertex[4] = @nscale1 * (scratchfloat4 + flip(scratchfloat))
		vertex[5] = @nscale1 * (scratchfloat2 + flip(scratchfloat3))
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @nscale1 * (scratchfloat2 + flip(scratchfloat3))
		vertex[8] = @nscale1 * (scratchfloat2 + flip(-scratchfloat3))
		vertex[9] = @nscale1 * (0,0)
		vertex[10] = @nscale1 * (scratchfloat2 + flip(-scratchfloat3))
		vertex[11] = @nscale1 * (scratchfloat4 + flip(-scratchfloat))
		vertex[12] = @nscale1 * (0,0)
		vertex[13] = @nscale1 * (scratchfloat4 + flip(-scratchfloat))
		vertex[14] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 30 ; "pentagram"
		cursality = 1
		numbervertices = 6
		cincrement = 6 ; numbervertices/cursality
		scratchfloat = 0.951056516295153572
		scratchfloat2 = -0.809016994374947424
		scratchfloat3 = 0.587785252292473129
		scratchfloat4 = 0.309016994374947424
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (scratchfloat2 + flip(scratchfloat3))
		vertex[2] = @nscale1 * (scratchfloat4 + flip(-scratchfloat))
		vertex[3] = @nscale1 * (scratchfloat4 + flip(scratchfloat))
		vertex[4] = @nscale1 * (scratchfloat2 + flip(-scratchfloat3))
		vertex[5] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 31 ; "pentagram 2"
		cursality = 1
		numbervertices = 11 ; 10 + cursality for closed figure
		cincrement = 11 ; numbervertices/cursality
		vertex[0] = @nscale1 * (-0.48541,0.352671)
		vertex[1] = @nscale1 * (-0.488084,-1.09625)
		vertex[2] = @nscale1 * (0.18541,0.570634)
		vertex[3] = @nscale1 * (-1.19343,0.125434)
		vertex[4] = @nscale1 * (0.6,0)
		vertex[5] = @nscale1 * (-0.249494,1.17378)
		vertex[6] = @nscale1 * (0.18541,-0.570634)
		vertex[7] = @nscale1 * (1.03923,0.6)
		vertex[8] = @nscale1 * (-0.48541,-0.352671)
		vertex[9] = @nscale1 * (0.891774,-0.802957)
		vertex[10] = @nscale1 * (-0.48541,0.352671)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 32 ; "pentagram 3"
		cursality = 1
		numbervertices = 11 ; 10 + cursality for closed figure
		cincrement = 11 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.965926, 0.258819)
		vertex[1] = @nscale1 * (-0.62932, 0.777146)
		vertex[2] = @nscale1 * (-0.93358, 0.358368)
		vertex[3] = @nscale1 * (0.052336, -0.99863)
		vertex[4] = @nscale1 * (0.544639, -0.838671)
		vertex[5] = @nscale1 * (0.544639, 0.838671)
		vertex[6] = @nscale1 * (0.052336, 0.99863)
		vertex[7] = @nscale1 * (-0.93358, -0.358368)
		vertex[8] = @nscale1 * (-0.62932, -0.777146)
		vertex[9] = @nscale1 * (0.965926, -0.258819)
		vertex[10] = @nscale1 * (0.965926, 0.258819)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 33 ; "pentagram 4"
		cursality = 1
		numbervertices = 11 ; 10 + cursality for closed figure
		cincrement = 11 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.965926, 0.258819)
		vertex[1] = @nscale1 * (-0.93358, -0.358368)
		vertex[2] = @nscale1 * (-0.93358, 0.358368)
		vertex[3] = @nscale1 * (0.965926, -0.258819)
		vertex[4] = @nscale1 * (0.544639, -0.838671)
		vertex[5] = @nscale1 * (-0.62932, 0.777146)
		vertex[6] = @nscale1 * (0.052336, 0.99863)
		vertex[7] = @nscale1 * (0.052336, -0.99863)
		vertex[8] = @nscale1 * (-0.62932, -0.777146)
		vertex[9] = @nscale1 * (0.544639, 0.838671)
		vertex[10] = @nscale1 * (0.965926, 0.258819)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 68 ; "pentagram 5"
		cursality = 1
		numbervertices = 11 ; 10 + cursality for closed figure
		cincrement = 11 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.913545, -0.406737)
		vertex[2] = @nscale1 * (-0.913545, 0.406737)
		vertex[3] = @nscale1 * (0.978148, -0.207912)
		vertex[4] = @nscale1 * (0.5, -0.866025)
		vertex[5] = @nscale1 * (-0.669131, 0.743145)
		vertex[6] = @nscale1 * (0.104528, 0.994522)
		vertex[7] = @nscale1 * (0.104528, -0.994522)
		vertex[8] = @nscale1 * (-0.669131, -0.743145)
		vertex[9] = @nscale1 * (0.5, 0.866025)
		vertex[10] = @nscale1 * (0.978148, 0.207912)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 34 ; "5-asterisk"
		cursality = 5
		numbervertices = 10 ; n + cursality
		cincrement = 2 ; numbervertices/cursality
		scratchfloat = 0.951056 ;516295153572
		scratchfloat2 = -0.809016 ;994374947424
		scratchfloat3 = 0.587785 ;252292473129
		scratchfloat4 = 0.309016 ;994374947424
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @leafAlength * @nscale1 * (1,0)
		vertex[2] = @nscale1 * (0,0)
		vertex[3] = @leafBlength * @nscale1 * (scratchfloat4 + flip(scratchfloat))
		vertex[4] = @nscale1 * (0,0)
		vertex[5] = @leafClength * @nscale1 * (scratchfloat2 + flip(scratchfloat3))
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @leafDlength * @nscale1 * (scratchfloat2 + flip(-scratchfloat3))
		vertex[8] = @nscale1 * (0,0)
		vertex[9] = @leafElength * @nscale1 * (scratchfloat4 + flip(-scratchfloat))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 35 ; "5-star"
		cursality = 1
		numbervertices = 11 ; n + cursality
		cincrement = 11 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.625,0)
		vertex[1] = @starspikiness * @nscale1 * (1.01127,0.734732)
		vertex[2] = @nscale1 * (0.193136,0.59441)
		vertex[3] = @starspikiness * @nscale1 * (-0.386271,1.18882)
		vertex[4] = @nscale1 * (-0.505636,0.367366)
		vertex[5] = @starspikiness * @nscale1 * (-1.25,0)
		vertex[6] = @nscale1 * (-0.505636,-0.367366)
		vertex[7] = @starspikiness * @nscale1 * (-0.386271,-1.18882)
		vertex[8] = @nscale1 * (0.193136,-0.59441)
		vertex[9] = @starspikiness * @nscale1 * (1.01127,-0.734732)
		vertex[10] = @nscale1 * (0.625,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 65 ; "5-star 2"
		cursality = 1
		numbervertices = 11 ; n + cursality
		cincrement = 11 ; numbervertices/cursality
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.5, 0)
		vertex[2] = @nscale1 * (0.309017, 0.951057)
		vertex[3] = @nscale1 * (0.154508, 0.475528)
		vertex[4] = @nscale1 * (-0.809017, 0.587785)
		vertex[5] = @nscale1 * (-0.404508, 0.293893)
		vertex[6] = @nscale1 * (-0.809017, -0.587785)
		vertex[7] = @nscale1 * (-0.404508, -0.293893)
		vertex[8] = @nscale1 * (0.309017, -0.951057)
		vertex[9] = @nscale1 * (0.154508, -0.475528)
		vertex[10] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 70 ; "5-star 3"
		cursality = 1
		numbervertices = 11 ; n + cursality
		cincrement = 11 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.866025, 0.5)
		vertex[1] = @nscale1 * (0.433013, -0.25)
		vertex[2] = @nscale1 * (-0.207912, 0.978148)
		vertex[3] = @nscale1 * (0.371572, 0.334565)
		vertex[4] = @nscale1 * (-0.994522, 0.104528)
		vertex[5] = @nscale1 * (-0.203368, 0.456773)
		vertex[6] = @nscale1 * (-0.406737, -0.913545)
		vertex[7] = @nscale1 * (-0.497261, -0.0522642)
		vertex[8] = @nscale1 * (0.743145, -0.669131)
		vertex[9] = @nscale1 * (-0.103956, -0.489074)
		vertex[10] = @nscale1 * (0.866025, 0.5)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 36 ; "nested pentagons"
		cursality = 2
		numbervertices = 12 ; 10 + cursality
		cincrement = 6 ; numbervertices/cursality
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.309017,0.951057)
		vertex[2] = @nscale1 * (-0.809017,0.587785)
		vertex[3] = @nscale1 * (-0.809017,-0.587785)
		vertex[4] = @nscale1 * (0.309017,-0.951057)
		vertex[5] = @nscale1 * (1,0)
		vertex[6] = @innerscale * @nscale1 * (0.4,0)
		vertex[7] = @innerscale * @nscale1 * (0.123607,0.380423)
		vertex[8] = @innerscale * @nscale1 * (-0.323607,0.235114)
		vertex[9] = @innerscale * @nscale1 * (-0.323607,-0.235114)
		vertex[10] = @innerscale * @nscale1 * (0.123607,-0.380423)
		vertex[11] = @innerscale * @nscale1 * (0.4,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 37 ; "nested pentagon 2"
		cursality = 2
		numbervertices = 12 ; 10 + cursality
		cincrement = 6 ; numbervertices/cursality
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.309017,0.951057)
		vertex[2] = @nscale1 * (-0.809017,0.587785)
		vertex[3] = @nscale1 * (-0.809017,-0.587785)
		vertex[4] = @nscale1 * (0.309017,-0.951057)
		vertex[5] = @nscale1 * (1,0)
		vertex[6] = @innerscale * @nscale1 * (0.323607,0.235114)
		vertex[7] = @innerscale * @nscale1 * (-0.123607,0.380423)
		vertex[8] = @innerscale * @nscale1 * (-0.4,0)
		vertex[9] = @innerscale * @nscale1 * (-0.123607,-0.380423)
		vertex[10] = @innerscale * @nscale1 * (0.323607,-0.235114)
		vertex[11] = @innerscale * @nscale1 * (0.323607,0.235114)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 38 ; "twisted pentagons"
		cursality = 3
		numbervertices = 18 ; n + cursality for closed curves
		cincrement = 6 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1, 0)
		vertex[1] = @nscale1 * (0.309017,0.951057)
		vertex[2] = @nscale1 * (-0.809017,0.587785)
		vertex[3] = @nscale1 * (-0.809017,-0.587785)
		vertex[4] = @nscale1 * (0.309017,-0.951057)
		vertex[5] = @nscale1 * (1,0)
		vertex[6] = @nscale1 * (0.553432,0.614648)
		vertex[7] = @nscale1 * (-0.413545,0.716282)
		vertex[8] = @nscale1 * (-0.809017,-0.171962)
		vertex[9] = @nscale1 * (-0.0864545,-0.82256)
		vertex[10] = @nscale1 * (0.755585,-0.336408)
		vertex[11] = @nscale1 * (0.553432,0.614648)
		vertex[12] = @nscale1 * (-0.0715058,0.680332)
		vertex[13] = @nscale1 * (-0.669131,0.142228)
		vertex[14] = @nscale1 * (-0.34204,-0.59243)
		vertex[15] = @nscale1 * (0.457738,-0.50837)
		vertex[16] = @nscale1 * (0.624938,0.27824)
		vertex[17] = @nscale1 * (-0.0715058,0.680332)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 39 ; "twisted pentagon 2"
		cursality = 4
		numbervertices = 24 ; n + cursality for closed curves
		cincrement = 6 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1, 0)
		vertex[1] = @nscale1 * (0.309017,0.951057)
		vertex[2] = @nscale1 * (-0.809017,0.587785)
		vertex[3] = @nscale1 * (-0.809017,-0.587785)
		vertex[4] = @nscale1 * (0.309017,-0.951057)
		vertex[5] = @nscale1 * (1,0)
		vertex[6] = @nscale1 * (0.553432,0.614648)
		vertex[7] = @nscale1 * (-0.413545,0.716282)
		vertex[8] = @nscale1 * (-0.809017,-0.171962)
		vertex[9] = @nscale1 * (-0.0864545,-0.82256)
		vertex[10] = @nscale1 * (0.755585,-0.336408)
		vertex[11] = @nscale1 * (0.553432,0.614648)
		vertex[12] = @nscale1 * (-0.0715058,0.680332)
		vertex[13] = @nscale1 * (-0.669131,0.142228)
		vertex[14] = @nscale1 * (-0.34204,-0.59243)
		vertex[15] = @nscale1 * (0.457738,-0.50837)
		vertex[16] = @nscale1 * (0.624938,0.27824)
		vertex[17] = @nscale1 * (-0.0715058,0.680332)
		vertex[18] = @nscale1 * (-0.457738,0.332566)
		vertex[19] = @nscale1 * (-0.457738,-0.332566)
		vertex[20] = @nscale1 * (0.174841,-0.538104)
		vertex[21] = @nscale1 * (0.565796,0)
		vertex[22] = @nscale1 * (0.174841,0.538104)
		vertex[23] = @nscale1 * (-0.457738,0.332566)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 40 ; "hexagon"
		cursality = 1
		numbervertices = 7 ; n + cursality for closed curves
		cincrement = 7 ; numbervertices/cursality
		scratchfloat = sqrt(3)/2 ; for some vertext coordinates
		; initialize arrays
		vertex[0] = @nscale1 * (0,1)
		vertex[1] = @nscale1 * (-scratchfloat + flip(0.5))
		vertex[2] = @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[3] = @nscale1 * (0,-1)
		vertex[4] = @nscale1 * (scratchfloat + flip(-0.5))
		vertex[5] = @nscale1 * (scratchfloat + flip(0.5))
		vertex[6] = @nscale1 * (0,1)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 41 ; "hexagon 2"
		cursality = 6
		numbervertices = 18 ; open curves
		cincrement = 3 ; numbervertices/cursality
		scratchfloat = sqrt(3)/2 ; for some vertext coordinates
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @nscale1 * (0,1)
		vertex[2] = @nscale1 * (-scratchfloat + flip(0.5))
		vertex[3] = @nscale1 * (0,0)
		vertex[4] = @nscale1 * (-scratchfloat + flip(0.5))
		vertex[5] = @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[8] = @nscale1 * (0,-1)
		vertex[9] = @nscale1 * (0,0)
		vertex[10] = @nscale1 * (0,-1)
		vertex[11] = @nscale1 * (scratchfloat + flip(-0.5))
		vertex[12] = @nscale1 * (0,0)
		vertex[13] = @nscale1 * (scratchfloat + flip(-0.5))
		vertex[14] = @nscale1 * (scratchfloat + flip(0.5))
		vertex[15] = @nscale1 * (0,0)
		vertex[16] = @nscale1 * (scratchfloat + flip(0.5))
		vertex[17] = @nscale1 * (0,1)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 42 ; "hexagram"
		cursality = 2
		numbervertices = 8 ; n + cursality for closed curves
		cincrement = 4 ; numbervertices/cursality
		scratchfloat = sqrt(3)/2 ; for some vertext coordinates
		; initialize arrays
		vertex[0] = @nscale1 * (0,1)
		vertex[1] = @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[2] = @nscale1 * (scratchfloat + flip(-0.5))
		vertex[3] = @nscale1 * (0,1)
		vertex[4] = @nscale1 * (-scratchfloat + flip(0.5))
		vertex[5] = @nscale1 * (0,-1)
		vertex[6] = @nscale1 * (scratchfloat + flip(0.5))
		vertex[7] = @nscale1 * (-scratchfloat + flip(0.5))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 43 ; "hexagram 2"
		cursality = 1
		numbervertices = 7 ; n + cursality for closed curves
		cincrement = 7 ; numbervertices/cursality
		scratchfloat = sqrt(3)/2 ; for some vertext coordinates
		; initialize arrays
		vertex[0] = @nscale1 * (0,1)
		vertex[1] = @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[2] = @nscale1 * (scratchfloat + flip(0.5))
		vertex[3] = @nscale1 * (0,-1)
		vertex[4] = @nscale1 * (-scratchfloat + flip(0.5))
		vertex[5] = @nscale1 * (scratchfloat + flip(-0.5))
		vertex[6] = @nscale1 * (0,1)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 44 ; "hexagram 3"
		cursality = 1
		numbervertices = 13 ; 10 + cursality for closed figure
		cincrement = 13 ; numbervertices/cursality
		vertex[0] = @nscale1 * (-0.3,0.519615)
		vertex[1] = @nscale1 * (-0.879474,-0.475947)
		vertex[2] = @nscale1 * (0.3,0.519615)
		vertex[3] = @nscale1 * (-0.851919,0.523673)
		vertex[4] = @nscale1 * (0.6,0)
		vertex[5] = @nscale1 * (0.0275543,0.99962)
		vertex[6] = @nscale1 * (0.3,-0.519615)
		vertex[7] = @nscale1 * (0.879474,0.475947)
		vertex[8] = @nscale1 * (-0.3,-0.519615)
		vertex[9] = @nscale1 * (0.851919,-0.523673)
		vertex[10] = @nscale1 * (-0.6,0)
		vertex[11] = @nscale1 * (-0.0275543,-0.99962)
		vertex[12] = @nscale1 * (-0.3,0.519615)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 45 ; "hexagram 4"
		cursality = 2
		numbervertices = 14 ; 12 + cursality for closed figures
		cincrement = 7 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.309017, 0.951057)
		vertex[2] = @nscale1 * (-0.669131, 0.743145)
		vertex[3] = @nscale1 * (-0.669131, -0.743145)
		vertex[4] = @nscale1 * (-0.309017, -0.951057)
		vertex[5] = @nscale1 * (0.978148, -0.207912)
		vertex[6] = @nscale1 * (0.978148, 0.207912)
		vertex[7] = @nscale1 * (0.309017, 0.951057)
		vertex[8] = @nscale1 * (-0.978148, 0.207912)
		vertex[9] = @nscale1 * (-0.978148, -0.207912)
		vertex[10] = @nscale1 * (0.309017, -0.951057)
		vertex[11] = @nscale1 * (0.669131, -0.743145)
		vertex[12] = @nscale1 * (0.669131, 0.743145)
		vertex[13] = @nscale1 * (0.309017, 0.951057)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 46 ; "hexagram 5"
		cursality = 3
		numbervertices = 15 ; 12 + cursality for closed figures
		cincrement = 5 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.978148, 0.207912)
		vertex[2] = @nscale1 * (-0.978148, -0.207912)
		vertex[3] = @nscale1 * (0.978148, -0.207912)
		vertex[4] = @nscale1 * (0.978148, 0.207912)
		vertex[5] = @nscale1 * (0.309017, 0.951057)
		vertex[6] = @nscale1 * (-0.669131, -0.743145)
		vertex[7] = @nscale1 * (-0.309017, -0.951057)
		vertex[8] = @nscale1 * (0.669131, 0.743145)
		vertex[9] = @nscale1 * (0.309017, 0.951057)
		vertex[10] = @nscale1 * (-0.669131, 0.743145)
		vertex[11] = @nscale1 * (0.309017, -0.951057)
		vertex[12] = @nscale1 * (0.669131, -0.743145)
		vertex[13] = @nscale1 * (-0.309017, 0.951057)
		vertex[14] = @nscale1 * (-0.669131, 0.743145)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 47 ; "hexagram 6"
		cursality = 3
		numbervertices = 15 ; 12 + cursality for closed figures
		cincrement = 5 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.978148, -0.207912)
		vertex[2] = @nscale1 * (-0.978148, 0.207912)
		vertex[3] = @nscale1 * (0.978148, -0.207912)
		vertex[4] = @nscale1 * (0.978148, 0.207912)
		vertex[5] = @nscale1 * (0.309017, 0.951057)
		vertex[6] = @nscale1 * (-0.309017, -0.951057)
		vertex[7] = @nscale1 * (-0.669131, -0.743145)
		vertex[8] = @nscale1 * (0.669131, 0.743145)
		vertex[9] = @nscale1 * (0.309017, 0.951057)
		vertex[10] = @nscale1 * (-0.669131, 0.743145)
		vertex[11] = @nscale1 * (0.669131, -0.743145)
		vertex[12] = @nscale1 * (0.309017, -0.951057)
		vertex[13] = @nscale1 * (-0.309017, 0.951057)
		vertex[14] = @nscale1 * (-0.669131, 0.743145)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 48 ; "hexagram 7"
		cursality = 2
		numbervertices = 14 ; 12 + cursality for closed figures
		cincrement = 7 ; numbervertices/cursality
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.978148, 0.207912)
		vertex[2] = @nscale1 * (-0.669131, 0.743145)
		vertex[3] = @nscale1 * (0.309017, -0.951057)
		vertex[4] = @nscale1 * (-0.309017, -0.951057)
		vertex[5] = @nscale1 * (0.669131, 0.743145)
		vertex[6] = @nscale1 * (0.978148, 0.207912)
		vertex[7] = @nscale1 * (0.309017, 0.951057)
		vertex[8] = @nscale1 * (-0.669131, -0.743145)
		vertex[9] = @nscale1 * (-0.978148, -0.207912)
		vertex[10] = @nscale1 * (0.978148, -0.207912)
		vertex[11] = @nscale1 * (0.669131, -0.743145)
		vertex[12] = @nscale1 * (-0.309017, 0.951057)
		vertex[13] = @nscale1 * (0.309017, 0.951057)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 49 ; "6-asterisk"
		cursality = 6
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 2 ; numbervertices/cursality
		scratchfloat = sqrt(3)/2 ; for some vertext coordinates
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @leafAlength * @nscale1 * (0,1)
		vertex[2] = @nscale1 * (0,0)
		vertex[3] = @leafBlength * @nscale1 * (-scratchfloat + flip(0.5))
		vertex[4] = @nscale1 * (0,0)
		vertex[5] = @leafClength * @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @leafDlength * @nscale1 * (0,-1)
		vertex[8] = @nscale1 * (0,0)
		vertex[9] = @leafElength * @nscale1 * (scratchfloat + flip(-0.5))
		vertex[10] = @nscale1 * (0,0)
		vertex[11] = @leafFlength * @nscale1 * (scratchfloat + flip(0.5))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 50 ; "6-star"
		cursality = 1
		numbervertices = 13 ; n + cursality for closed curves
		cincrement = 13 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.7,0)
		vertex[1] = @starspikiness * @nscale1 * (1.08253,0.625)
		vertex[2] = @nscale1 * (0.35,0.606218)
		vertex[3] = @starspikiness * @nscale1 * (0,1.25)
		vertex[4] = @nscale1 * (-0.35,0.606218)
		vertex[5] = @starspikiness * @nscale1 * (-1.08253,0.625)
		vertex[6] = @nscale1 * (-0.7,0)
		vertex[7] = @starspikiness * @nscale1 * (-1.08253,-0.625)
		vertex[8] = @nscale1 * (-0.35,-0.606218)
		vertex[9] = @starspikiness * @nscale1 * (0,-1.125)
		vertex[10] = @nscale1 * (0.35,-0.606218)
		vertex[11] = @starspikiness * @nscale1 * (1.08253,-0.625)
		vertex[12] = @nscale1 * (0.7,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 71 ; "6-star 2"
		cursality = 1
		numbervertices = 13 ; n + cursality for closed curves
		cincrement = 13 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.5,0)
		vertex[2] = @nscale1 * (0.5, 0.866025)
		vertex[3] = @nscale1 * (0.25, 0.433013)
		vertex[4] = @nscale1 * (-0.5, 0.866025)
		vertex[5] = @nscale1 * (-0.25, 0.433013)
		vertex[6] = @nscale1 * (-1,0)
		vertex[7] = @nscale1 * (-0.5,0)
		vertex[8] = @nscale1 * (-0.5, -0.866025)
		vertex[9] = @nscale1 * (-0.25, -0.433013)
		vertex[10] = @nscale1 * (0.5, -0.866025)
		vertex[11] = @nscale1 * (0.25, -0.433013)
		vertex[12] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 72 ; "6-star 3"
		cursality = 1
		numbervertices = 13 ; n + cursality for closed curves
		cincrement = 13 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.720775, 0.347107)
		vertex[1] = @nscale1 * (0.450484, -0.216942)
		vertex[2] = @nscale1 * (0.0597841, 0.797763)
		vertex[3] = @nscale1 * (0.413119, 0.28166)
		vertex[4] = @nscale1 * (-0.660991, 0.450656)
		vertex[5] = @nscale1 * (-0.037365, 0.498602)
		vertex[6] = @nscale1 * (-0.720775, -0.347107)
		vertex[7] = @nscale1 * (-0.450484, 0.216942)
		vertex[8] = @nscale1 * (-0.0597841, -0.797763)
		vertex[9] = @nscale1 * (-0.413119, -0.28166)
		vertex[10] = @nscale1 * (0.660991, -0.450656)
		vertex[11] = @nscale1 * (0.037365, -0.498602)
		vertex[12] = @nscale1 * (0.720775, 0.347107)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 51 ; "nested hexagons"
		cursality = 2
		numbervertices = 14 ; 10 + cursality
		cincrement = 7 ; numbervertices/cursality
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.5,0.866025)
		vertex[2] = @nscale1 * (-0.5,0.866025)
		vertex[3] = @nscale1 * (-1,0)
		vertex[4] = @nscale1 * (-0.5,-0.866025)
		vertex[5] = @nscale1 * (0.5,-0.866025)
		vertex[6] = @nscale1 * (1,0)
		vertex[7] = @innerscale * @nscale1 * (0.4,0)
		vertex[8] = @innerscale * @nscale1 * (0.2,0.34641)
		vertex[9] = @innerscale * @nscale1 * (-0.2,0.34641)
		vertex[10] = @innerscale * @nscale1 * (-0.4,0)
		vertex[11] = @innerscale * @nscale1 * (-0.2,-0.34641)
		vertex[12] = @nscale1 * (0.2,-0.34641)
		vertex[13] = @innerscale * @nscale1 * (0.4,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 52 ; "nested hexagon 2"
		cursality = 2
		numbervertices = 14 ; 10 + cursality
		cincrement = 7 ; numbervertices/cursality
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.5,0.866025)
		vertex[2] = @nscale1 * (-0.5,0.866025)
		vertex[3] = @nscale1 * (-1,0)
		vertex[4] = @nscale1 * (-0.5,-0.866025)
		vertex[5] = @nscale1 * (0.5,-0.866025)
		vertex[6] = @nscale1 * (1,0)
		vertex[7] = @innerscale * @nscale1 * (0.34641,0.2)
		vertex[8] = @innerscale * @nscale1 * (0,0.4)
		vertex[9] = @innerscale * @nscale1 * (-0.34641,0.2)
		vertex[10] = @innerscale * @nscale1 * (-0.34641,-0.2)
		vertex[11] = @innerscale * @nscale1 * (0,-0.4)
		vertex[12] = @nscale1 * (0.34641,-0.2)
		vertex[13] = @innerscale * @nscale1 * (0.34641,0.2)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 53 ; "twisted hexagons"
		cursality = 3
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 7 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1, 0)
		vertex[1] = @nscale1 * (0.5,0.866025)
		vertex[2] = @nscale1 * (-0.5,0.866025)
		vertex[3] = @nscale1 * (-1,0)
		vertex[4] = @nscale1 * (-0.5,-0.866025)
		vertex[5] = @nscale1 * (0.5,-0.866025)
		vertex[6] = @nscale1 * (1,0)
		vertex[7] = @nscale1 * (0.704489,0.511841)
		vertex[8] = @nscale1 * (-0.0910229,0.866025)
		vertex[9] = @nscale1 * (-0.795511,0.354185)
		vertex[10] = @nscale1 * (-0.704489,-0.511841)
		vertex[11] = @nscale1 * (0.0910229,-0.866025)
		vertex[12] = @nscale1 * (0.795511,-0.354185)
		vertex[13] = @nscale1 * (0.704489,0.511841)
		vertex[14] = @nscale1 * (0.234323,0.721172)
		vertex[15] = @nscale1 * (-0.507392,0.563516)
		vertex[16] = @nscale1 * (-0.741715,-0.157656)
		vertex[17] = @nscale1 * (-0.234323,-0.721172)
		vertex[18] = @nscale1 * (0.507392,-0.563516)
		vertex[19] = @nscale1 * (0.741715,0.157656)
		vertex[20] = @nscale1 * (0.234323,0.721172)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 54 ; "twisted hexagon 2"
		cursality = 4
		numbervertices = 28 ; n + cursality for closed curves
		cincrement = 7 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1, 0)
		vertex[1] = @nscale1 * (0.5,0.866025)
		vertex[2] = @nscale1 * (-0.5,0.866025)
		vertex[3] = @nscale1 * (-1,0)
		vertex[4] = @nscale1 * (-0.5,-0.866025)
		vertex[5] = @nscale1 * (0.5,-0.866025)
		vertex[6] = @nscale1 * (1,0)
		vertex[7] = @nscale1 * (0.673648, 0.565258)
		vertex[8] = @nscale1 * (-0.152704, 0.866025)
		vertex[9] = @nscale1 * (-0.826352, 0.300767)
		vertex[10] = @nscale1 * (-0.673648, -0.565258)
		vertex[11] = @nscale1 * (0.152704, -0.866025)
		vertex[12] = @nscale1 * (0.826352, -0.300767)
		vertex[13] = @nscale1 * (0.673648, 0.565258)
		vertex[14] = @nscale1 * (0.134285, 0.76157)
		vertex[15] = @nscale1 * (-0.592396, 0.497079)
		vertex[16] = @nscale1 * (-0.726682, -0.26449)
		vertex[17] = @nscale1 * (-0.134285, -0.76157)
		vertex[18] = @nscale1 * (0.592396, -0.497079)
		vertex[19] = @nscale1 * (0.726682, 0.26449)
		vertex[20] = @nscale1 * (0.134285, 0.76157)
		vertex[21] = @nscale1 * (-0.340022, 0.588936)
		vertex[22] = @nscale1 * (-0.680045, 0)
		vertex[23] = @nscale1 * (-0.340022, -0.588936)
		vertex[24] = @nscale1 * (0.340022, -0.588936)
		vertex[25] = @nscale1 * (0.680045, 0)
		vertex[26] = @nscale1 * (0.340022, 0.588936)
		vertex[27] = @nscale1 * (-0.340022, 0.588936)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 77 ; "heptagon"
		cursality = 1
		numbervertices = 8 ; n + cursality for closed curves
		cincrement = 8 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.62349, 0.781831)
		vertex[2] = @nscale1 * (-0.222521, 0.974928)
		vertex[3] = @nscale1 * (-0.900969, 0.433884)
		vertex[4] = @nscale1 * (-0.900969, -0.433884)
		vertex[5] = @nscale1 * (-0.222521, -0.974928)
		vertex[6] = @nscale1 * (0.62349, -0.781831)
		vertex[7] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 78 ; "heptagon 2"
		cursality = 7
		numbervertices = 21 ; open curves
		cincrement = 3 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @nscale1 * (1,0)
		vertex[2] = @nscale1 * (0.62349, 0.781831)
		vertex[3] = @nscale1 * (0,0)
		vertex[4] = @nscale1 * (0.62349, 0.781831)
		vertex[5] = @nscale1 * (-0.222521, 0.974928)
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @nscale1 * (-0.222521, 0.974928)
		vertex[8] = @nscale1 * (-0.900969, 0.433884)
		vertex[9] = @nscale1 * (0,0)
		vertex[10] = @nscale1 * (-0.900969, 0.433884)
		vertex[11] = @nscale1 * (-0.900969, -0.433884)
		vertex[12] = @nscale1 * (0,0)
		vertex[13] = @nscale1 * (-0.900969, -0.433884)
		vertex[14] = @nscale1 * (-0.222521, -0.974928)
		vertex[15] = @nscale1 * (0,0)
		vertex[16] = @nscale1 * (-0.222521, -0.974928)
		vertex[17] = @nscale1 * (0.62349, -0.781831)
		vertex[18] = @nscale1 * (0,0)
		vertex[19] = @nscale1 * (0.62349, -0.781831)
		vertex[20] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 79 ; "heptagram"
		cursality = 1
		numbervertices = 8 ; n + cursality for closed curves
		cincrement = 8 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.222521, 0.974928)
		vertex[2] = @nscale1 * (-0.900969, -0.433884)
		vertex[3] = @nscale1 * (0.62349, -0.781831)
		vertex[4] = @nscale1 * (0.62349, 0.781831)
		vertex[5] = @nscale1 * (-0.900969, 0.433884)
		vertex[6] = @nscale1 * (-0.222521, -0.974928)
		vertex[7] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 80 ; "heptagram 2"
		cursality = 1
		numbervertices = 8 ; n + cursality for closed curves
		cincrement = 8 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.900969, 0.433884)
		vertex[2] = @nscale1 * (0.62349, -0.781831)
		vertex[3] = @nscale1 * (-0.222521, 0.974928)
		vertex[4] = @nscale1 * (-0.222521, -0.974928)
		vertex[5] = @nscale1 * (0.62349, 0.781831)
		vertex[6] = @nscale1 * (-0.900969, -0.433884)
		vertex[7] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 81 ; "heptagram 3"
		cursality = 1
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 15 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.133513, 0.584957)
		vertex[1] = @nscale1 * (-0.995974, -0.0896393)
		vertex[2] = @nscale1 * (0.374094, 0.469099)
		vertex[3] = @nscale1 * (-0.691063, 0.722795)
		vertex[4] = @nscale1 * (0.6, 0)
		vertex[5] = @nscale1 * (0.134233, 0.99095)
		vertex[6] = @nscale1 * (0.374094, -0.469099)
		vertex[7] = @nscale1 * (0.858449, 0.512899)
		vertex[8] = @nscale1 * (-0.133513, -0.584957)
		vertex[9] = @nscale1 * (0.936235, -0.351375)
		vertex[10] = @nscale1 * (-0.540581, -0.26033)
		vertex[11] = @nscale1 * (0.309017, -0.951057)
		vertex[12] = @nscale1 * (-0.540581, 0.26033)
		vertex[13] = @nscale1 * (-0.550897, -0.834573)
		vertex[14] = @nscale1 * (-0.133513, 0.584957)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 82 ; "heptagram 4"
		cursality = 1
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 15 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.0149594, 0.999888)
		vertex[2] = @nscale1 * (-0.420357, 0.907359)
		vertex[3] = @nscale1 * (-0.97149, -0.23708)
		vertex[4] = @nscale1 * (-0.791071, -0.611724)
		vertex[5] = @nscale1 * (0.447313, -0.894377)
		vertex[6] = @nscale1 * (0.772417, -0.635116)
		vertex[7] = @nscale1 * (0.772417, 0.635116)
		vertex[8] = @nscale1 * (0.447313, 0.894377)
		vertex[9] = @nscale1 * (-0.791071, 0.611724)
		vertex[10] = @nscale1 * (-0.97149, 0.23708)
		vertex[11] = @nscale1 * (-0.420357, -0.907359)
		vertex[12] = @nscale1 * (-0.0149594, -0.999888)
		vertex[13] = @nscale1 * (0.978148, -0.207912)
		vertex[14] = @nscale1 * (0.978148, 0.207912)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 83 ; "heptagram 5"
		cursality = 1
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 15 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.791071, 0.611724)
		vertex[2] = @nscale1 * (-0.97149, 0.23708)
		vertex[3] = @nscale1 * (0.447313, -0.894377)
		vertex[4] = @nscale1 * (0.772417, -0.635116)
		vertex[5] = @nscale1 * (-0.0149594, 0.999888)
		vertex[6] = @nscale1 * (-0.420357, 0.907359)
		vertex[7] = @nscale1 * (-0.420357, -0.907359)
		vertex[8] = @nscale1 * (-0.0149594, -0.999888)
		vertex[9] = @nscale1 * (0.772417, 0.635116)
		vertex[10] = @nscale1 * (0.447313, 0.894377)
		vertex[11] = @nscale1 * (-0.97149, -0.23708)
		vertex[12] = @nscale1 * (-0.791071, -0.611724)
		vertex[13] = @nscale1 * (0.978148, -0.207912)
		vertex[14] = @nscale1 * (0.978148, 0.207912)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 84 ; "heptagram 6"
		cursality = 1
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 15 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.791071, 0.611724)
		vertex[2] = @nscale1 * (-0.420357, 0.907359)
		vertex[3] = @nscale1 * (-0.420357, -0.907359)
		vertex[4] = @nscale1 * (-0.791071, -0.611724)
		vertex[5] = @nscale1 * (0.978148, -0.207912)
		vertex[6] = @nscale1 * (0.772417, -0.635116)
		vertex[7] = @nscale1 * (-0.0149594, 0.999888)
		vertex[8] = @nscale1 * (0.447313, 0.894377)
		vertex[9] = @nscale1 * (-0.97149, -0.23708)
		vertex[10] = @nscale1 * (-0.97149, 0.23708)
		vertex[11] = @nscale1 * (0.447313, -0.894377)
		vertex[12] = @nscale1 * (-0.0149594, -0.999888)
		vertex[13] = @nscale1 * (0.772417, 0.635116)
		vertex[14] = @nscale1 * (0.978148, 0.207912)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 85 ; "heptagram 7"
		cursality = 1
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 15 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.97149, -0.23708)
		vertex[2] = @nscale1 * (-0.97149, 0.23708)
		vertex[3] = @nscale1 * (0.978148, -0.207912)
		vertex[4] = @nscale1 * (0.772417, -0.635116)
		vertex[5] = @nscale1 * (-0.791071, 0.611724)
		vertex[6] = @nscale1 * (-0.420357, 0.907359)
		vertex[7] = @nscale1 * (0.447313, -0.894377)
		vertex[8] = @nscale1 * (-0.0149594, -0.999888)
		vertex[9] = @nscale1 * (-0.0149594, 0.999888)
		vertex[10] = @nscale1 * (0.447313, 0.894377)
		vertex[11] = @nscale1 * (-0.420357, -0.907359)
		vertex[12] = @nscale1 * (-0.791071, -0.611724)
		vertex[13] = @nscale1 * (0.772417, 0.635116)
		vertex[14] = @nscale1 * (0.978148, 0.207912)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 86 ; "7-asterisk"
		cursality = 7
		numbervertices = 14 ; n for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @leafAlength * @nscale1 * (1,0)
		vertex[2] = @nscale1 * (0,0)
		vertex[3] = @leafBlength * @nscale1 * (0.62349, 0.781831)
		vertex[4] = @nscale1 * (0,0)
		vertex[5] = @leafClength * @nscale1 * (-0.222521, 0.974928)
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @leafDlength * @nscale1 * (-0.900969, 0.433884)
		vertex[8] = @nscale1 * (0,0)
		vertex[9] = @leafElength * @nscale1 * (-0.900969, -0.433884)
		vertex[10] = @nscale1 * (0,0)
		vertex[11] = @leafFlength * @nscale1 * (-0.222521, -0.974928)
		vertex[12] = @nscale1 * (0,0)
		vertex[13] = @leafGlength * @nscale1 * (0.62349, -0.781831)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 87 ; "7-star"
		cursality = 1
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 15 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @starspikiness * @nscale1 * (0.900969, 0.433884)
		vertex[2] = @nscale1 * (0.311745, 0.390916)
		vertex[3] = @starspikiness * @nscale1 * (0.222521, 0.974928)
		vertex[4] = @nscale1 * (-0.11126, 0.487464)
		vertex[5] = @starspikiness * @nscale1 * (-0.62349, 0.781831)
		vertex[6] = @nscale1 * (-0.450484, 0.216942)
		vertex[7] = @starspikiness * @nscale1 * (-1,0)
		vertex[8] = @nscale1 * (-0.450484, -0.216942)
		vertex[9] = @starspikiness * @nscale1 * (-0.62349, -0.781831)
		vertex[10] = @nscale1 * (-0.11126, -0.487464)
		vertex[11] = @starspikiness * @nscale1 * (0.222521, -0.974928)
		vertex[12] = @nscale1 * (0.311745, -0.390916)
		vertex[13] = @starspikiness * @nscale1 * (0.900969, -0.433884)
		vertex[14] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 88 ; "7-star 2"
		cursality = 1
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 15 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.5,0)
		vertex[2] = @nscale1 * (0.62349, 0.781831)
		vertex[3] = @nscale1 * (0.311745, 0.390916)
		vertex[4] = @nscale1 * (-0.222521, 0.974928)
		vertex[5] = @nscale1 * (-0.11126, 0.487464)
		vertex[6] = @nscale1 * (-0.900969, 0.433884)
		vertex[7] = @nscale1 * (-0.450484, 0.216942)
		vertex[8] = @nscale1 * (-0.900969, -0.433884)
		vertex[9] = @nscale1 * (-0.450484, -0.216942)
		vertex[10] = @nscale1 * (-0.222521, -0.974928)
		vertex[11] = @nscale1 * (-0.11126, -0.487464)
		vertex[12] = @nscale1 * (0.62349, -0.781831)
		vertex[13] = @nscale1 * (0.311745, -0.390916)
		vertex[14] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 110 ; "7-star 3"
		cursality = 1
		numbervertices = 22 ; n + cursality for closed curves
		cincrement = 22 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.675727, 0.325413)
		vertex[2] = @nscale1 * (0.205644, 0.455753)
		vertex[3] = @nscale1 * (-0.222521, 0.974928)
		vertex[4] = @nscale1 * (-0.467617, 0.586374)
		vertex[5] = @nscale1 * (-0.490086, 0.0990731)
		vertex[6] = @nscale1 * (-0.900969, -0.433884)
		vertex[7] = @nscale1 * (-0.467617, -0.586374)
		vertex[8] = @nscale1 * (0.0124653, -0.499845)
		vertex[9] = @nscale1 * (0.62349, -0.781831)
		vertex[10] = @nscale1 * (0.675727, -0.325413)
		vertex[11] = @nscale1 * (0.484539, 0.123379)
		vertex[12] = @nscale1 * (0.62349, 0.781831)
		vertex[13] = @nscale1 * (0.166891, 0.731196)
		vertex[14] = @nscale1 * (-0.228105, 0.444936)
		vertex[15] = @nscale1 * (-0.900969, 0.433884)
		vertex[16] = @nscale1 * (-0.75, 0)
		vertex[17] = @nscale1 * (-0.383022, -0.321394)
		vertex[18] = @nscale1 * (-0.222521, -0.974928)
		vertex[19] = @nscale1 * (0.166891, -0.731196)
		vertex[20] = @nscale1 * (0.398566, -0.301902)
		vertex[21] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 89 ; "nested heptagons"
		cursality = 2
		numbervertices = 16 ; n + cursality for closed curves
		cincrement = 8 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.62349, 0.781831)
		vertex[2] = @nscale1 * (-0.222521, 0.974928)
		vertex[3] = @nscale1 * (-0.900969, 0.433884)
		vertex[4] = @nscale1 * (-0.900969, -0.433884)
		vertex[5] = @nscale1 * (-0.222521, -0.974928)
		vertex[6] = @nscale1 * (0.62349, -0.781831)
		vertex[7] = @nscale1 * (1,0)
		vertex[8] = @innerscale * @nscale1 * (0.5,0)
		vertex[9] = @innerscale * @nscale1 * (0.311745, 0.390916)
		vertex[10] = @innerscale * @nscale1 * (-0.11126, 0.487464)
		vertex[11] = @innerscale * @nscale1 * (-0.450484, 0.216942)
		vertex[12] = @innerscale * @nscale1 * (-0.450484, -0.216942)
		vertex[13] = @innerscale * @nscale1 * (-0.11126, -0.487464)
		vertex[14] = @innerscale * @nscale1 * (0.311745, -0.390916)
		vertex[15] = @innerscale * @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 90 ; "nested heptagon 2"
		cursality = 2
		numbervertices = 16 ; n + cursality for closed curves
		cincrement = 8 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.900969, 0.433884)
		vertex[1] = @nscale1 * (0.222521, 0.974928)
		vertex[2] = @nscale1 * (-0.62349, 0.781831)
		vertex[3] = @nscale1 * (-1,0)
		vertex[4] = @nscale1 * (-0.62349, -0.781831)
		vertex[5] = @nscale1 * (0.222521, -0.974928)
		vertex[6] = @nscale1 * (0.900969, -0.433884)
		vertex[7] = @nscale1 * (0.900969, 0.433884)
		vertex[8] = @innerscale * @nscale1 * (0.5,0)
		vertex[9] = @innerscale * @nscale1 * (0.311745, 0.390916)
		vertex[10] = @innerscale * @nscale1 * (-0.11126, 0.487464)
		vertex[11] = @innerscale * @nscale1 * (-0.450484, 0.216942)
		vertex[12] = @innerscale * @nscale1 * (-0.450484, -0.216942)
		vertex[13] = @innerscale * @nscale1 * (-0.11126, -0.487464)
		vertex[14] = @innerscale * @nscale1 * (0.311745, -0.390916)
		vertex[15] = @innerscale * @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 91 ; "twisted heptagons"
		cursality = 3
		numbervertices = 24 ; n + cursality for closed curves
		cincrement = 8 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1, 0)
		vertex[1] = @nscale1 * (0.62349, 0.781831)
		vertex[2] = @nscale1 * (-0.222521, 0.974928)
		vertex[3] = @nscale1 * (-0.900969, 0.433884)
		vertex[4] = @nscale1 * (-0.900969, -0.433884)
		vertex[5] = @nscale1 * (-0.222521, -0.974928)
		vertex[6] = @nscale1 * (0.62349, -0.781831)
		vertex[7] = @nscale1 * (1,0)
		vertex[8] = @nscale1 * (0.887876, 0.232828)
		vertex[9] = @nscale1 * (0.371549, 0.839335)
		vertex[10] = @nscale1 * (-0.424562, 0.813806)
		vertex[11] = @nscale1 * (-0.900969, 0.175464)
		vertex[12] = @nscale1 * (-0.698928, -0.595006)
		vertex[13] = @nscale1 * (0.02942, -0.917424)
		vertex[14] = @nscale1 * (0.735614, -0.549003)
		vertex[15] = @nscale1 * (0.887876, 0.232828)
		vertex[16] = @nscale1 * (0.734114, 0.413445)
		vertex[17] = @nscale1 * (0.134468, 0.831733)
		vertex[18] = @nscale1 * (-0.566435, 0.623708)
		vertex[19] = @nscale1 * (-0.840801, -0.0539812)
		vertex[20] = @nscale1 * (-0.482027, -0.691022)
		vertex[21] = @nscale1 * (0.239724, -0.807709)
		vertex[22] = @nscale1 * (0.780957, -0.316175)
		vertex[23] = @nscale1 * (0.734114, 0.413445)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 92 ; "twisted heptagon 2"
		cursality = 5
		numbervertices = 40 ; n + cursality for closed curves
		cincrement = 8 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1, 0)
		vertex[1] = @nscale1 * (0.62349, 0.781831)
		vertex[2] = @nscale1 * (-0.222521, 0.974928)
		vertex[3] = @nscale1 * (-0.900969, 0.433884)
		vertex[4] = @nscale1 * (-0.900969, -0.433884)
		vertex[5] = @nscale1 * (-0.222521, -0.974928)
		vertex[6] = @nscale1 * (0.62349, -0.781831)
		vertex[7] = @nscale1 * (1,0)
		vertex[8] = @nscale1 * (0.761342, 0.495579)
		vertex[9] = @nscale1 * (0.0872299, 0.904229)
		vertex[10] = @nscale1 * (-0.652568, 0.631977)
		vertex[11] = @nscale1 * (-0.900969, -0.116167)
		vertex[12] = @nscale1 * (-0.470922, -0.776835)
		vertex[13] = @nscale1 * (0.313739, -0.85253)
		vertex[14] = @nscale1 * (0.862148, -0.286253)
		vertex[15] = @nscale1 * (0.761342, 0.495579)
		vertex[16] = @nscale1 * (0.334043, 0.75461)
		vertex[17] = @nscale1 * (-0.381705, 0.731657)
		vertex[18] = @nscale1 * (-0.810022, 0.157752)
		vertex[19] = @nscale1 * (-0.628375, -0.534944)
		vertex[20] = @nscale1 * (0.0264502, -0.824816)
		vertex[21] = @nscale1 * (0.661358, -0.493585)
		vertex[22] = @nscale1 * (0.79825, 0.209326)
		vertex[23] = @nscale1 * (0.334043, 0.75461)
		vertex[24] = @nscale1 * (-0.119647, 0.740061)
		vertex[25] = @nscale1 * (-0.653202, 0.367876)
		vertex[26] = @nscale1 * (-0.694882, -0.281326)
		vertex[27] = @nscale1 * (-0.213302, -0.718685)
		vertex[28] = @nscale1 * (0.428899, -0.614859)
		vertex[29] = @nscale1 * (0.74813, -0.0480315)
		vertex[30] = @nscale1 * (0.504004, 0.554964)
		vertex[31] = @nscale1 * (-0.119647, 0.740061)
		vertex[32] = @nscale1 * (-0.457851, 0.504145)
		vertex[33] = @nscale1 * (-0.679621, -0.0436331)
		vertex[34] = @nscale1 * (-0.389623, -0.558554)
		vertex[35] = @nscale1 * (0.193769, -0.652873)
		vertex[36] = @nscale1 * (0.631249, -0.255565)
		vertex[37] = @nscale1 * (0.593386, 0.334189)
		vertex[38] = @nscale1 * (0.108691, 0.672291)
		vertex[39] = @nscale1 * (-0.457851, 0.504145)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 55 ; "hand"
		cursality = 5
		numbervertices = 10 ; n + cursality for closed curves
		cincrement = 2 ; numbervertices/cursality
		scratchfloat = sqrt(3)/2 ; for some vertext coordinates
		; initialize arrays
		vertex[0] = @nscale1 * (0,1)
		vertex[1] = @finger1length * @nscale1 * (-scratchfloat + flip(0.5))
		vertex[2] = @nscale1 * (0,1)
		vertex[3] = @finger2length * @nscale1 * (-scratchfloat + flip(-0.5))
		vertex[4] = @nscale1 * (0,1)
		vertex[5] = @finger3length * @nscale1 * (0,-1)
		vertex[6] = @nscale1 * (0,1)
		vertex[7] = @finger4length * @nscale1 * (scratchfloat + flip(-0.5))
		vertex[8] = @nscale1 * (0,1)
		vertex[9] = @finger5length * @nscale1 * (scratchfloat + flip(0.5))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 111 ; "lissajous 1"
		cursality = 1
		numbervertices = 77 ; n + cursality for closed curves
		cincrement = 77 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		scratchfloat = 0.0
		scratchfloat2 = (3 * twopi + 0.2)/numbervertices
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * sin(0.66667 * scratchfloat)
			ycoord[glindex] = @nscale1 * sin(scratchfloat)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			scratchfloat = scratchfloat + scratchfloat2
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 133 ; "lissajous 2"
		cursality = 1
		numbervertices = 77 ; n + cursality for closed curves
		cincrement = 77 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		scratchfloat = 0.0
		scratchfloat2 = (4 * twopi + 0.2)/numbervertices
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * sin(0.75 * scratchfloat)
			ycoord[glindex] = @nscale1 * sin(scratchfloat)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			scratchfloat = scratchfloat + scratchfloat2
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 147 ; "lissajous 3"
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1
		cursality = 1
		numbervertices = granularity2 ; n + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		scratchfloat = lissajdomain/granularity2 ; angular domain increment
		glindex = 0
		while glindex < granularity
			xcoord[glindex] = @nscale1 * (@lissaamp1 * cos(@lissafreq1*glindex*scratchfloat - @lissaphase1))
			ycoord[glindex] = @nscale1 * (@lissaamp2 * cos(@lissafreq2*glindex*scratchfloat - @lissaphase2))
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[glindex] = xcoord[0] ; close the curve
		ycoord[glindex] = ycoord[0]
		vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
		if @lissaopen ; do not connect the first and last points of the curve
			numbervertices = numbervertices - 1
			cincrement = cincrement - 1
		endif ; lissaopen
	elseif traparray == 56 ; "zigzag-3"
		cursality = 1
		numbervertices = 3 ; n for open curves
		cincrement = 3 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.8,-0.4)
		vertex[1] = @nscale1 * (0,0.4)
		vertex[2] = @nscale1 * (0.8,-0.4)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 57 ; "zigzag-4"
		cursality = 1
		numbervertices = 4 ; n for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.9,-0.3)
		vertex[1] = @nscale1 * (-0.3,0.3)
		vertex[2] = @nscale1 * (0.3,-0.3)
		vertex[3] = @nscale1 * (0.9,0.3)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 58 ; "zigzag-5"
		cursality = 1
		numbervertices = 5 ; n for open curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.8,0.2)
		vertex[1] = @nscale1 * (-0.4,-0.2)
		vertex[2] = @nscale1 * (0,0.2)
		vertex[3] = @nscale1 * (0.4,-0.2)
		vertex[4] = @nscale1 * (0.8,0.2)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 59 ; "zigzag-6"
		cursality = 1
		numbervertices = 6 ; n for open curves
		cincrement = 6 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-1,0.2)
		vertex[1] = @nscale1 * (-0.6,-0.2)
		vertex[2] = @nscale1 * (-0.2,0.2)
		vertex[3] = @nscale1 * (0.2,-0.2)
		vertex[4] = @nscale1 * (0.6,0.2)
		vertex[5] = @nscale1 * (1,-0.2)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 60 ; "zigzag-7"
		cursality = 1
		numbervertices = 7 ; n for open curves
		cincrement = 7 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.6,-0.1)
		vertex[1] = @nscale1 * (-0.4,0.1)
		vertex[2] = @nscale1 * (-0.2,-0.1)
		vertex[3] = @nscale1 * (0,0.1)
		vertex[4] = @nscale1 * (0.2,-0.1)
		vertex[5] = @nscale1 * (0.4,0.1)
		vertex[6] = @nscale1 * (0.6,-0.1)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 61 ; "sawtooth-1"
		cursality = 1
		numbervertices = 3 ; n for open curves
		cincrement = 3 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.1,-0.3)
		vertex[1] = @nscale1 * (0.1 + flip(@sawheight * 0.3))
		vertex[2] = @nscale1 * (0.1,-0.3)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 62 ; "sawtooth-2"
		cursality = 1
		numbervertices = 5 ; n for open curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.2,-0.3)
		vertex[1] = @sawheight * @nscale1 * (0,0.3)
		vertex[2] = @nscale1 * (0,-0.3)
		vertex[3] = @nscale1 * (0.2 + flip(@sawheight * 0.3))
		vertex[4] = @nscale1 * (0.2,-0.3)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 63 ; "sawtooth-3"
		cursality = 1
		numbervertices = 7 ; n for open curves
		cincrement = 7 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.3,-0.3)
		vertex[1] = @nscale1 * (-0.1 + flip(@sawheight * 0.3))
		vertex[2] = @nscale1 * (-0.1,-0.3)
		vertex[3] = @nscale1 * (0.1 + flip(@sawheight * 0.3))
		vertex[4] = @nscale1 * (0.1,-0.3)
		vertex[5] = @nscale1 * (0.3 + flip(@sawheight * 0.3))
		vertex[6] = @nscale1 * (0.3,-0.3)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 64 ; "sawtooth-4"
		cursality = 1
		numbervertices = 9 ; n for open curves
		cincrement = 9 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.4,-0.3)
		vertex[1] = @nscale1 * (-0.2 + flip(@sawheight * 0.3))
		vertex[2] = @nscale1 * (-0.2,-0.3)
		vertex[3] = @sawheight * @nscale1 * (0,0.3)
		vertex[4] = @nscale1 * (0,-0.3)
		vertex[5] = @nscale1 * (0.2 + flip(@sawheight * 0.3))
		vertex[6] = @nscale1 * (0.2,-0.3)
		vertex[7] = @nscale1 * (0.4 + flip(@sawheight * 0.3))
		vertex[8] = @nscale1 * (0.4,-0.3)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 73 ; "square-1"
		cursality = 1
		numbervertices = 6 ; n for open curves
		cincrement = 6 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * ((@sqrwidth * -0.8) + flip(@sqrheight * -0.4))
		vertex[1] = @nscale1 * ((@sqrwidth * -0.4) + flip(@sqrheight * -0.4))
		vertex[2] = @nscale1 * ((@sqrwidth * -0.4) + flip(@sqrheight * 0.4))
		vertex[3] = @nscale1 * ((@sqrwidth * 0.4) + flip(@sqrheight * 0.4))
		vertex[4] = @nscale1 * ((@sqrwidth * 0.4) + flip(@sqrheight * -0.4))
		vertex[5] = @nscale1 * ((@sqrwidth * 0.8) + flip(@sqrheight * -0.4))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 74 ; "square-2"
		cursality = 1
		numbervertices = 10 ; n for open curves
		cincrement = 10 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * ((@sqrwidth * -0.8) + flip(@sqrheight * -0.2))
		vertex[1] = @nscale1 * ((@sqrwidth * -0.6) + flip(@sqrheight * -0.2))
		vertex[2] = @nscale1 * ((@sqrwidth * -0.6) + flip(@sqrheight * 0.2))
		vertex[3] = @nscale1 * ((@sqrwidth * -0.2) + flip(@sqrheight * 0.2))
		vertex[4] = @nscale1 * ((@sqrwidth * -0.2) + flip(@sqrheight * -0.2))
		vertex[5] = @nscale1 * ((@sqrwidth * 0.2) + flip(@sqrheight * -0.2))
		vertex[6] = @nscale1 * ((@sqrwidth * 0.2) + flip(@sqrheight * 0.2))
		vertex[7] = @nscale1 * ((@sqrwidth * 0.6) + flip(@sqrheight * 0.2))
		vertex[8] = @nscale1 * ((@sqrwidth * 0.6) + flip(@sqrheight * -0.2))
		vertex[9] = @nscale1 * ((@sqrwidth * 0.8) + flip(@sqrheight * -0.2))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 75 ; "square-3"
		cursality = 1
		numbervertices = 14 ; n for open curves
		cincrement = 14 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * ((@sqrwidth * -1.2) + flip(@sqrheight * -0.2))
		vertex[1] = @nscale1 * ((@sqrwidth * -1) + flip(@sqrheight * -0.2))
		vertex[2] = @nscale1 * ((@sqrwidth * -1) + flip(@sqrheight * 0.2))
		vertex[3] = @nscale1 * ((@sqrwidth * -0.6) + flip(@sqrheight * 0.2))
		vertex[4] = @nscale1 * ((@sqrwidth * -0.6) + flip(@sqrheight * -0.2))
		vertex[5] = @nscale1 * ((@sqrwidth * -0.2) + flip(@sqrheight * -0.2))
		vertex[6] = @nscale1 * ((@sqrwidth * -0.2) + flip(@sqrheight * 0.2))
		vertex[7] = @nscale1 * ((@sqrwidth * 0.2) + flip(@sqrheight * 0.2))
		vertex[8] = @nscale1 * ((@sqrwidth * 0.2) + flip(@sqrheight * -0.2))
		vertex[9] = @nscale1 * ((@sqrwidth * 0.6) + flip(@sqrheight * -0.2))
		vertex[10] = @nscale1 * ((@sqrwidth * 0.6) + flip(@sqrheight * 0.2))
		vertex[11] = @nscale1 * ((@sqrwidth * 1) + flip(@sqrheight * 0.2))
		vertex[12] = @nscale1 * ((@sqrwidth * 1) + flip(@sqrheight * -0.2))
		vertex[13] = @nscale1 * ((@sqrwidth * 1.2) + flip(@sqrheight * -0.2))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 76 ; "square-4"
		cursality = 1
		numbervertices = 18 ; n for open curves
		cincrement = 18 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * ((@sqrwidth * -1.6) + flip(@sqrheight * -0.2))
		vertex[1] = @nscale1 * ((@sqrwidth * -1.4) + flip(@sqrheight * -0.2))
		vertex[2] = @nscale1 * ((@sqrwidth * -1.4) + flip(@sqrheight * 0.2))
		vertex[3] = @nscale1 * ((@sqrwidth * -1) + flip(@sqrheight * 0.2))
		vertex[4] = @nscale1 * ((@sqrwidth * -1) + flip(@sqrheight * -0.2))
		vertex[5] = @nscale1 * ((@sqrwidth * -0.6) + flip(@sqrheight * -0.2))
		vertex[6] = @nscale1 * ((@sqrwidth * -0.6) + flip(@sqrheight * 0.2))
		vertex[7] = @nscale1 * ((@sqrwidth * -0.2) + flip(@sqrheight * 0.2))
		vertex[8] = @nscale1 * ((@sqrwidth * -0.2) + flip(@sqrheight * -0.2))
		vertex[9] = @nscale1 * ((@sqrwidth * 0.2) + flip(@sqrheight * -0.2))
		vertex[10] = @nscale1 * ((@sqrwidth * 0.2) + flip(@sqrheight * 0.2))
		vertex[11] = @nscale1 * ((@sqrwidth * 0.6) + flip(@sqrheight * 0.2))
		vertex[12] = @nscale1 * ((@sqrwidth * 0.6) + flip(@sqrheight * -0.2))
		vertex[13] = @nscale1 * ((@sqrwidth * 1) + flip(@sqrheight * -0.2))
		vertex[14] = @nscale1 * ((@sqrwidth * 1) + flip(@sqrheight * 0.2))
		vertex[15] = @nscale1 * ((@sqrwidth * 1.4) + flip(@sqrheight * 0.2))
		vertex[16] = @nscale1 * ((@sqrwidth * 1.4) + flip(@sqrheight * -0.2))
		vertex[17] = @nscale1 * ((@sqrwidth * 1.6) + flip(@sqrheight * -0.2))
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 93 ; "peano curve"
		cursality = 1
		numbervertices = 42 ; n for open curves
		cincrement = 42 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.6, -0.6)
		vertex[1] = @nscale1 * (-0.3,-0.6)
		vertex[2] = @nscale1 * (-0.3,-0.45)
		vertex[3] = @nscale1 * (-0.6,-0.45)
		vertex[4] = @nscale1 * (-0.6,-0.3)
		vertex[5] = @nscale1 * (0.15,-0.3)
		vertex[6] = @nscale1 * (0.15,-0.45)
		vertex[7] = @nscale1 * (-0.15,-0.45)
		vertex[8] = @nscale1 * (-0.15,-0.6)
		vertex[9] = @nscale1 * (0.6,-0.6)
		vertex[10] = @nscale1 * (0.6,-0.45)
		vertex[11] = @nscale1 * (0.3,-0.45)
		vertex[12] = @nscale1 * (0.3,-0.3)
		vertex[13] = @nscale1 * (0.6,-0.3)
		vertex[14] = @nscale1 * (0.6,-0.15)
		vertex[15] = @nscale1 * (0.3,-0.15)
		vertex[16] = @nscale1 * (0.3,0)
		vertex[17] = @nscale1 * (0.6,0)
		vertex[18] = @nscale1 * (0.6,0.15)
		vertex[19] = @nscale1 * (-0.15,0.15)
		vertex[20] = @nscale1 * (-0.15,0)
		vertex[21] = @nscale1 * (0.15,0)
		vertex[22] = @nscale1 * (0.15,-0.15)
		vertex[23] = @nscale1 * (-0.6,-0.15)
		vertex[24] = @nscale1 * (-0.6,0)
		vertex[25] = @nscale1 * (-0.3,0)
		vertex[26] = @nscale1 * (-0.3,0.15)
		vertex[27] = @nscale1 * (-0.6,0.15)
		vertex[28] = @nscale1 * (-0.6,0.3)
		vertex[29] = @nscale1 * (-0.3,0.3)
		vertex[30] = @nscale1 * (-0.3,0.45)
		vertex[31] = @nscale1 * (-0.6,0.45)
		vertex[32] = @nscale1 * (-0.6,0.6)
		vertex[33] = @nscale1 * (0.15,0.6)
		vertex[34] = @nscale1 * (0.15,0.45)
		vertex[35] = @nscale1 * (-0.15,0.45)
		vertex[36] = @nscale1 * (-0.15,0.3)
		vertex[37] = @nscale1 * (0.6,0.3)
		vertex[38] = @nscale1 * (0.6,0.45)
		vertex[39] = @nscale1 * (0.3,0.45)
		vertex[40] = @nscale1 * (0.3,0.6)
		vertex[41] = @nscale1 * (0.6,0.6)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 94 ; "octagon"
		cursality = 1
		numbervertices = 9 ; n + cursality for closed curves
		cincrement = 9 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.707107, 0.707107)
		vertex[2] = @nscale1 * (0,1)
		vertex[3] = @nscale1 * (-0.707107, 0.707107)
		vertex[4] = @nscale1 * (-1,0)
		vertex[5] = @nscale1 * (-0.707107, -0.707107)
		vertex[6] = @nscale1 * (0,-1)
		vertex[7] = @nscale1 * (0.707107, -0.707107)
		vertex[8] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 95 ; "octagon 2"
		cursality = 8
		numbervertices = 24 ; open curves
		cincrement = 3 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @nscale1 * (1,0)
		vertex[2] = @nscale1 * (0.707107, 0.707107)
		vertex[3] = @nscale1 * (0,0)
		vertex[4] = @nscale1 * (0.707107, 0.707107)
		vertex[5] = @nscale1 * (0,1)
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @nscale1 * (0,1)
		vertex[8] = @nscale1 * (-0.707107, 0.707107)
		vertex[9] = @nscale1 * (0,0)
		vertex[10] = @nscale1 * (-0.707107, 0.707107)
		vertex[11] = @nscale1 * (-1,0)
		vertex[12] = @nscale1 * (0,0)
		vertex[13] = @nscale1 * (-1,0)
		vertex[14] = @nscale1 * (-0.707107, -0.707107)
		vertex[15] = @nscale1 * (0,0)
		vertex[16] = @nscale1 * (-0.707107, -0.707107)
		vertex[17] = @nscale1 * (0,-1)
		vertex[18] = @nscale1 * (0,0)
		vertex[19] = @nscale1 * (0,-1)
		vertex[20] = @nscale1 * (0.707107, -0.707107)
		vertex[21] = @nscale1 * (0,0)
		vertex[22] = @nscale1 * (0.707107, -0.707107)
		vertex[23] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 96 ; "octagram"
		cursality = 2
		numbervertices = 10 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0,1)
		vertex[2] = @nscale1 * (-1,0)
		vertex[3] = @nscale1 * (0,-1)
		vertex[4] = @nscale1 * (1,0)
		vertex[5] = @nscale1 * (0.707107, 0.707107)
		vertex[6] = @nscale1 * (-0.707107, 0.707107)
		vertex[7] = @nscale1 * (-0.707107, -0.707107)
		vertex[8] = @nscale1 * (0.707107, -0.707107)
		vertex[9] = @nscale1 * (0.707107, 0.707107)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 97 ; "octagram 2"
		cursality = 1
		numbervertices = 9 ; n + cursality for closed curves
		cincrement = 9 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.707107, 0.707107)
		vertex[2] = @nscale1 * (0,-1)
		vertex[3] = @nscale1 * (0.707107, 0.707107)
		vertex[4] = @nscale1 * (-1,0)
		vertex[5] = @nscale1 * (0.707107, -0.707107)
		vertex[6] = @nscale1 * (0,1)
		vertex[7] = @nscale1 * (-0.707107, -0.707107)
		vertex[8] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 98 ; "octagram 3"
		cursality = 1
		numbervertices = 17 ; n + cursality for closed curves
		cincrement = 17 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.424264, -0.424264)
		vertex[1] = @nscale1 * (0.834573, 0.550897)
		vertex[2] = @nscale1 * (0,-0.6)
		vertex[3] = @nscale1 * (0.979675, -0.200589)
		vertex[4] = @nscale1 * (-0.424264, -0.424264)
		vertex[5] = @nscale1 * (0.550897, -0.834573)
		vertex[6] = @nscale1 * (-0.6,0)
		vertex[7] = @nscale1 * (-0.200589, -0.979675)
		vertex[8] = @nscale1 * (-0.424264, 0.424264)
		vertex[9] = @nscale1 * (-0.834573, -0.550897)
		vertex[10] = @nscale1 * (0,0.6)
		vertex[11] = @nscale1 * (-0.979675, 0.200589)
		vertex[12] = @nscale1 * (0.424264, 0.424264)
		vertex[13] = @nscale1 * (-0.550897, 0.834573)
		vertex[14] = @nscale1 * (0.6,0)
		vertex[15] = @nscale1 * (0.200589, 0.979675)
		vertex[16] = @nscale1 * (0.424264, -0.424264)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 99 ; "octagram 4"
		cursality = 2
		numbervertices = 18 ; n + cursality for closed curves
		cincrement = 9 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (0.207912, 0.978148)
		vertex[2] = @nscale1 * (-0.207912, 0.978148)
		vertex[3] = @nscale1 * (-0.978148, 0.207912)
		vertex[4] = @nscale1 * (-0.978148, -0.207912)
		vertex[5] = @nscale1 * (-0.207912, -0.978148)
		vertex[6] = @nscale1 * (0.207912, -0.978148)
		vertex[7] = @nscale1 * (0.978148, -0.207912)
		vertex[8] = @nscale1 * (0.978148, 0.207912)
		vertex[9] = @nscale1 * (0.544639, 0.838671)
		vertex[10] = @nscale1 * (-0.544639, 0.838671)
		vertex[11] = @nscale1 * (-0.838671, 0.544639)
		vertex[12] = @nscale1 * (-0.838671, -0.544639)
		vertex[13] = @nscale1 * (-0.544639, -0.838671)
		vertex[14] = @nscale1 * (0.544639, -0.838671)
		vertex[15] = @nscale1 * (0.838671, -0.544639)
		vertex[16] = @nscale1 * (0.838671, 0.544639)
		vertex[17] = @nscale1 * (0.544639, 0.838671)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 100 ; "octagram 5"
		cursality = 1
		numbervertices = 17 ; n + cursality for closed curves
		cincrement = 17 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.544639, 0.838671)
		vertex[2] = @nscale1 * (-0.838671, 0.544639)
		vertex[3] = @nscale1 * (-0.207912, -0.978148)
		vertex[4] = @nscale1 * (0.207912, -0.978148)
		vertex[5] = @nscale1 * (0.838671, 0.544639)
		vertex[6] = @nscale1 * (0.544639, 0.838671)
		vertex[7] = @nscale1 * (-0.978148, 0.207912)
		vertex[8] = @nscale1 * (-0.978148, -0.207912)
		vertex[9] = @nscale1 * (0.544639, -0.838671)
		vertex[10] = @nscale1 * (0.838671, -0.544639)
		vertex[11] = @nscale1 * (0.207912, 0.978148)
		vertex[12] = @nscale1 * (-0.207912, 0.978148)
		vertex[13] = @nscale1 * (-0.838671, -0.544639)
		vertex[14] = @nscale1 * (-0.544639, -0.838671)
		vertex[15] = @nscale1 * (0.978148, -0.207912)
		vertex[16] = @nscale1 * (0.978148, 0.207912)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 101 ; "octagram 6"
		cursality = 2
		numbervertices = 18 ; n + cursality for closed curves
		cincrement = 9 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.987688, 0.156434)
		vertex[1] = @nscale1 * (-0.587785, 0.809017)
		vertex[2] = @nscale1 * (-0.156434, 0.987688)
		vertex[3] = @nscale1 * (-0.809017, -0.587785)
		vertex[4] = @nscale1 * (-0.987688, -0.156434)
		vertex[5] = @nscale1 * (0.587785, -0.809017)
		vertex[6] = @nscale1 * (0.156434, -0.987688)
		vertex[7] = @nscale1 * (0.809017, 0.587785)
		vertex[8] = @nscale1 * (0.987688, 0.156434)
		vertex[9] = @nscale1 * (0.587785, 0.809017)
		vertex[10] = @nscale1 * (-0.987688, 0.156434)
		vertex[11] = @nscale1 * (-0.809017, 0.587785)
		vertex[12] = @nscale1 * (-0.156434, -0.987688)
		vertex[13] = @nscale1 * (-0.587785, -0.809017)
		vertex[14] = @nscale1 * (0.987688, -0.156434)
		vertex[15] = @nscale1 * (0.809017, -0.587785)
		vertex[16] = @nscale1 * (0.156434, 0.987688)
		vertex[17] = @nscale1 * (0.587785, 0.809017)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 102 ; "octagram 7"
		cursality = 1
		numbervertices = 17 ; n + cursality for closed curves
		cincrement = 17 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.978148, 0.207912)
		vertex[1] = @nscale1 * (-0.978148, 0.207912)
		vertex[2] = @nscale1 * (-0.838671, 0.544639)
		vertex[3] = @nscale1 * (0.544639, -0.838671)
		vertex[4] = @nscale1 * (0.207912, -0.978148)
		vertex[5] = @nscale1 * (0.207912, 0.978148)
		vertex[6] = @nscale1 * (0.544639, 0.838671)
		vertex[7] = @nscale1 * (-0.838671, -0.544639)
		vertex[8] = @nscale1 * (-0.978148, -0.207912)
		vertex[9] = @nscale1 * (0.978148, -0.207912)
		vertex[10] = @nscale1 * (0.838671, -0.544639)
		vertex[11] = @nscale1 * (-0.544639, 0.838671)
		vertex[12] = @nscale1 * (-0.207912, 0.978148)
		vertex[13] = @nscale1 * (-0.207912, -0.978148)
		vertex[14] = @nscale1 * (-0.544639, -0.838671)
		vertex[15] = @nscale1 * (0.838671, 0.544639)
		vertex[16] = @nscale1 * (0.978148, 0.207912)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 103 ; "8-asterisk"
		cursality = 8
		numbervertices = 16 ; n for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @leafAlength * @nscale1 * (1,0)
		vertex[2] = @nscale1 * (0,0)
		vertex[3] = @leafBlength * @nscale1 * (0.707107, 0.707107)
		vertex[4] = @nscale1 * (0,0)
		vertex[5] = @leafClength * @nscale1 * (0,1)
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @leafDlength * @nscale1 * (-0.707107, 0.707107)
		vertex[8] = @nscale1 * (0,0)
		vertex[9] = @leafElength * @nscale1 * (-1,0)
		vertex[10] = @nscale1 * (0,0)
		vertex[11] = @leafFlength * @nscale1 * (-0.707107, -0.707107)
		vertex[12] = @nscale1 * (0,0)
		vertex[13] = @leafGlength * @nscale1 * (0,-1)
		vertex[14] = @nscale1 * (0,0)
		vertex[15] = @leafHlength * @nscale1 * (0.707107, -0.707107)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 104 ; "8-star"
		cursality = 1
		numbervertices = 17 ; n + cursality for closed curves
		cincrement = 17 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @starspikiness * @nscale1 * (0.92388, 0.382683)
		vertex[2] = @nscale1 * (0.353553, 0.353553)
		vertex[3] = @starspikiness * @nscale1 * (0.382683, 0.92388)
		vertex[4] = @nscale1 * (0,0.5)
		vertex[5] = @starspikiness * @nscale1 * (-0.382683, 0.92388)
		vertex[6] = @nscale1 * (-0.353553, 0.353553)
		vertex[7] = @starspikiness * @nscale1 * (-0.92388, 0.382683)
		vertex[8] = @nscale1 * (-0.5,0)
		vertex[9] = @starspikiness * @nscale1 * (-0.92388, -0.382683)
		vertex[10] = @nscale1 * (-0.353553, -0.353553)
		vertex[11] = @starspikiness * @nscale1 * (-0.382683, -0.92388)
		vertex[12] = @nscale1 * (0,-0.5)
		vertex[13] = @starspikiness * @nscale1 * (0.382683, -0.92388)
		vertex[14] = @nscale1 * (0.353553, -0.353553)
		vertex[15] = @starspikiness * @nscale1 * (0.92388, -0.382683)
		vertex[16] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 105 ; "8-star 2"
		cursality = 1
		numbervertices = 17 ; n + cursality for closed curves
		cincrement = 17 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.5,0)
		vertex[2] = @nscale1 * (0.707107, 0.707107)
		vertex[3] = @nscale1 * (0.353553, 0.353553)
		vertex[4] = @nscale1 * (0,1)
		vertex[5] = @nscale1 * (0,0.5)
		vertex[6] = @nscale1 * (-0.707107, 0.707107)
		vertex[7] = @nscale1 * (-0.353553, 0.353553)
		vertex[8] = @nscale1 * (-1,0)
		vertex[9] = @nscale1 * (-0.5,0)
		vertex[10] = @nscale1 * (-0.707107, -0.707107)
		vertex[11] = @nscale1 * (-0.353553, -0.353553)
		vertex[12] = @nscale1 * (0,-1)
		vertex[13] = @nscale1 * (0,-0.5)
		vertex[14] = @nscale1 * (0.707107, -0.707107)
		vertex[15] = @nscale1 * (0.353553, -0.353553)
		vertex[16] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 106 ; "octagram 8"
		cursality = 1
		numbervertices = 9 ; n + cursality for closed curves
		cincrement = 9 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.707107, 0.707107)
		vertex[1] = @nscale1 * (-0.6667, 0)
		vertex[2] = @nscale1 * (0.707107, -0.707107)
		vertex[3] = @nscale1 * (0, 0.6667)
		vertex[4] = @nscale1 * (-0.707107, -0.707107)
		vertex[5] = @nscale1 * (0.6667, 0)
		vertex[6] = @nscale1 * (-0.707107, 0.707107)
		vertex[7] = @nscale1 * (0, -0.6667)
		vertex[8] = @nscale1 * (0.707107, 0.707107)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 107 ; "octagram 9"
		cursality = 4
		numbervertices = 20 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.987688, 0.156434)
		vertex[1] = @nscale1 * (0.809017, 0.587785)
		vertex[2] = @nscale1 * (-0.809017, -0.587785)
		vertex[3] = @nscale1 * (-0.987688, -0.156434)
		vertex[4] = @nscale1 * (0.987688, 0.156434)
		vertex[5] = @nscale1 * (0.587785, 0.809017)
		vertex[6] = @nscale1 * (0.156434, 0.987688)
		vertex[7] = @nscale1 * (-0.156434, -0.987688)
		vertex[8] = @nscale1 * (-0.587785, -0.809017)
		vertex[9] = @nscale1 * (0.587785, 0.809017)
		vertex[10] = @nscale1 * (-0.156434, 0.987688)
		vertex[11] = @nscale1 * (-0.587785, 0.809017)
		vertex[12] = @nscale1 * (0.587785, -0.809017)
		vertex[13] = @nscale1 * (0.156434, -0.987688)
		vertex[14] = @nscale1 * (-0.156434, 0.987688)
		vertex[15] = @nscale1 * (-0.809017, 0.587785)
		vertex[16] = @nscale1 * (-0.987688, 0.156434)
		vertex[17] = @nscale1 * (0.987688, -0.156434)
		vertex[18] = @nscale1 * (0.809017, -0.587785)
		vertex[19] = @nscale1 * (-0.809017, 0.587785)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 108 ; "octagram 10"
		cursality = 4
		numbervertices = 20 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.987688, 0.156434)
		vertex[1] = @nscale1 * (-0.809017, -0.587785)
		vertex[2] = @nscale1 * (-0.987688, -0.156434)
		vertex[3] = @nscale1 * (0.809017, 0.587785)
		vertex[4] = @nscale1 * (0.987688, 0.156434)
		vertex[5] = @nscale1 * (0.587785, 0.809017)
		vertex[6] = @nscale1 * (-0.156434, -0.987688)
		vertex[7] = @nscale1 * (-0.587785, -0.809017)
		vertex[8] = @nscale1 * (0.156434, 0.987688)
		vertex[9] = @nscale1 * (0.587785, 0.809017)
		vertex[10] = @nscale1 * (-0.156434, 0.987688)
		vertex[11] = @nscale1 * (0.587785, -0.809017)
		vertex[12] = @nscale1 * (0.156434, -0.987688)
		vertex[13] = @nscale1 * (-0.587785, 0.809017)
		vertex[14] = @nscale1 * (-0.156434, 0.987688)
		vertex[15] = @nscale1 * (-0.809017, 0.587785)
		vertex[16] = @nscale1 * (0.987688, -0.156434)
		vertex[17] = @nscale1 * (0.809017, -0.587785)
		vertex[18] = @nscale1 * (-0.987688, 0.156434)
		vertex[19] = @nscale1 * (-0.809017, 0.587785)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 109 ; "roots of unity"
		if @fixtrapbug
			singleroot = @singleroot1
			unityroots = @unityroot1
			whichroot = @whichroot1
			if whichroot < 1
				whichroot = 1
			elseif whichroot > unityroots
				whichroot = unityroots
			endif ; whichroot
		endif ; @fixtrapbug
		if !singleroot ; plot all the roots
			cursality = unityroots
			numbervertices = unityroots ; single points, not line segments
			cincrement = 1 ; numbervertices/cursality
			; initialize arrays
			glindex = 0
			while glindex < numbervertices
				xcoord[glindex] = @nscale1 * cos(glindex * twopi / unityroots)
				ycoord[glindex] = @nscale1 * sin(glindex * twopi / unityroots)
				vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
				glindex = glindex + 1
			endwhile ; glindex
		else ; plot only a single root
			cursality = 1
			numbervertices = 1 ; single point, not line segments
			cincrement = 1 ; numbervertices/cursality
			; initialize arrays
			glindex = 0
			while glindex < numbervertices
				xcoord[glindex] = @nscale1 * cos(whichroot * twopi / unityroots)
				ycoord[glindex] = @nscale1 * sin(whichroot * twopi / unityroots)
				vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
				glindex = glindex + 1
			endwhile ; glindex
		endif ; !singleroot[]
	elseif traparray == 112 ; "nonagon"
		cursality = 1
		numbervertices = 10 ; vertices + cursality for closed curves
		cincrement = 10 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(glindex * twopi / 9)
			ycoord[glindex] = @nscale1 * sin(glindex * twopi / 9)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 113 ; "nonagram"
		cursality = 1
		numbervertices = 10 ; vertices + cursality for closed curves
		cincrement = 10 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(2 * glindex * twopi / 9)
			ycoord[glindex] = @nscale1 * sin(2 * glindex * twopi / 9)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 114 ; "nonagram 2"
		cursality = 3
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.5, 0.866025)
		vertex[2] = @nscale1 * (-0.5, -0.866025)
		vertex[3] = @nscale1 * (1,0)
		vertex[4] = @nscale1 * (0.766044, 0.642788)
		vertex[5] = @nscale1 * (-0.939693, 0.34202)
		vertex[6] = @nscale1 * (0.173648, -0.984808)
		vertex[7] = @nscale1 * (0.766044, 0.642788)
		vertex[8] = @nscale1 * (0.173648, 0.984808)
		vertex[9] = @nscale1 * (-0.939693, -0.34202)
		vertex[10] = @nscale1 * (0.766044, -0.642788)
		vertex[11] = @nscale1 * (0.173648, 0.984808)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 115 ; "nonagram 3"
		cursality = 1
		numbervertices = 10 ; vertices + cursality for closed curves
		cincrement = 10 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(4 * glindex * twopi / 9)
			ycoord[glindex] = @nscale1 * sin(4 * glindex * twopi / 9)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 116 ; "nonagram 4"
		cursality = 1
		numbervertices = 19 ; n + cursality for closed curves
		cincrement = 19 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.459627, -0.385673)
		vertex[1] = @nscale1 * (0.815028, 0.579421)
		vertex[2] = @nscale1 * (0.104189, -0.590885)
		vertex[3] = @nscale1 * (0.996793, -0.0800278)
		vertex[4] = @nscale1 * (-0.3, -0.519615)
		vertex[5] = @nscale1 * (0.712147, -0.702031)
		vertex[6] = @nscale1 * (-0.563816, -0.205212)
		vertex[7] = @nscale1 * (0.0942792, -0.995546)
		vertex[8] = @nscale1 * (-0.563816, 0.205212)
		vertex[9] = @nscale1 * (-0.567702, -0.823234)
		vertex[10] = @nscale1 * (-0.3, 0.519615)
		vertex[11] = @nscale1 * (-0.96405, -0.265722)
		vertex[12] = @nscale1 * (0.104189, 0.590885)
		vertex[13] = @nscale1 * (-0.909308, 0.416125)
		vertex[14] = @nscale1 * (0.459627, 0.385673)
		vertex[15] = @nscale1 * (-0.42909, 0.903262)
		vertex[16] = @nscale1 * (0.6, 0)
		vertex[17] = @nscale1 * (0.251903, 0.967752)
		vertex[18] = @nscale1 * (0.459627, -0.385673)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 117 ; "nonagram 5"
		cursality = 1
		numbervertices = 19 ; n + cursality for closed curves
		cincrement = 19 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.992115, 0.125333)
		vertex[1] = @nscale1 * (-0.889416, 0.457098)
		vertex[2] = @nscale1 * (0.0488498, 0.998806)
		vertex[3] = @nscale1 * (-0.604599, -0.79653)
		vertex[4] = @nscale1 * (-0.975149, 0.221548)
		vertex[5] = @nscale1 * (0.679441, -0.73373)
		vertex[6] = @nscale1 * (-0.387516, -0.921863)
		vertex[7] = @nscale1 * (0.840567, 0.541708)
		vertex[8] = @nscale1 * (0.840567, -0.541708)
		vertex[9] = @nscale1 * (-0.387516, 0.921863)
		vertex[10] = @nscale1 * (0.679441, 0.73373)
		vertex[11] = @nscale1 * (-0.975149, -0.221548)
		vertex[12] = @nscale1 * (-0.604599, 0.79653)
		vertex[13] = @nscale1 * (0.0488498, -0.998806)
		vertex[14] = @nscale1 * (-0.889416, -0.457098)
		vertex[15] = @nscale1 * (0.992115, -0.125333)
		vertex[16] = @nscale1 * (0.295708, -0.955278)
		vertex[17] = @nscale1 * (0.295708, 0.955278)
		vertex[18] = @nscale1 * (0.992115, 0.125333)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 118 ; "nonagram 6"
		cursality = 1
		numbervertices = 19 ; n + cursality for closed curves
		cincrement = 19 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.939693, 0.34202)
		vertex[1] = @nscale1 * (-0.766044, 0.642788)
		vertex[2] = @nscale1 * (-0.173648, 0.984808)
		vertex[3] = @nscale1 * (-0.766044, -0.642788)
		vertex[4] = @nscale1 * (-1,0)
		vertex[5] = @nscale1 * (0.5, -0.866025)
		vertex[6] = @nscale1 * (-0.173648, -0.984808)
		vertex[7] = @nscale1 * (0.939693, 0.34202)
		vertex[8] = @nscale1 * (0.939693, -0.34202)
		vertex[9] = @nscale1 * (-0.173648, 0.984808)
		vertex[10] = @nscale1 * (0.5, 0.866025)
		vertex[11] = @nscale1 * (-1,0)
		vertex[12] = @nscale1 * (-0.766044, 0.642788)
		vertex[13] = @nscale1 * (-0.173648, -0.984808)
		vertex[14] = @nscale1 * (-0.766044, -0.642788)
		vertex[15] = @nscale1 * (0.939693, -0.34202)
		vertex[16] = @nscale1 * (0.5, -0.866025)
		vertex[17] = @nscale1 * (0.5, 0.866025)
		vertex[18] = @nscale1 * (0.939693, 0.34202)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 151 ; "nonagram 7"
		cursality = 1
		numbervertices = 10 ; n + cursality for closed curves
		cincrement = 10 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.704769, 0.256515)
		vertex[2] = @nscale1 * (0.383022, -0.321394)
		vertex[3] = @nscale1 * (-0.5, 0.866025)
		vertex[4] = @nscale1 * (0.130236, -0.738606)
		vertex[5] = @nscale1 * (0.0868241, 0.492404)
		vertex[6] = @nscale1 * (-0.5, -0.866025)
		vertex[7] = @nscale1 * (0.574533, 0.482091)
		vertex[8] = @nscale1 * (-0.469846, -0.17101)
		vertex[9] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 119 ; "9-star"
		cursality = 1
		numbervertices = 19 ; n + cursality for closed curves
		cincrement = 19 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @starspikiness * @nscale1 * (0.939693, 0.34202)
		vertex[2] = @nscale1 * (0.383022, 0.321394)
		vertex[3] = @starspikiness * @nscale1 * (0.5, 0.866025)
		vertex[4] = @nscale1 * (0.0868241, 0.492404)
		vertex[5] = @starspikiness * @nscale1 * (-0.173648, 0.984808)
		vertex[6] = @nscale1 * (-0.25, 0.433013)
		vertex[7] = @starspikiness * @nscale1 * (-0.766044, 0.642788)
		vertex[8] = @nscale1 * (-0.469846, 0.17101)
		vertex[9] = @starspikiness * @nscale1 * (-1,0)
		vertex[10] = @nscale1 * (-0.469846, -0.17101)
		vertex[11] = @starspikiness * @nscale1 * (-0.766044, -0.642788)
		vertex[12] = @nscale1 * (-0.25, -0.433013)
		vertex[13] = @starspikiness * @nscale1 * (-0.173648, -0.984808)
		vertex[14] = @nscale1 * (0.0868241, -0.492404)
		vertex[15] = @starspikiness * @nscale1 * (0.5, -0.866025)
		vertex[16] = @nscale1 * (0.383022, -0.321394)
		vertex[17] = @starspikiness * @nscale1 * (0.939693, -0.34202)
		vertex[18] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 120 ; "9-asterisk"
		cursality = 9
		numbervertices = 18 ; vertices only for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			vertex[glindex] = (0,0)
			xcoord[glindex + 1] = @nscale1 * cos(glindex * #pi / 9)
			ycoord[glindex + 1] = @nscale1 * sin(glindex * #pi / 9)
			glindex = glindex + 1
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		vertex[1] = @leafAlength * vertex[1]
		xcoord[1] = real(vertex[1])
		ycoord[1] = imag(vertex[1])
		vertex[3] = @leafBlength * vertex[3]
		xcoord[3] = real(vertex[3])
		ycoord[3] = imag(vertex[3])
		vertex[5] = @leafClength * vertex[5]
		xcoord[5] = real(vertex[5])
		ycoord[5] = imag(vertex[5])
		vertex[7] = @leafDlength * vertex[7]
		xcoord[7] = real(vertex[7])
		ycoord[7] = imag(vertex[7])
		vertex[9] = @leafElength * vertex[9]
		xcoord[9] = real(vertex[9])
		ycoord[9] = imag(vertex[9])
		vertex[11] = @leafFlength * vertex[11]
		xcoord[11] = real(vertex[11])
		ycoord[11] = imag(vertex[11])
		vertex[13] = @leafGlength * vertex[13]
		xcoord[13] = real(vertex[13])
		ycoord[13] = imag(vertex[13])
		vertex[15] = @leafHlength * vertex[15]
		xcoord[15] = real(vertex[15])
		ycoord[15] = imag(vertex[15])
		vertex[17] = @leafIlength * vertex[17]
		xcoord[17] = real(vertex[17])
		ycoord[17] = imag(vertex[17])
	elseif traparray == 121 ; "9-star 2"
		cursality = 1
		numbervertices = 19 ; n + cursality for closed curves
		cincrement = 19 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.965926, 0.258819)
		vertex[1] = @nscale1 * (-0.996195, -0.0871557)
		vertex[2] = @nscale1 * (-0.996195, 0.0871557)
		vertex[3] = @nscale1 * (0.965926, -0.258819)
		vertex[4] = @nscale1 * (0.906308, -0.422618)
		vertex[5] = @nscale1 * (-0.819152, 0.573576)
		vertex[6] = @nscale1 * (-0.707107, 0.707107)
		vertex[7] = @nscale1 * (0.573576, -0.819152)
		vertex[8] = @nscale1 * (0.422618, -0.906308)
		vertex[9] = @nscale1 * (-0.258819, 0.965926)
		vertex[10] = @nscale1 * (-0.0871557, 0.996195)
		vertex[11] = @nscale1 * (-0.0871557, -0.996195)
		vertex[12] = @nscale1 * (-0.258819, -0.965926)
		vertex[13] = @nscale1 * (0.422618, 0.906308)
		vertex[14] = @nscale1 * (0.573576, 0.819152)
		vertex[15] = @nscale1 * (-0.707107, -0.707107)
		vertex[16] = @nscale1 * (-0.819152, -0.573576)
		vertex[17] = @nscale1 * (0.906308, 0.422618)
		vertex[18] = @nscale1 * (0.965926, 0.258819)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 122 ; "9-star 3"
		cursality = 1
		numbervertices = 19 ; n + cursality for closed curves
		cincrement = 19 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (01,0)
		vertex[1] = @nscale1 * (0.5,0)
		vertex[2] = @nscale1 * (0.766044, 0.642788)
		vertex[3] = @nscale1 * (0.383022, 0.321394)
		vertex[4] = @nscale1 * (0.173648, 0.984808)
		vertex[5] = @nscale1 * (0.0868241, 0.492404)
		vertex[6] = @nscale1 * (-0.5, 0.866025)
		vertex[7] = @nscale1 * (-0.25, 0.433013)
		vertex[8] = @nscale1 * (-0.939693, 0.34202)
		vertex[9] = @nscale1 * (-0.469846, 0.17101)
		vertex[10] = @nscale1 * (-0.939693, -0.34202)
		vertex[11] = @nscale1 * (-0.469846, -0.17101)
		vertex[12] = @nscale1 * (-0.5, -0.866025)
		vertex[13] = @nscale1 * (-0.25, -0.433013)
		vertex[14] = @nscale1 * (0.173648, -0.984808)
		vertex[15] = @nscale1 * (0.0868241, -0.492404)
		vertex[16] = @nscale1 * (0.766044, -0.642788)
		vertex[17] = @nscale1 * (0.383022, -0.321394)
		vertex[18] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 123 ; "decagon"
		cursality = 1
		numbervertices = 11 ; vertices + cursality for closed curves
		cincrement = 11 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(glindex * twopi / 10)
			ycoord[glindex] = @nscale1 * sin(glindex * twopi / 10)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 124 ; "10-asterisk"
		cursality = 10
		numbervertices = 20 ; vertices only for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			vertex[glindex] = (0,0)
			xcoord[glindex + 1] = @nscale1 * cos(glindex * #pi / 10)
			ycoord[glindex + 1] = @nscale1 * sin(glindex * #pi / 10)
			glindex = glindex + 1
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		vertex[1] = @leafAlength * vertex[1]
		xcoord[1] = real(vertex[1])
		ycoord[1] = imag(vertex[1])
		vertex[3] = @leafBlength * vertex[3]
		xcoord[3] = real(vertex[3])
		ycoord[3] = imag(vertex[3])
		vertex[5] = @leafClength * vertex[5]
		xcoord[5] = real(vertex[5])
		ycoord[5] = imag(vertex[5])
		vertex[7] = @leafDlength * vertex[7]
		xcoord[7] = real(vertex[7])
		ycoord[7] = imag(vertex[7])
		vertex[9] = @leafElength * vertex[9]
		xcoord[9] = real(vertex[9])
		ycoord[9] = imag(vertex[9])
		vertex[11] = @leafFlength * vertex[11]
		xcoord[11] = real(vertex[11])
		ycoord[11] = imag(vertex[11])
		vertex[13] = @leafGlength * vertex[13]
		xcoord[13] = real(vertex[13])
		ycoord[13] = imag(vertex[13])
		vertex[15] = @leafHlength * vertex[15]
		xcoord[15] = real(vertex[15])
		ycoord[15] = imag(vertex[15])
		vertex[17] = @leafIlength * vertex[17]
		xcoord[17] = real(vertex[17])
		ycoord[17] = imag(vertex[17])
		vertex[19] = @leafJlength * vertex[19]
		xcoord[19] = real(vertex[19])
		ycoord[19] = imag(vertex[19])
	elseif traparray == 125 ; "decagram"
		cursality = 2
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 6 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.309017, 0.951057)
		vertex[2] = @nscale1 * (-0.809017, 0.587785)
		vertex[3] = @nscale1 * (-0.809017, -0.587785)
		vertex[4] = @nscale1 * (0.309017, -0.951057)
		vertex[5] = @nscale1 * (1,0)
		vertex[6] = @nscale1 * (0.809017, 0.587785)
		vertex[7] = @nscale1 * (-0.309017, 0.951057)
		vertex[8] = @nscale1 * (-1,0)
		vertex[9] = @nscale1 * (-0.309017, -0.951057)
		vertex[10] = @nscale1 * (0.809017, -0.587785)
		vertex[11] = @nscale1 * (0.809017, 0.587785)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 126 ; "decagram 2"
		cursality = 1
		numbervertices = 11 ; vertices + cursality for closed curves
		cincrement = 11 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(3 * glindex * twopi / 10)
			ycoord[glindex] = @nscale1 * sin(3 * glindex * twopi / 10)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 127 ; "decagram 3"
		cursality = 2
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 6 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.809017, 0.587785)
		vertex[2] = @nscale1 * (0.309017, -0.951057)
		vertex[3] = @nscale1 * (0.309017, 0.951057)
		vertex[4] = @nscale1 * (-0.809017, -0.587785)
		vertex[5] = @nscale1 * (1,0)
		vertex[6] = @nscale1 * (0.809017, 0.587785)
		vertex[7] = @nscale1 * (-1,0)
		vertex[8] = @nscale1 * (0.809017, -0.587785)
		vertex[9] = @nscale1 * (-0.309017, 0.951057)
		vertex[10] = @nscale1 * (-0.309017, -0.951057)
		vertex[11] = @nscale1 * (0.809017, 0.587785)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 128 ; "decagram 4"
		cursality = 1
		numbervertices = 11 ; n + cursality for closed curves
		cincrement = 11 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.809017, 0.587785)
		vertex[1] = @nscale1 * (-0.647214, 0.470228)
		vertex[2] = @nscale1 * (-0.309017, -0.951057)
		vertex[3] = @nscale1 * (0.8,0)
		vertex[4] = @nscale1 * (-0.309017, 0.951057)
		vertex[5] = @nscale1 * (-0.647214, -0.470228)
		vertex[6] = @nscale1 * (0.809017, -0.587785)
		vertex[7] = @nscale1 * (0.247214, 0.760845)
		vertex[8] = @nscale1 * (-1,0)
		vertex[9] = @nscale1 * (0.247214, -0.760845)
		vertex[10] = @nscale1 * (0.809017, 0.587785)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 129 ; "10-star"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @starspikiness * @nscale1 * (0.951057, 0.309017)
		vertex[2] = @nscale1 * (0.404508, 0.293893)
		vertex[3] = @starspikiness * @nscale1 * (0.587785, 0.809017)
		vertex[4] = @nscale1 * (0.154508, 0.475528)
		vertex[5] = @starspikiness * @nscale1 * (0,1)
		vertex[6] = @nscale1 * (-0.154508, 0.475528)
		vertex[7] = @starspikiness * @nscale1 * (-0.587785, 0.809017)
		vertex[8] = @nscale1 * (-0.404508, 0.293893)
		vertex[9] = @starspikiness * @nscale1 * (-0.951057, 0.309017)
		vertex[10] = @nscale1 * (-0.5,0)
		vertex[11] = @starspikiness * @nscale1 * (-0.951057, -0.309017)
		vertex[12] = @nscale1 * (-0.404508, -0.293893)
		vertex[13] = @starspikiness * @nscale1 * (-0.587785, -0.809017)
		vertex[14] = @nscale1 * (-0.154508, -0.475528)
		vertex[15] = @starspikiness * @nscale1 * (0,-1)
		vertex[16] = @nscale1 * (0.154508, -0.475528)
		vertex[17] = @starspikiness * @nscale1 * (0.587785, -0.809017)
		vertex[18] = @nscale1 * (0.404508, -0.293893)
		vertex[19] = @starspikiness * @nscale1 * (0.951057, -0.309017)
		vertex[20] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 130 ; "10-star 2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.5,0)
		vertex[2] = @nscale1 * (0.809017, 0.587785)
		vertex[3] = @nscale1 * (0.404508, 0.293893)
		vertex[4] = @nscale1 * (0.309017, 0.951057)
		vertex[5] = @nscale1 * (0.154508, 0.475528)
		vertex[6] = @nscale1 * (-0.309017, 0.951057)
		vertex[7] = @nscale1 * (-0.154508, 0.475528)
		vertex[8] = @nscale1 * (-0.809017, 0.587785)
		vertex[9] = @nscale1 * (-0.404508, 0.293893)
		vertex[10] = @nscale1 * (-1,0)
		vertex[11] = @nscale1 * (-0.5,0)
		vertex[12] = @nscale1 * (-0.809017, -0.587785)
		vertex[13] = @nscale1 * (-0.404508, -0.293893)
		vertex[14] = @nscale1 * (-0.309017, -0.951057)
		vertex[15] = @nscale1 * (-0.154508, -0.475528)
		vertex[16] = @nscale1 * (0.309017, -0.951057)
		vertex[17] = @nscale1 * (0.154508, -0.475528)
		vertex[18] = @nscale1 * (0.809017, -0.587785)
		vertex[19] = @nscale1 * (0.404508, -0.293893)
		vertex[20] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 131 ; "10-star 3"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.707107, 0.707107)
		vertex[1] = @nscale1 * (0.494975, -0.494975)
		vertex[2] = @nscale1 * (0.156434, 0.987688)
		vertex[3] = @nscale1 * (0.691382, -0.109504)
		vertex[4] = @nscale1 * (-0.45399, 0.891007)
		vertex[5] = @nscale1 * (0.623705, 0.317793)
		vertex[6] = @nscale1 * (-0.891007, 0.45399)
		vertex[7] = @nscale1 * (0.317793, 0.623705)
		vertex[8] = @nscale1 * (-0.987688, -0.156434)
		vertex[9] = @nscale1 * (-0.109504, 0.691382)
		vertex[10] = @nscale1 * (-0.707107, -0.707107)
		vertex[11] = @nscale1 * (-0.494975, 0.494975)
		vertex[12] = @nscale1 * (-0.156434, -0.987688)
		vertex[13] = @nscale1 * (-0.691382, 0.109504)
		vertex[14] = @nscale1 * (0.45399, -0.891007)
		vertex[15] = @nscale1 * (-0.623705, -0.317793)
		vertex[16] = @nscale1 * (0.891007, -0.45399)
		vertex[17] = @nscale1 * (-0.317793, -0.623705)
		vertex[18] = @nscale1 * (0.987688, 0.156434)
		vertex[19] = @nscale1 * (0.109504, -0.691382)
		vertex[20] = @nscale1 * (0.707107, 0.707107)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 132 ; "decagram 5"
		cursality = 2
		numbervertices = 22 ; n + cursality for closed curves
		cincrement = 11 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.987688, 0.156434)
		vertex[1] = @nscale1 * (-0.156434, 0.987688)
		vertex[2] = @nscale1 * (0.156434, 0.987688)
		vertex[3] = @nscale1 * (-0.987688, 0.156434)
		vertex[4] = @nscale1 * (-0.891007, 0.45399)
		vertex[5] = @nscale1 * (-0.45399, -0.891007)
		vertex[6] = @nscale1 * (-0.707107, -0.707107)
		vertex[7] = @nscale1 * (0.707107, -0.707107)
		vertex[8] = @nscale1 * (0.45399, -0.891007)
		vertex[9] = @nscale1 * (0.891007, 0.45399)
		vertex[10] = @nscale1 * (0.987688, 0.156434)
		vertex[11] = @nscale1 * (0.707107, 0.707107)
		vertex[12] = @nscale1 * (-0.707107, 0.707107)
		vertex[13] = @nscale1 * (-0.45399, 0.891007)
		vertex[14] = @nscale1 * (-0.891007, -0.45399)
		vertex[15] = @nscale1 * (-0.987688, -0.156434)
		vertex[16] = @nscale1 * (0.156434, -0.987688)
		vertex[17] = @nscale1 * (-0.156434, -0.987688)
		vertex[18] = @nscale1 * (0.987688, -0.156434)
		vertex[19] = @nscale1 * (0.891007, -0.45399)
		vertex[20] = @nscale1 * (0.45399, 0.891007)
		vertex[21] = @nscale1 * (0.707107, 0.707107)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 134 ; "collinear spots"
		if @fixtrapbug
			collinearspots = @collinearspot1
		endif ; @fixtrapbug
		cursality = collinearspots
		numbervertices = collinearspots ; single points, not line segments
		cincrement = 1 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		if numbervertices == 1
			xcoord[glindex] = 0.0
			ycoord[glindex] = 0.0
			vertex[glindex] = (0,0)
			glindex = glindex + 1
		else
			scratchfloat = @nscale1/(numbervertices - 1)
			xcoord[glindex] = -0.5 * @nscale1
			ycoord[glindex] = 0.0
			vertex[glindex] = (-0.5,0) * @nscale1
			glindex = glindex + 1
			while glindex < numbervertices
				xcoord[glindex] = xcoord[glindex - 1] + scratchfloat
				ycoord[glindex] = 0.0
				vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
				glindex = glindex + 1
			endwhile ; glindex
		endif ; numbervertices
	elseif traparray == 135 ; "square array"
		squaresize = @squarespot1
		cursality = sqr(squaresize)
		numbervertices = cursality ; single points, not line segments
		cincrement = 1 ; numbervertices/cursality
		; initialize arrays
		scratchfloat = (1.5 * @nscale1)/(squaresize - 1) ; distance between adjacent points
		scratchfloat2 = @nscale1 * -0.75 ; starting x-coordinate (upper left of array)
		scratchfloat3 = @nscale1 * 0.75 ; starting y-coordinate (upper left of array)
		scratchint = 0 ; index for calculation of y-coordinate
		glindex = 0
		while glindex <= numbervertices
			glindex3 = 0
			while glindex3 < squaresize
				scratchint2 = glindex + glindex3
				xcoord[scratchint2] = scratchfloat2 + scratchfloat * glindex3
				ycoord[scratchint2] = scratchfloat3 - scratchfloat * scratchint
				vertex[scratchint2] = xcoord[scratchint2] + flip(ycoord[scratchint2])
				glindex3 = glindex3 + 1
			endwhile ; glindex3
			glindex = glindex + squaresize
			scratchint = scratchint + 1
		endwhile ; glindex
	elseif traparray == 136 ; "triangular array"
		if @fixtrapbug
			triarraysize = @triarray1
		endif ; @fixtrapbug
		cursality = round(3*triarraysize*(triarraysize-1)/2 + 1) ; centered triangular numbers
		numbervertices = cursality ; single points, not line segments
		cincrement = 1 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @nscale1 * (0.333333, 0)
		vertex[2] = @nscale1 * (-0.166667, 0.288675)
		vertex[3] = @nscale1 * (-0.166667, -0.288675)
		vertex[4] = @nscale1 * (0.666667, 0)
		vertex[5] = @nscale1 * (0.166667, 0.288675)
		vertex[6] = @nscale1 * (-0.333333, 0.57735)
		vertex[7] = @nscale1 * (-0.333333, 0)
		vertex[8] = @nscale1 * (-0.333333, -0.57735)
		vertex[9] = @nscale1 * (0.166667, -0.288675)
		vertex[10] = @nscale1 * (1,0)
		vertex[11] = @nscale1 * (0.5, 0.288675)
		vertex[12] = @nscale1 * (0., 0.57735)
		vertex[13] = @nscale1 * (-0.5, 0.866025)
		vertex[14] = @nscale1 * (-0.5, 0.288675)
		vertex[15] = @nscale1 * (-0.5, -0.288675)
		vertex[16] = @nscale1 * (-0.5, -0.866025)
		vertex[17] = @nscale1 * (0., -0.57735)
		vertex[18] = @nscale1 * (0.5, -0.288675)
		glindex = 0
		while glindex <= numbervertices
				xcoord[glindex] = real(vertex[glindex])
				ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 137 ; "triangular spiral"
		if @fixtrapbug
			spiralsize = @spiralorder1
		endif ; @fixtrapbug
		cursality = 1
		if spiralsize == 1
			numbervertices = 4
			cincrement = 4 ; numbervertices/cursality
		elseif spiralsize == 2
			numbervertices = 7
			cincrement = 7
		elseif spiralsize == 3
			numbervertices = 10
			cincrement = 10
		elseif spiralsize == 4
			numbervertices = 13
			cincrement = 13
		endif ; spiralsize[]
		; initialize arrays
		vertex[0] = shrink2 * @nscale1 * (0.3,0)
		vertex[1] = shrink2 * @nscale1 * (-0.2, 0.34641)
		vertex[2] = shrink2 * @nscale1 * (-0.3, -0.519615)
		vertex[3] = shrink2 * @nscale1 * (0.8,0)
		vertex[4] = shrink2 * @nscale1 * (-0.5, 0.866025)
		vertex[5] = shrink2 * @nscale1 * (-0.6, -1.03923)
		vertex[6] = shrink2 * @nscale1 * (1.4,0)
		vertex[7] = shrink2 * @nscale1 * (-0.8, 1.38564)
		vertex[8] = shrink2 * @nscale1 * (-0.9, -1.55885)
		vertex[9] = shrink2 * @nscale1 * (2,0)
		vertex[10] = shrink2 * @nscale1 * (-1.1, 1.90526)
		vertex[11] = shrink2 * @nscale1 * (-1.2, -2.07846)
		vertex[12] = shrink2 * @nscale1 * (2.6,0)
		glindex = 0
		while glindex <= numbervertices
				xcoord[glindex] = real(vertex[glindex])
				ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 138 ; "square spiral"
		if @fixtrapbug
			spiralsize = @spiralorder1
		endif ; @fixtrapbug
		cursality = 1
		if spiralsize == 1
			numbervertices = 5
			cincrement = 5 ; numbervertices/cursality
		elseif spiralsize == 2
			numbervertices = 9
			cincrement = 9
		elseif spiralsize == 3
			numbervertices = 13
			cincrement = 13
		elseif spiralsize == 4
			numbervertices = 17
			cincrement = 17
		endif ; spiralsize[]
		; initialize arrays
		vertex[0] = shrink2 * @nscale1 * (0.3,0)
		vertex[1] = shrink2 * @nscale1 * (0,0.4)
		vertex[2] = shrink2 * @nscale1 * (-0.6,0)
		vertex[3] = shrink2 * @nscale1 * (0,-0.8)
		vertex[4] = shrink2 * @nscale1 * (1,0)
		vertex[5] = shrink2 * @nscale1 * (0,1.2)
		vertex[6] = shrink2 * @nscale1 * (-1.4,0)
		vertex[7] = shrink2 * @nscale1 * (0,-1.6)
		vertex[8] = shrink2 * @nscale1 * (1.8,0)
		vertex[9] = shrink2 * @nscale1 * (0,2)
		vertex[10] = shrink2 * @nscale1 * (-2.2,0)
		vertex[11] = shrink2 * @nscale1 * (0,-2.4)
		vertex[12] = shrink2 * @nscale1 * (2.6,0)
		vertex[13] = shrink2 * @nscale1 * (0,2.8)
		vertex[14] = shrink2 * @nscale1 * (-3,0)
		vertex[15] = shrink2 * @nscale1 * (0,-3.2)
		vertex[16] = shrink2 * @nscale1 * (3.4,0)
		glindex = 0
		while glindex <= numbervertices
				xcoord[glindex] = real(vertex[glindex])
				ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 139 ; "pentagonal array"
		if @fixtrapbug
			triarraysize = @triarray1
		endif ; @fixtrapbug
		scratchint = triarraysize - 1
		cursality = round((5*sqr(scratchint)+(5*scratchint)+2)/2) ; centered pentagonal numbers
		numbervertices = cursality ; single points, not line segments
		cincrement = 1 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @nscale1 * (0.333333, 0)
		vertex[2] = @nscale1 * (0.103006, 0.317019)
		vertex[3] = @nscale1 * (-0.269672, 0.195928)
		vertex[4] = @nscale1 * (-0.269672, -0.195928)
		vertex[5] = @nscale1 * (0.103006, -0.317019)
		vertex[6] = @nscale1 * (0.666667, 0)
		vertex[7] = @nscale1 * (0.436339, 0.317019)
		vertex[8] = @nscale1 * (0.206011, 0.634038)
		vertex[9] = @nscale1 * (-0.166667, 0.512947)
		vertex[10] = @nscale1 * (-0.539345, 0.391857)
		vertex[11] = @nscale1 * (-0.539345, 0)
		vertex[12] = @nscale1 * (-0.539345, -0.391857)
		vertex[13] = @nscale1 * (-0.166667, -0.512947)
		vertex[14] = @nscale1 * (0.206011, -0.634038)
		vertex[15] = @nscale1 * (0.436339, -0.317019)
		vertex[16] = @nscale1 * (1,0)
		vertex[17] = @nscale1 * (0.769672, 0.317019)
		vertex[18] = @nscale1 * (0.539345, 0.634038)
		vertex[19] = @nscale1 * (0.309017, 0.951057)
		vertex[20] = @nscale1 * (-0.063661, 0.829966)
		vertex[21] = @nscale1 * (-0.436339, 0.708876)
		vertex[22] = @nscale1 * (-0.809017, 0.587785)
		vertex[23] = @nscale1 * (-0.809017, 0.195928)
		vertex[24] = @nscale1 * (-0.809017, -0.195928)
		vertex[25] = @nscale1 * (-0.809017, -0.587785)
		vertex[26] = @nscale1 * (-0.436339, -0.708876)
		vertex[27] = @nscale1 * (-0.063661, -0.829966)
		vertex[28] = @nscale1 * (0.309017, -0.951057)
		vertex[29] = @nscale1 * (0.539345, -0.634038)
		vertex[30] = @nscale1 * (0.769672, -0.317019)
		glindex = 0
		while glindex <= numbervertices
				xcoord[glindex] = real(vertex[glindex])
				ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 140 ; "hexagonal array"
		if @fixtrapbug
			triarraysize = @triarray1
		endif ; @fixtrapbug
		cursality = round(3*(triarraysize-1)*(triarraysize)+1) ; centered hexagonal numbers
		numbervertices = cursality ; single points, not line segments
		cincrement = 1 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0,0)
		vertex[1] = @nscale1 * (0.333333, 0)
		vertex[2] = @nscale1 * (0.166667, 0.288675)
		vertex[3] = @nscale1 * (-0.166667, 0.288675)
		vertex[4] = @nscale1 * (-0.333333, 0)
		vertex[5] = @nscale1 * (-0.166667, -0.288675)
		vertex[6] = @nscale1 * (0.166667, -0.288675)
		vertex[7] = @nscale1 * (0.666667, 0)
		vertex[8] = @nscale1 * (0.5, 0.288675)
		vertex[9] = @nscale1 * (0.333333, 0.57735)
		vertex[10] = @nscale1 * (0., 0.57735)
		vertex[11] = @nscale1 * (-0.333333, 0.57735)
		vertex[12] = @nscale1 * (-0.5, 0.288675)
		vertex[13] = @nscale1 * (-0.666667, 0)
		vertex[14] = @nscale1 * (-0.5, -0.288675)
		vertex[15] = @nscale1 * (-0.333333, -0.57735)
		vertex[16] = @nscale1 * (0., -0.57735)
		vertex[17] = @nscale1 * (0.333333, -0.57735)
		vertex[18] = @nscale1 * (0.5, -0.288675)
		vertex[19] = @nscale1 * (1,0)
		vertex[20] = @nscale1 * (0.833333, 0.288675)
		vertex[21] = @nscale1 * (0.666667, 0.57735)
		vertex[22] = @nscale1 * (0.5, 0.866025)
		vertex[23] = @nscale1 * (0.166667, 0.866025)
		vertex[24] = @nscale1 * (-0.5, 0.866025)
		vertex[25] = @nscale1 * (-0.666667, 0.57735)
		vertex[26] = @nscale1 * (-0.833333, 0.288675)
		vertex[27] = @nscale1 * (-1,0)
		vertex[28] = @nscale1 * (-0.833333, -0.288675)
		vertex[29] = @nscale1 * (-0.166667, 0.866025)
		vertex[30] = @nscale1 * (-0.666667, -0.57735)
		vertex[31] = @nscale1 * (-0.5, -0.866025)
		vertex[32] = @nscale1 * (-0.166667, -0.866025)
		vertex[33] = @nscale1 * (0.166667, -0.866025)
		vertex[34] = @nscale1 * (0.5, -0.866025)
		vertex[35] = @nscale1 * (0.666667, -0.57735)
		vertex[36] = @nscale1 * (0.833333, -0.288675)
		glindex = 0
		while glindex <= numbervertices
				xcoord[glindex] = real(vertex[glindex])
				ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 141 ; "pentagonal spiral"
		if @fixtrapbug
			spiralsize = @spiralorder1
		endif ; @fixtrapbug
		cursality = 1
		if spiralsize == 1
			numbervertices = 6
			cincrement = 6 ; numbervertices/cursality
		elseif spiralsize == 2
			numbervertices = 11
			cincrement = 11
		elseif spiralsize == 3
			numbervertices = 16
			cincrement = 16
		elseif spiralsize == 4
			numbervertices = 21
			cincrement = 21
		endif ; spiralsize[]
		; initialize arrays
		vertex[0] = shrink3 * @nscale1 * (0.3,0)
		vertex[1] = shrink3 * @nscale1 * (0.123607, 0.380423)
		vertex[2] = shrink3 * @nscale1 * (-0.48541, 0.352671)
		vertex[3] = shrink3 * @nscale1 * (-0.647214, -0.470228)
		vertex[4] = shrink3 * @nscale1 * (0.309017, -0.951057)
		vertex[5] = shrink3 * @nscale1 * (1.2,0)
		vertex[6] = shrink3 * @nscale1 * (0.432624, 1.33148)
		vertex[7] = shrink3 * @nscale1 * (-1.29443, 0.940456)
		vertex[8] = shrink3 * @nscale1 * (-1.45623, -1.05801)
		vertex[9] = shrink3 * @nscale1 * (0.618034, -1.90211)
		vertex[10] = shrink3 * @nscale1 * (2.2,0)
		vertex[11] = shrink3 * @nscale1 * (0.741641, 2.28254)
		vertex[12] = shrink3 * @nscale1 * (-2.10344, 1.52824)
		vertex[13] = shrink3 * @nscale1 * (-2.26525, -1.6458)
		vertex[14] = shrink3 * @nscale1 * (0.927051, -2.85317)
		vertex[15] = shrink3 * @nscale1 * (3.2,0)
		vertex[16] = shrink3 * @nscale1 * (1.05066, 3.23359)
		vertex[17] = shrink3 * @nscale1 * (-2.91246, 2.11603)
		vertex[18] = shrink3 * @nscale1 * (-3.07426, -2.23358)
		vertex[19] = shrink3 * @nscale1 * (1.23607, -3.80423)
		vertex[20] = shrink3 * @nscale1 * (4.2,0)
		glindex = 0
		while glindex <= numbervertices
				xcoord[glindex] = real(vertex[glindex])
				ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 142 ; "hexagonal spiral"
		if @fixtrapbug
			spiralsize = @spiralorder1
		endif ; @fixtrapbug
		cursality = 1
		if spiralsize == 1
			numbervertices = 7
			cincrement = 7 ; numbervertices/cursality
		elseif spiralsize == 2
			numbervertices = 13
			cincrement = 13
		elseif spiralsize == 3
			numbervertices = 19
			cincrement = 19
		elseif spiralsize == 4
			numbervertices = 25
			cincrement = 25
		endif ; spiralsize[]
		; initialize arrays
		vertex[0] = shrink3 * @nscale1 * (0.3,0)
		vertex[1] = shrink3 * @nscale1 * (0.2, 0.34641)
		vertex[2] = shrink3 * @nscale1 * (-0.3, 0.519615)
		vertex[3] = shrink3 * @nscale1 * (-0.8, 0)
		vertex[4] = shrink3 * @nscale1 * (-0.5, -0.866025)
		vertex[5] = shrink3 * @nscale1 * (0.6, -1.03923)
		vertex[6] = shrink3 * @nscale1 * (1.4,0)
		vertex[7] = shrink3 * @nscale1 * (0.8, 1.38564)
		vertex[8] = shrink3 * @nscale1 * (-0.9, 1.55885)
		vertex[9] = shrink3 * @nscale1 * (-2,0)
		vertex[10] = shrink3 * @nscale1 * (-1.1, -1.90526)
		vertex[11] = shrink3 * @nscale1 * (1.2, -2.07846)
		vertex[12] = shrink3 * @nscale1 * (2.6,0)
		vertex[13] = shrink3 * @nscale1 * (1.4, 2.42487)
		vertex[14] = shrink3 * @nscale1 * (-1.5, 2.59808)
		vertex[15] = shrink3 * @nscale1 * (-3.2,0)
		vertex[16] = shrink3 * @nscale1 * (-1.7, -2.94449)
		vertex[17] = shrink3 * @nscale1 * (1.8, -3.11769)
		vertex[18] = shrink3 * @nscale1 * (3.8,0)
		vertex[19] = shrink3 * @nscale1 * (2, 3.4641)
		vertex[20] = shrink3 * @nscale1 * (-2.1, 3.63731)
		vertex[21] = shrink3 * @nscale1 * (-4.4,0)
		vertex[22] = shrink3 * @nscale1 * (-2.3, -3.98372)
		vertex[23] = shrink3 * @nscale1 * (2.4, -4.15692)
		vertex[24] = shrink3 * @nscale1 * (5,0)
		glindex = 0
		while glindex <= numbervertices
				xcoord[glindex] = real(vertex[glindex])
				ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 143 ; "octagonal spiral"
		if @fixtrapbug
			spiralsize = @spiralorder1
		endif ; @fixtrapbug
		cursality = 1
		if spiralsize == 1
			numbervertices = 9
			cincrement = 9 ; numbervertices/cursality
		elseif spiralsize == 2
			numbervertices = 17
			cincrement = 17
		elseif spiralsize == 3
			numbervertices = 25
			cincrement = 25
		elseif spiralsize == 4
			numbervertices = 33
			cincrement = 33
		endif ; spiralsize[]
		; initialize arrays
		vertex[0] = shrink3 * @nscale1 * (0.3,0)
		vertex[1] = shrink3 * @nscale1 * (0.282843, 0.282843)
		vertex[2] = shrink3 * @nscale1 * (0,0.6)
		vertex[3] = shrink3 * @nscale1 * (-0.565685, 0.565685)
		vertex[4] = shrink3 * @nscale1 * (-1,0)
		vertex[5] = shrink3 * @nscale1 * (-0.848528, -0.848528)
		vertex[6] = shrink3 * @nscale1 * (0,-1.4)
		vertex[7] = shrink3 * @nscale1 * (1.13137, -1.13137)
		vertex[8] = shrink3 * @nscale1 * (1.8,0)
		vertex[9] = shrink3 * @nscale1 * (1.41421, 1.41421)
		vertex[10] = shrink3 * @nscale1 * (0,2.2)
		vertex[11] = shrink3 * @nscale1 * (-1.69706, 1.69706)
		vertex[12] = shrink3 * @nscale1 * (-2.6,0)
		vertex[13] = shrink3 * @nscale1 * (-1.9799, -1.9799)
		vertex[14] = shrink3 * @nscale1 * (0,-3)
		vertex[15] = shrink3 * @nscale1 * (2.26274, -2.26274)
		vertex[16] = shrink3 * @nscale1 * (3.4,0)
		vertex[17] = shrink3 * @nscale1 * (2.54558, 2.54558)
		vertex[18] = shrink3 * @nscale1 * (0,3.8)
		vertex[19] = shrink3 * @nscale1 * (-2.82843, 2.82843)
		vertex[20] = shrink3 * @nscale1 * (-4.2,0)
		vertex[21] = shrink3 * @nscale1 * (-3.11127, -3.11127)
		vertex[22] = shrink3 * @nscale1 * (0,-4.6)
		vertex[23] = shrink3 * @nscale1 * (3.39411, -3.39411)
		vertex[24] = shrink3 * @nscale1 * (5,0)
		vertex[25] = shrink3 * @nscale1 * (3.67696, 3.67696)
		vertex[26] = shrink3 * @nscale1 * (0,5.4)
		vertex[27] = shrink3 * @nscale1 * (-3.9598, 3.9598)
		vertex[28] = shrink3 * @nscale1 * (-5.8,0)
		vertex[29] = shrink3 * @nscale1 * (-4.24264, -4.24264)
		vertex[30] = shrink3 * @nscale1 * (0,-6.2)
		vertex[31] = shrink3 * @nscale1 * (4.52548, -4.52548)
		vertex[32] = shrink3 * @nscale1 * (6.6,0)
		glindex = 0
		while glindex <= numbervertices
				xcoord[glindex] = real(vertex[glindex])
				ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 144 ; "superellipse"
		if @fixtrapbug
			ellipseX = @ellipseexponent1
			ellipseH = @ellipseheight1
			ellipseW = @ellipsewidth1
		endif ; @fixtrapbug
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		cursality = 1
		numbervertices = granularity ; open curve as plotted
		cincrement = granularity ; numbervertices/cursality
		scratchfloat = 2/ellipseX
		scratchint = round(granularity/2)
		scratchint2 = round(granularity/4)
		; initialize arrays
		glindex = 0
		while glindex < scratchint2
			xcoord[glindex] = @nscale1 * ellipseH * (cos(glindex * halfpi/scratchint2)^scratchfloat)
			ycoord[glindex] = @nscale1 * ellipseW * (sin(glindex * halfpi /scratchint2)^scratchfloat)
			glindex = glindex + 1
		endwhile ; glindex
		glindex = 0
		while glindex < scratchint2
			xcoord[glindex + scratchint2] = -xcoord[scratchint2-1-glindex]
			ycoord[glindex + scratchint2] = ycoord[scratchint2-1-glindex]
			glindex = glindex + 1
		endwhile ; glindex
		glindex = 0
		while glindex < scratchint
			xcoord[glindex + scratchint] = xcoord[scratchint-1-glindex]
			ycoord[glindex + 36] = -ycoord[scratchint-1-glindex]
			glindex = glindex + 1
		endwhile ; glindex
		glindex = 0
		while glindex < granularity
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 145 ; "hypotrochoid"
		if @fixtrapbug
			hypotroA = @hypotrochA1
			hypotroB = @hypotrochB1
			hypotroH = @hypotrochH1
		endif ; @fixtrapbug
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1
		cursality = 1
		numbervertices = granularity2 ; vertices + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		scratchfloat = hypotroA - hypotroB
		scratchfloat2 = scratchfloat/hypotroB
		scratchfloat3 = twopi/granularity
		while glindex < granularity2
			xcoord[glindex] = @nscale1 * (scratchfloat * cos(glindex * scratchfloat3) + hypotroH * cos(scratchfloat2 * glindex * scratchfloat3))
			ycoord[glindex] = @nscale1 * (scratchfloat * sin(glindex * scratchfloat3) - hypotroH * sin(scratchfloat2 * glindex * scratchfloat3))
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[granularity2] = xcoord[0]
		ycoord[granularity2] = ycoord[0]
		vertex[granularity2] = xcoord[granularity2] + flip(ycoord[granularity2])
	elseif traparray == 146 ; "epitrochoid"
		if @fixtrapbug
			hypotroA = @hypotrochA1
			hypotroB = @hypotrochB1
			hypotroH = @hypotrochH1
		endif ; @fixtrapbug
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1
		cursality = 1
		numbervertices = granularity2 ; vertices + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		scratchfloat = hypotroA + hypotroB
		scratchfloat2 = scratchfloat/hypotroB
		scratchfloat3 = twopi/granularity
		while glindex < granularity2
			xcoord[glindex] = @nscale1 * (scratchfloat * cos(glindex * scratchfloat3) - hypotroH * cos(scratchfloat2 * glindex * scratchfloat3))
			ycoord[glindex] = @nscale1 *  (scratchfloat * sin(glindex * scratchfloat3) - hypotroH * sin(scratchfloat2 * glindex * scratchfloat3))
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[granularity2] = xcoord[0]
		ycoord[granularity2] = ycoord[0]
		vertex[granularity2] = xcoord[granularity2] + flip(ycoord[granularity2])
	elseif traparray == 148 ; "honeycomb"
		cursality = 6
		numbervertices = 36 ; n for open curves
		cincrement = 6 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @nscale1 * (0.25, 0.433013)
		vertex[2] = @nscale1 * (0.5, 0.866026)
		vertex[3] = @nscale1 * (1., 0.866026)
		vertex[4] = @nscale1 * (1.25, 0.433013)
		vertex[5] = @nscale1 * (1,0)
		vertex[6] = @nscale1 * (0.25, 0.433013)
		vertex[7] = @nscale1 * (-0.25, 0.433013)
		vertex[8] = @nscale1 * (-0.5, 0.866026)
		vertex[9] = @nscale1 * (-0.25, 1.29904)
		vertex[10] = @nscale1 * (0.25, 1.29904)
		vertex[11] = @nscale1 * (0.5, 0.866026)
		vertex[12] = @nscale1 * (-0.25, 0.433013)
		vertex[13] = @nscale1 * (-0.5,0)
		vertex[14] = @nscale1 * (-1,0)
		vertex[15] = @nscale1 * (-1.25, 0.433013)
		vertex[16] = @nscale1 * (-1., 0.866026)
		vertex[17] = @nscale1 * (-0.5, 0.866026)
		vertex[18] = @nscale1 * (-0.5,0)
		vertex[19] = @nscale1 * (-0.25, -0.433013)
		vertex[20] = @nscale1 * (-0.5, -0.866026)
		vertex[21] = @nscale1 * (-1., -0.866026)
		vertex[22] = @nscale1 * (-1.25, -0.433013)
		vertex[23] = @nscale1 * (-1,0)
		vertex[24] = @nscale1 * (-0.25, -0.433013)
		vertex[25] = @nscale1 * (0.25, -0.433013)
		vertex[26] = @nscale1 * (0.5, -0.866026)
		vertex[27] = @nscale1 * (0.25, -1.29904)
		vertex[28] = @nscale1 * (-0.25, -1.29904)
		vertex[29] = @nscale1 * (-0.5, -0.866026)
		vertex[30] = @nscale1 * (0.25, -0.433013)
		vertex[31] = @nscale1 * (0.5,0)
		vertex[32] = @nscale1 * (1,0)
		vertex[33] = @nscale1 * (1.25, -0.433013)
		vertex[34] = @nscale1 * (1., -0.866026)
		vertex[35] = @nscale1 * (0.5, -0.866026)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 149 ; "nested circles"
		if @fixtrapbug
			numbercircles = @circlenum1
		endif ; @fixtrapbug
		glindex3 = 0
		if numbercircles == 2
			cursality = 2
			numbervertices = 120
			cincrement = 60 ; numbervertices/cursality
			scratchfloat = twopi/59 ; angle increment, cincrement - 1 to close curve
			; initialize arrays
			while glindex3 < 2 ; cursality
				scratchfloat2 = (glindex3+1)/2 * @nscale1 ; fixes radius of the various circles
				glindex = 0
				while glindex < 60 ; cincrement
					scratchint = glindex3*60 + glindex ; saves a bit of redundant calculation
					xcoord[scratchint] = scratchfloat2 * cos(scratchfloat*glindex)
					ycoord[scratchint] = scratchfloat2 * sin(scratchfloat*glindex)
					vertex[scratchint] = xcoord[scratchint] + flip(ycoord[scratchint])
					glindex = glindex + 1
				endwhile ; glindex
				glindex3 = glindex3 + 1
			endwhile ; glindex3
		elseif numbercircles == 3
			cursality = 3
			numbervertices = 150
			cincrement = 50 ; numbervertices/cursality
			scratchfloat = twopi/49 ; angle increment
			; initialize arrays
			while glindex3 < 3
				scratchfloat2 = (glindex3+1)/3 * @nscale1 ; fixes radius of the various circles
				glindex = 0
				while glindex < 50
					scratchint = glindex3*50 + glindex
					xcoord[scratchint] = scratchfloat2 * cos(scratchfloat*glindex)
					ycoord[scratchint] = scratchfloat2 * sin(scratchfloat*glindex)
					vertex[scratchint] = xcoord[scratchint] + flip(ycoord[scratchint])
					glindex = glindex + 1
				endwhile ; glindex
				glindex3 = glindex3 + 1
			endwhile ; glindex3
		elseif numbercircles == 4
			cursality = 4
			numbervertices = 200
			cincrement = 50 ; numbervertices/cursality
			scratchfloat = twopi/49 ; angle increment
			; initialize arrays
			while glindex3 < 4
				scratchfloat2 = (glindex3+1)/4 * @nscale1 ; fixes radius of the various circles
				glindex = 0
				while glindex < 50
					scratchint = glindex3*50 + glindex
					xcoord[scratchint] = scratchfloat2 * cos(scratchfloat*glindex)
					ycoord[scratchint] = scratchfloat2 * sin(scratchfloat*glindex)
					vertex[scratchint] = xcoord[scratchint] + flip(ycoord[scratchint])
					glindex = glindex + 1
				endwhile ; glindex
				glindex3 = glindex3 + 1
			endwhile ; glindex3
		endif ; numbercircles[]
	elseif traparray == 150 ; "osculant circles"
		if @fixtrapbug
			numbercircles = @circlenum1
		endif ; @fixtrapbug
		glindex3 = 0
		if numbercircles == 2
			cursality = 2
			numbervertices = 120
			cincrement = 60 ; numbervertices/cursality
			scratchfloat = twopi/59 ; angle increment, cincrement - 1 to close curve
			; initialize arrays
			while glindex3 < 2 ; cursality
				scratchfloat2 = (glindex3+1)/2 * @nscale1 ; fixes radius of the various circles
				scratchfloat3 = @nscale1 - scratchfloat2 ; distance to translate current circle to touch largest circle
				glindex = 0
				while glindex < 60 ; cincrement
					scratchint = glindex3*60 + glindex ; saves a bit of redundant calculation
					xcoord[scratchint] = scratchfloat2 * cos(scratchfloat*glindex) + scratchfloat3
					ycoord[scratchint] = scratchfloat2 * sin(scratchfloat*glindex)
					vertex[scratchint] = xcoord[scratchint] + flip(ycoord[scratchint])
					glindex = glindex + 1
				endwhile ; glindex
				glindex3 = glindex3 + 1
			endwhile ; glindex3
		elseif numbercircles == 3
			cursality = 3
			numbervertices = 150
			cincrement = 50 ; numbervertices/cursality
			scratchfloat = twopi/49 ; angle increment
			; initialize arrays
			while glindex3 < 3
				scratchfloat2 = (glindex3+1)/3 * @nscale1 ; fixes radius of the various circles
				scratchfloat3 = @nscale1 - scratchfloat2 ; distance to translate current circle to touch largest circle
				glindex = 0
				while glindex < 50
					scratchint = glindex3*50 + glindex
					xcoord[scratchint] = scratchfloat2 * cos(scratchfloat*glindex) + scratchfloat3
					ycoord[scratchint] = scratchfloat2 * sin(scratchfloat*glindex)
					vertex[scratchint] = xcoord[scratchint] + flip(ycoord[scratchint])
					glindex = glindex + 1
				endwhile ; glindex
				glindex3 = glindex3 + 1
			endwhile ; glindex3
		elseif numbercircles == 4
			cursality = 4
			numbervertices = 200
			cincrement = 50 ; numbervertices/cursality
			scratchfloat = twopi/49 ; angle increment
			; initialize arrays
			while glindex3 < 4
				scratchfloat2 = (glindex3+1)/4 * @nscale1 ; fixes radius of the various circles
				scratchfloat3 = @nscale1 - scratchfloat2 ; distance to translate current circle to touch largest circle
				glindex = 0
				while glindex < 50
					scratchint = glindex3*50 + glindex
					xcoord[scratchint] = scratchfloat2 * cos(scratchfloat*glindex) + scratchfloat3
					ycoord[scratchint] = scratchfloat2 * sin(scratchfloat*glindex)
					vertex[scratchint] = xcoord[scratchint] + flip(ycoord[scratchint])
					glindex = glindex + 1
				endwhile ; glindex
				glindex3 = glindex3 + 1
			endwhile ; glindex3
		endif ; numbercircles[]
	elseif traparray == 152 ; "11-gon"
		cursality = 1
		numbervertices = 12 ; vertices + cursality for closed curves
		cincrement = 12 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(glindex * twopi / 11)
			ycoord[glindex] = @nscale1 * sin(glindex * twopi / 11)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 157 ; "12-gon"
		cursality = 1
		numbervertices = 13 ; vertices + cursality for closed curves
		cincrement = 13 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(glindex * twopi / 12)
			ycoord[glindex] = @nscale1 * sin(glindex * twopi / 12)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 153 ; "11-gram 1"
		cursality = 1
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 12 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.415415, 0.909632)
		vertex[2] = @nscale1 * (-0.654861, 0.75575)
		vertex[3] = @nscale1 * (-0.959493, -0.281733)
		vertex[4] = @nscale1 * (-0.142315, -0.989821)
		vertex[5] = @nscale1 * (0.841254, -0.540641)
		vertex[6] = @nscale1 * (0.841254, 0.540641)
		vertex[7] = @nscale1 * (-0.142315, 0.989821)
		vertex[8] = @nscale1 * (-0.959493, 0.281733)
		vertex[9] = @nscale1 * (-0.654861, -0.75575)
		vertex[10] = @nscale1 * (0.415415, -0.909632)
		vertex[11] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 154 ; "11-gram 2"
		cursality = 1
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 12 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.142315, 0.989821)
		vertex[2] = @nscale1 * (-0.959493, -0.281733)
		vertex[3] = @nscale1 * (0.415415, -0.909632)
		vertex[4] = @nscale1 * (0.841254, 0.540641)
		vertex[5] = @nscale1 * (-0.654861, 0.75575)
		vertex[6] = @nscale1 * (-0.654861, -0.75575)
		vertex[7] = @nscale1 * (0.841254, -0.540641)
		vertex[8] = @nscale1 * (0.415415, 0.909632)
		vertex[9] = @nscale1 * (-0.959493, 0.281733)
		vertex[10] = @nscale1 * (-0.142315, -0.989821)
		vertex[11] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 155 ; "11-gram 3"
		cursality = 1
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 12 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.654861, 0.75575)
		vertex[2] = @nscale1 * (-0.142315, -0.989821)
		vertex[3] = @nscale1 * (0.841254, 0.540641)
		vertex[4] = @nscale1 * (-0.959493, 0.281733)
		vertex[5] = @nscale1 * (0.415415, -0.909632)
		vertex[6] = @nscale1 * (0.415415, 0.909632)
		vertex[7] = @nscale1 * (-0.959493, -0.281733)
		vertex[8] = @nscale1 * (0.841254, -0.540641)
		vertex[9] = @nscale1 * (-0.142315, 0.989821)
		vertex[10] = @nscale1 * (-0.654861, -0.75575)
		vertex[11] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 156 ; "11-gram 4"
		cursality = 1
		numbervertices = 12 ; n + cursality for closed curves
		cincrement = 12 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.959493, 0.281733)
		vertex[2] = @nscale1 * (0.841254, -0.540641)
		vertex[3] = @nscale1 * (-0.654861, 0.75575)
		vertex[4] = @nscale1 * (0.415415, -0.909632)
		vertex[5] = @nscale1 * (-0.142315, 0.989821)
		vertex[6] = @nscale1 * (-0.142315, -0.989821)
		vertex[7] = @nscale1 * (0.415415, 0.909632)
		vertex[8] = @nscale1 * (-0.654861, -0.75575)
		vertex[9] = @nscale1 * (0.841254, 0.540641)
		vertex[10] = @nscale1 * (-0.959493, -0.281733)
		vertex[11] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 158 ; "12-gram 1"
		cursality = 2
		numbervertices = 14 ; n + cursality for closed curves
		cincrement = 7 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0.5, 0.866025)
		vertex[2] = @nscale1 * (-0.5, 0.866025)
		vertex[3] = @nscale1 * (-1,0)
		vertex[4] = @nscale1 * (-0.5, -0.866025)
		vertex[5] = @nscale1 * (0.5, -0.866025)
		vertex[6] = @nscale1 * (1,0)
		vertex[7] = @nscale1 * (0.866025, 0.5)
		vertex[8] = @nscale1 * (0,1)
		vertex[9] = @nscale1 * (-0.866025, 0.5)
		vertex[10] = @nscale1 * (-0.866025, -0.5)
		vertex[11] = @nscale1 * (0,-1)
		vertex[12] = @nscale1 * (0.866025, -0.5)
		vertex[13] = @nscale1 * (0.866025, 0.5)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 159 ; "12-gram 2"
		cursality = 3
		numbervertices = 15 ; n + cursality for closed curves
		cincrement = 5 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (0,1)
		vertex[2] = @nscale1 * (-1,0)
		vertex[3] = @nscale1 * (0,-1)
		vertex[4] = @nscale1 * (1,0)
		vertex[5] = @nscale1 * (0.866025, 0.5)
		vertex[6] = @nscale1 * (-0.5, 0.866025)
		vertex[7] = @nscale1 * (-0.866025, -0.5)
		vertex[8] = @nscale1 * (0.5, -0.866025)
		vertex[9] = @nscale1 * (0.866025, 0.5)
		vertex[10] = @nscale1 * (0.5, 0.866025)
		vertex[11] = @nscale1 * (-0.866025, 0.5)
		vertex[12] = @nscale1 * (-0.5, -0.866025)
		vertex[13] = @nscale1 * (0.866025, -0.5)
		vertex[14] = @nscale1 * (0.5, 0.866025)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 160 ; "12-gram 3"
		cursality = 4
		numbervertices = 16 ; n + cursality for closed curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.5, 0.866025)
		vertex[2] = @nscale1 * (-0.5, -0.866025)
		vertex[3] = @nscale1 * (1,0)
		vertex[4] = @nscale1 * (0.866025, 0.5)
		vertex[5] = @nscale1 * (-0.866025, 0.5)
		vertex[6] = @nscale1 * (0,-1)
		vertex[7] = @nscale1 * (0.866025, 0.5)
		vertex[8] = @nscale1 * (0.5, 0.866025)
		vertex[9] = @nscale1 * (-1,0)
		vertex[10] = @nscale1 * (0.5, -0.866025)
		vertex[11] = @nscale1 * (0.5, 0.866025)
		vertex[12] = @nscale1 * (0,1)
		vertex[13] = @nscale1 * (-0.866025, -0.5)
		vertex[14] = @nscale1 * (0.866025, -0.5)
		vertex[15] = @nscale1 * (0,1)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 161 ; "12-gram 4"
		cursality = 1
		numbervertices = 13 ; n + cursality for closed curves
		cincrement = 13 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (1,0)
		vertex[1] = @nscale1 * (-0.866025, 0.5)
		vertex[2] = @nscale1 * (0.5, -0.866025)
		vertex[3] = @nscale1 * (0,1)
		vertex[4] = @nscale1 * (-0.5, -0.866025)
		vertex[5] = @nscale1 * (0.866025, 0.5)
		vertex[6] = @nscale1 * (-1,0)
		vertex[7] = @nscale1 * (0.866025, -0.5)
		vertex[8] = @nscale1 * (-0.5, 0.866025)
		vertex[9] = @nscale1 * (0,-1)
		vertex[10] = @nscale1 * (0.5, 0.866025)
		vertex[11] = @nscale1 * (-0.866025, -0.5)
		vertex[12] = @nscale1 * (1,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 162 ; "12-gram 5"
		cursality = 1
		numbervertices = 13 ; n + cursality for closed curves
		cincrement = 13 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.866025, 0.5)
		vertex[1] = @nscale1 * (-0.375, -0.649519)
		vertex[2] = @nscale1 * (0,1)
		vertex[3] = @nscale1 * (0.375, -0.649519)
		vertex[4] = @nscale1 * (-0.866025, 0.5)
		vertex[5] = @nscale1 * (0.75,0)
		vertex[6] = @nscale1 * (-0.866025, -0.5)
		vertex[7] = @nscale1 * (0.375, 0.649519)
		vertex[8] = @nscale1 * (0,-1)
		vertex[9] = @nscale1 * (-0.375, 0.649519)
		vertex[10] = @nscale1 * (0.866025, -0.5)
		vertex[11] = @nscale1 * (-0.75,0)
		vertex[12] = @nscale1 * (0.866025, 0.5)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 163 ; "11-star"
		cursality = 1
		numbervertices = 23 ; n + cursality for closed curves
		cincrement = 23 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @starspikiness * @nscale1 * (0.959493, 0.281733)
		vertex[2] = @nscale1 * (0.420627, 0.27032)
		vertex[3] = @starspikiness * @nscale1 * (0.654861, 0.75575)
		vertex[4] = @nscale1 * (0.207708, 0.454816)
		vertex[5] = @starspikiness * @nscale1 * (0.142315, 0.989821)
		vertex[6] = @nscale1 * (-0.0711574, 0.494911)
		vertex[7] = @starspikiness * @nscale1 * (-0.415415, 0.909632)
		vertex[8] = @nscale1 * (-0.32743, 0.377875)
		vertex[9] = @starspikiness * @nscale1 * (-0.841254, 0.540641)
		vertex[10] = @nscale1 * (-0.479746, 0.140866)
		vertex[11] = @starspikiness * @nscale1 * (-1,0)
		vertex[12] = @nscale1 * (-0.479746, -0.140866)
		vertex[13] = @starspikiness * @nscale1 * (-0.841254, -0.540641)
		vertex[14] = @nscale1 * (-0.32743, -0.377875)
		vertex[15] = @starspikiness * @nscale1 * (-0.415415, -0.909632)
		vertex[16] = @nscale1 * (-0.0711574, -0.494911)
		vertex[17] = @starspikiness * @nscale1 * (0.142315, -0.989821)
		vertex[18] = @nscale1 * (0.207708, -0.454816)
		vertex[19] = @starspikiness * @nscale1 * (0.654861, -0.75575)
		vertex[20] = @nscale1 * (0.420627, -0.27032)
		vertex[21] = @starspikiness * @nscale1 * (0.959493, -0.281733)
		vertex[22] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 165 ; "11-star 2"
		cursality = 1
		numbervertices = 23 ; n + cursality for closed curves
		cincrement = 23 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @nscale1 * (1,0)
		vertex[2] = @nscale1 * (0.420627, 0.27032)
		vertex[3] = @nscale1 * (0.841254, 0.540641)
		vertex[4] = @nscale1 * (0.207708, 0.454816)
		vertex[5] = @nscale1 * (0.415415, 0.909632)
		vertex[6] = @nscale1 * (-0.0711574, 0.494911)
		vertex[7] = @nscale1 * (-0.142315, 0.989821)
		vertex[8] = @nscale1 * (-0.32743, 0.377875)
		vertex[9] = @nscale1 * (-0.654861, 0.75575)
		vertex[10] = @nscale1 * (-0.479746, 0.140866)
		vertex[11] = @nscale1 * (-0.959493, 0.281733)
		vertex[12] = @nscale1 * (-0.479746, -0.140866)
		vertex[13] = @nscale1 * (-0.959493, -0.281733)
		vertex[14] = @nscale1 * (-0.32743, -0.377875)
		vertex[15] = @nscale1 * (-0.654861, -0.75575)
		vertex[16] = @nscale1 * (-0.0711574, -0.494911)
		vertex[17] = @nscale1 * (-0.142315, -0.989821)
		vertex[18] = @nscale1 * (0.207708, -0.454816)
		vertex[19] = @nscale1 * (0.415415, -0.909632)
		vertex[20] = @nscale1 * (0.420627, -0.27032)
		vertex[21] = @nscale1 * (0.841254, -0.540641)
		vertex[22] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 164 ; "11-asterisk"
		cursality = 11
		numbervertices = 22 ; vertices only for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			vertex[glindex] = (0,0)
			xcoord[glindex + 1] = @nscale1 * cos(glindex * #pi / 11)
			ycoord[glindex + 1] = @nscale1 * sin(glindex * #pi / 11)
			glindex = glindex + 1
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		vertex[1] = @leafAlength * vertex[1]
		xcoord[1] = real(vertex[1])
		ycoord[1] = imag(vertex[1])
		vertex[3] = @leafBlength * vertex[3]
		xcoord[3] = real(vertex[3])
		ycoord[3] = imag(vertex[3])
		vertex[5] = @leafClength * vertex[5]
		xcoord[5] = real(vertex[5])
		ycoord[5] = imag(vertex[5])
		vertex[7] = @leafDlength * vertex[7]
		xcoord[7] = real(vertex[7])
		ycoord[7] = imag(vertex[7])
		vertex[9] = @leafElength * vertex[9]
		xcoord[9] = real(vertex[9])
		ycoord[9] = imag(vertex[9])
		vertex[11] = @leafFlength * vertex[11]
		xcoord[11] = real(vertex[11])
		ycoord[11] = imag(vertex[11])
		vertex[13] = @leafGlength * vertex[13]
		xcoord[13] = real(vertex[13])
		ycoord[13] = imag(vertex[13])
		vertex[15] = @leafHlength * vertex[15]
		xcoord[15] = real(vertex[15])
		ycoord[15] = imag(vertex[15])
		vertex[17] = @leafIlength * vertex[17]
		xcoord[17] = real(vertex[17])
		ycoord[17] = imag(vertex[17])
		vertex[19] = @leafJlength * vertex[19]
		xcoord[19] = real(vertex[19])
		ycoord[19] = imag(vertex[19])
		vertex[21] = @leafKlength * vertex[21]
		xcoord[21] = real(vertex[21])
		ycoord[21] = imag(vertex[21])
	elseif traparray == 166 ; "12-star"
		cursality = 1
		numbervertices = 25 ; n + cursality for closed curves
		cincrement = 25 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @starspikiness * @nscale1 * (0.965926, 0.258819)
		vertex[2] = @nscale1 * (0.433013, 0.25)
		vertex[3] = @starspikiness * @nscale1 * (0.707107, 0.707107)
		vertex[4] = @nscale1 * (0.25, 0.433013)
		vertex[5] = @starspikiness * @nscale1 * (0.258819, 0.965926)
		vertex[6] = @nscale1 * (0,0.5)
		vertex[7] = @starspikiness * @nscale1 * (-0.258819, 0.965926)
		vertex[8] = @nscale1 * (-0.25, 0.433013)
		vertex[9] = @starspikiness * @nscale1 * (-0.707107, 0.707107)
		vertex[10] = @nscale1 * (-0.433013, 0.25)
		vertex[11] = @starspikiness * @nscale1 * (-0.965926, 0.258819)
		vertex[12] = @nscale1 * (-0.5, 0)
		vertex[13] = @starspikiness * @nscale1 * (-0.965926, -0.258819)
		vertex[14] = @nscale1 * (-0.433013, -0.25)
		vertex[15] = @starspikiness * @nscale1 * (-0.707107, -0.707107)
		vertex[16] = @nscale1 * (-0.25, -0.433013)
		vertex[17] = @starspikiness * @nscale1 * (-0.258819, -0.965926)
		vertex[18] = @nscale1 * (0,-0.5)
		vertex[19] = @starspikiness * @nscale1 * (0.258819, -0.965926)
		vertex[20] = @nscale1 * (0.25, -0.433013)
		vertex[21] = @starspikiness * @nscale1 * (0.707107, -0.707107)
		vertex[22] = @nscale1 * (0.433013, -0.25)
		vertex[23] = @starspikiness * @nscale1 * (0.965926, -0.258819)
		vertex[24] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 167 ; "12-star 2"
		cursality = 1
		numbervertices = 25 ; n + cursality for closed curves
		cincrement = 25 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5,0)
		vertex[1] = @nscale1 * (1,0)
		vertex[2] = @nscale1 * (0.433013, 0.25)
		vertex[3] = @nscale1 * (0.866025, 0.5)
		vertex[4] = @nscale1 * (0.25, 0.433013)
		vertex[5] = @nscale1 * (0.5, 0.866025)
		vertex[6] = @nscale1 * (0,0.5)
		vertex[7] = @nscale1 * (0,1)
		vertex[8] = @nscale1 * (-0.25, 0.433013)
		vertex[9] = @nscale1 * (-0.5, 0.866025)
		vertex[10] = @nscale1 * (-0.433013, 0.25)
		vertex[11] = @nscale1 * (-0.866025, 0.5)
		vertex[12] = @nscale1 * (-0.5,0)
		vertex[13] = @nscale1 * (-1,0)
		vertex[14] = @nscale1 * (-0.433013, -0.25)
		vertex[15] = @nscale1 * (-0.866025, -0.5)
		vertex[16] = @nscale1 * (-0.25, -0.433013)
		vertex[17] = @nscale1 * (-0.5, -0.866025)
		vertex[18] = @nscale1 * (0,-0.5)
		vertex[19] = @nscale1 * (0,-1)
		vertex[20] = @nscale1 * (0.25, -0.433013)
		vertex[21] = @nscale1 * (0.5, -0.866025)
		vertex[22] = @nscale1 * (0.433013, -0.25)
		vertex[23] = @nscale1 * (0.866025, -0.5)
		vertex[24] = @nscale1 * (0.5,0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 168 ; "12-asterisk"
		cursality = 12
		numbervertices = 24 ; vertices only for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			vertex[glindex] = (0,0)
			xcoord[glindex + 1] = @nscale1 * cos(glindex * #pi / 12)
			ycoord[glindex + 1] = @nscale1 * sin(glindex * #pi / 12)
			glindex = glindex + 1
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		vertex[1] = @leafAlength * vertex[1]
		xcoord[1] = real(vertex[1])
		ycoord[1] = imag(vertex[1])
		vertex[3] = @leafBlength * vertex[3]
		xcoord[3] = real(vertex[3])
		ycoord[3] = imag(vertex[3])
		vertex[5] = @leafClength * vertex[5]
		xcoord[5] = real(vertex[5])
		ycoord[5] = imag(vertex[5])
		vertex[7] = @leafDlength * vertex[7]
		xcoord[7] = real(vertex[7])
		ycoord[7] = imag(vertex[7])
		vertex[9] = @leafElength * vertex[9]
		xcoord[9] = real(vertex[9])
		ycoord[9] = imag(vertex[9])
		vertex[11] = @leafFlength * vertex[11]
		xcoord[11] = real(vertex[11])
		ycoord[11] = imag(vertex[11])
		vertex[13] = @leafGlength * vertex[13]
		xcoord[13] = real(vertex[13])
		ycoord[13] = imag(vertex[13])
		vertex[15] = @leafHlength * vertex[15]
		xcoord[15] = real(vertex[15])
		ycoord[15] = imag(vertex[15])
		vertex[17] = @leafIlength * vertex[17]
		xcoord[17] = real(vertex[17])
		ycoord[17] = imag(vertex[17])
		vertex[19] = @leafJlength * vertex[19]
		xcoord[19] = real(vertex[19])
		ycoord[19] = imag(vertex[19])
		vertex[21] = @leafKlength * vertex[21]
		xcoord[21] = real(vertex[21])
		ycoord[21] = imag(vertex[21])
		vertex[23] = @leafLlength * vertex[23]
		xcoord[23] = real(vertex[23])
		ycoord[23] = imag(vertex[23])
	elseif traparray == 169 ; "1,1,1,2,3;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.5, -0.25)
		vertex[1] = @nscale1 * (-0.25, -0.25)
		vertex[2] = @nscale1 * (-0.25, 0)
		vertex[3] = @nscale1 * (-0.5, 0)
		vertex[4] = @nscale1 * (-0.5, -0.5)
		vertex[5] = @nscale1 * (0.25, -0.5)
		vertex[6] = @nscale1 * (0.25, -0.25)
		vertex[7] = @nscale1 * (0., -0.25)
		vertex[8] = @nscale1 * (0., -0.5)
		vertex[9] = @nscale1 * (0.5, -0.5)
		vertex[10] = @nscale1 * (0.5, 0.25)
		vertex[11] = @nscale1 * (0.25, 0.25)
		vertex[12] = @nscale1 * (0.25, 0)
		vertex[13] = @nscale1 * (0.5, 0)
		vertex[14] = @nscale1 * (0.5, 0.5)
		vertex[15] = @nscale1 * (-0.25, 0.5)
		vertex[16] = @nscale1 * (-0.25, 0.25)
		vertex[17] = @nscale1 * (0., 0.25)
		vertex[18] = @nscale1 * (0., 0.5)
		vertex[19] = @nscale1 * (-0.5, 0.5)
		vertex[20] = @nscale1 * (-0.5, -0.25)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 170 ; "1,1,2,1,3;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.25, -0.25)
		vertex[1] = @nscale1 * (0., -0.25)
		vertex[2] = @nscale1 * (0, 0)
		vertex[3] = @nscale1 * (-0.5, 0)
		vertex[4] = @nscale1 * (-0.5, -0.25)
		vertex[5] = @nscale1 * (0.25, -0.25)
		vertex[6] = @nscale1 * (0.25, 0)
		vertex[7] = @nscale1 * (0,0)
		vertex[8] = @nscale1 * (0, -0.5)
		vertex[9] = @nscale1 * (0.25, -0.5)
		vertex[10] = @nscale1 * (0.25, 0.25)
		vertex[11] = @nscale1 * (0., 0.25)
		vertex[12] = @nscale1 * (0, 0)
		vertex[13] = @nscale1 * (0.5, 0)
		vertex[14] = @nscale1 * (0.5, 0.25)
		vertex[15] = @nscale1 * (-0.25, 0.25)
		vertex[16] = @nscale1 * (-0.25, 0)
		vertex[17] = @nscale1 * (0., 0)
		vertex[18] = @nscale1 * (0., 0.5)
		vertex[19] = @nscale1 * (-0.25, 0.5)
		vertex[20] = @nscale1 * (-0.25, -0.25)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 171 ; "1,1,2,2,4;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.333333, -0.166667)
		vertex[1] = @nscale1 * (-0.166667, -0.166667)
		vertex[2] = @nscale1 * (-0.166667, 0)
		vertex[3] = @nscale1 * (-0.5, 0)
		vertex[4] = @nscale1 * (-0.5, -0.333333)
		vertex[5] = @nscale1 * (0.166667, -0.333333)
		vertex[6] = @nscale1 * (0.166667, -0.166667)
		vertex[7] = @nscale1 * (0., -0.166667)
		vertex[8] = @nscale1 * (0., -0.5)
		vertex[9] = @nscale1 * (0.333333, -0.5)
		vertex[10] = @nscale1 * (0.333333, 0.166667)
		vertex[11] = @nscale1 * (0.166667, 0.166667)
		vertex[12] = @nscale1 * (0.166667, 0)
		vertex[13] = @nscale1 * (0.5, 0)
		vertex[14] = @nscale1 * (0.5, 0.333333)
		vertex[15] = @nscale1 * (-0.166667, 0.333333)
		vertex[16] = @nscale1 * (-0.166667, 0.166667)
		vertex[17] = @nscale1 * (0., 0.166667)
		vertex[18] = @nscale1 * (0., 0.5)
		vertex[19] = @nscale1 * (-0.333333, 0.5)
		vertex[20] = @nscale1 * (-0.333333, -0.166667)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 172 ; "1,1,4,5,4;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.227273, 0.136364)
		vertex[1] = @nscale1 * (-0.136364, 0.136364)
		vertex[2] = @nscale1 * (-0.136364, 0.227273)
		vertex[3] = @nscale1 * (-0.5, 0.227273)
		vertex[4] = @nscale1 * (-0.5, -0.227273)
		vertex[5] = @nscale1 * (-0.136364, -0.227273)
		vertex[6] = @nscale1 * (-0.136364, -0.136364)
		vertex[7] = @nscale1 * (-0.227273, -0.136364)
		vertex[8] = @nscale1 * (-0.227273, -0.5)
		vertex[9] = @nscale1 * (0.227273, -0.5)
		vertex[10] = @nscale1 * (0.227273, -0.136364)
		vertex[11] = @nscale1 * (0.136364, -0.136364)
		vertex[12] = @nscale1 * (0.136364, -0.227273)
		vertex[13] = @nscale1 * (0.5, -0.227273)
		vertex[14] = @nscale1 * (0.5, 0.227273)
		vertex[15] = @nscale1 * (0.136364, 0.227273)
		vertex[16] = @nscale1 * (0.136364, 0.136364)
		vertex[17] = @nscale1 * (0.227273, 0.136364)
		vertex[18] = @nscale1 * (0.227273, 0.5)
		vertex[19] = @nscale1 * (-0.227273, 0.5)
		vertex[20] = @nscale1 * (-0.227273, 0.136364)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 173 ; "1,2,2,2,5;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.333333, -0.333333)
		vertex[1] = @nscale1 * (-0.166667, -0.333333)
		vertex[2] = @nscale1 * (-0.166667, 0)
		vertex[3] = @nscale1 * (-0.5, 0)
		vertex[4] = @nscale1 * (-0.5, -0.333333)
		vertex[5] = @nscale1 * (0.333333, -0.333333)
		vertex[6] = @nscale1 * (0.333333, -0.166667)
		vertex[7] = @nscale1 * (0., -0.166667)
		vertex[8] = @nscale1 * (0., -0.5)
		vertex[9] = @nscale1 * (0.333333, -0.5)
		vertex[10] = @nscale1 * (0.333333, 0.333333)
		vertex[11] = @nscale1 * (0.166667, 0.333333)
		vertex[12] = @nscale1 * (0.166667, 0)
		vertex[13] = @nscale1 * (0.5, 0)
		vertex[14] = @nscale1 * (0.5, 0.333333)
		vertex[15] = @nscale1 * (-0.333333, 0.333333)
		vertex[16] = @nscale1 * (-0.333333, 0.166667)
		vertex[17] = @nscale1 * (0., 0.166667)
		vertex[18] = @nscale1 * (0., 0.5)
		vertex[19] = @nscale1 * (-0.333333, 0.5)
		vertex[20] = @nscale1 * (-0.333333, -0.333333)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 174 ; "1,2,5,3,5;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.1,0)
		vertex[1] = @nscale1 * (0,0)
		vertex[2] = @nscale1 * (0,0.2)
		vertex[3] = @nscale1 * (-0.5, 0.2)
		vertex[4] = @nscale1 * (-0.5, -0.1)
		vertex[5] = @nscale1 * (0., -0.1)
		vertex[6] = @nscale1 * (0,0)
		vertex[7] = @nscale1 * (-0.2, 0)
		vertex[8] = @nscale1 * (-0.2, -0.5)
		vertex[9] = @nscale1 * (0.1, -0.5)
		vertex[10] = @nscale1 * (0.1, 0)
		vertex[11] = @nscale1 * (0,0)
		vertex[12] = @nscale1 * (0., -0.2)
		vertex[13] = @nscale1 * (0.5, -0.2)
		vertex[14] = @nscale1 * (0.5, 0.1)
		vertex[15] = @nscale1 * (0., 0.1)
		vertex[16] = @nscale1 * (0,0)
		vertex[17] = @nscale1 * (0.2, 0)
		vertex[18] = @nscale1 * (0.2, 0.5)
		vertex[19] = @nscale1 * (-0.1, 0.5)
		vertex[20] = @nscale1 * (-0.1, 0)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 175 ; "2,2,1,4,3;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0., -0.166667)
		vertex[1] = @nscale1 * (0.333333, -0.166667)
		vertex[2] = @nscale1 * (0.333333, 0.166667)
		vertex[3] = @nscale1 * (0.166667, 0.166667)
		vertex[4] = @nscale1 * (0.166667, -0.5)
		vertex[5] = @nscale1 * (0.666667, -0.5)
		vertex[6] = @nscale1 * (0.666667, -0.166667)
		vertex[7] = @nscale1 * (0.333333, -0.166667)
		vertex[8] = @nscale1 * (0.333333, -0.333333)
		vertex[9] = @nscale1 * (1., -0.333333)
		vertex[10] = @nscale1 * (1., 0.166667)
		vertex[11] = @nscale1 * (0.666667, 0.166667)
		vertex[12] = @nscale1 * (0.666667, -0.166667)
		vertex[13] = @nscale1 * (0.833333, -0.166667)
		vertex[14] = @nscale1 * (0.833333, 0.5)
		vertex[15] = @nscale1 * (0.333333, 0.5)
		vertex[16] = @nscale1 * (0.333333, 0.166667)
		vertex[17] = @nscale1 * (0.666667, 0.166667)
		vertex[18] = @nscale1 * (0.666667, 0.333333)
		vertex[19] = @nscale1 * (0., 0.333333)
		vertex[20] = @nscale1 * (0., -0.166667)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 176 ; "2,2,4,4,3;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.214286, 0.0714286)
		vertex[1] = @nscale1 * (0.0714286, 0.0714286)
		vertex[2] = @nscale1 * (0.0714286, 0.357143)
		vertex[3] = @nscale1 * (-0.5, 0.357143)
		vertex[4] = @nscale1 * (-0.5, -0.214286)
		vertex[5] = @nscale1 * (-0.0714286, -0.214286)
		vertex[6] = @nscale1 * (-0.0714286, 0.0714286)
		vertex[7] = @nscale1 * (-0.357143, 0.0714286)
		vertex[8] = @nscale1 * (-0.357143, -0.5)
		vertex[9] = @nscale1 * (0.214286, -0.5)
		vertex[10] = @nscale1 * (0.214286, -0.0714286)
		vertex[11] = @nscale1 * (-0.0714286, -0.0714286)
		vertex[12] = @nscale1 * (-0.0714286, -0.357143)
		vertex[13] = @nscale1 * (0.5, -0.357143)
		vertex[14] = @nscale1 * (0.5, 0.214286)
		vertex[15] = @nscale1 * (0.0714286, 0.214286)
		vertex[16] = @nscale1 * (0.0714286, -0.0714286)
		vertex[17] = @nscale1 * (0.357143, -0.0714286)
		vertex[18] = @nscale1 * (0.357143, 0.5)
		vertex[19] = @nscale1 * (-0.214286, 0.5)
		vertex[20] = @nscale1 * (-0.214286, 0.0714286)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 177 ; "2,3,5,3,2;1/2"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.5, -0.357143)
		vertex[1] = @nscale1 * (0.785714, -0.357143)
		vertex[2] = @nscale1 * (0.785714, 0.0714286)
		vertex[3] = @nscale1 * (0.0714286, 0.0714286)
		vertex[4] = @nscale1 * (0.0714286, -0.357143)
		vertex[5] = @nscale1 * (0.357143, -0.357143)
		vertex[6] = @nscale1 * (0.357143, -0.0714286)
		vertex[7] = @nscale1 * (-0.0714286, -0.0714286)
		vertex[8] = @nscale1 * (-0.0714286, -0.785714)
		vertex[9] = @nscale1 * (0.357143, -0.785714)
		vertex[10] = @nscale1 * (0.357143, -0.5)
		vertex[11] = @nscale1 * (0.0714286, -0.5)
		vertex[12] = @nscale1 * (0.0714286, -0.928571)
		vertex[13] = @nscale1 * (0.785714, -0.928571)
		vertex[14] = @nscale1 * (0.785714, -0.5)
		vertex[15] = @nscale1 * (0.5, -0.5)
		vertex[16] = @nscale1 * (0.5, -0.785714)
		vertex[17] = @nscale1 * (0.928571, -0.785714)
		vertex[18] = @nscale1 * (0.928571, -0.0714286)
		vertex[19] = @nscale1 * (0.5, -0.0714286)
		vertex[20] = @nscale1 * (0.5, -0.357143)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 178 ; "1,6,6,6;1/4,1/4,-5/6"
		cursality = 1
		numbervertices = 37 ; n + cursality for closed curves
		cincrement = 37 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.166667, 0.2)
		vertex[1] = @nscale1 * (-0.133333, 0.2)
		vertex[2] = @nscale1 * (0.00808802, 0.341421)
		vertex[3] = @nscale1 * (0.00808802, 0.541421)
		vertex[4] = @nscale1 * (0.108088, 0.368216)
		vertex[5] = @nscale1 * (0.140286, 0.359589)
		vertex[6] = @nscale1 * (0.313491, 0.459589)
		vertex[7] = @nscale1 * (0.213491, 0.286384)
		vertex[8] = @nscale1 * (0.265254, 0.0931987)
		vertex[9] = @nscale1 * (0.294122, 0.0765321)
		vertex[10] = @nscale1 * (0.094122, 0.0765321)
		vertex[11] = @nscale1 * (-0.0472994, -0.0648893)
		vertex[12] = @nscale1 * (-0.0472994, -0.264889)
		vertex[13] = @nscale1 * (-0.0639661, -0.236022)
		vertex[14] = @nscale1 * (-0.257151, -0.184258)
		vertex[15] = @nscale1 * (-0.430356, -0.284258)
		vertex[16] = @nscale1 * (-0.330356, -0.111053)
		vertex[17] = @nscale1 * (-0.338984, -0.0788554)
		vertex[18] = @nscale1 * (-0.512189, 0.0211446)
		vertex[19] = @nscale1 * (-0.312189, 0.0211446)
		vertex[20] = @nscale1 * (-0.170767, 0.162566)
		vertex[21] = @nscale1 * (-0.170767, 0.195899)
		vertex[22] = @nscale1 * (-0.0707673, 0.0226942)
		vertex[23] = @nscale1 * (0.122418, -0.0290696)
		vertex[24] = @nscale1 * (0.295623, 0.0709304)
		vertex[25] = @nscale1 * (0.278956, 0.0420629)
		vertex[26] = @nscale1 * (0.33072, -0.151122)
		vertex[27] = @nscale1 * (0.503925, -0.251122)
		vertex[28] = @nscale1 * (0.303925, -0.251122)
		vertex[29] = @nscale1 * (0.280355, -0.274692)
		vertex[30] = @nscale1 * (0.280355, -0.474692)
		vertex[31] = @nscale1 * (0.180355, -0.301487)
		vertex[32] = @nscale1 * (-0.0128303, -0.249724)
		vertex[33] = @nscale1 * (-0.0416978, -0.26639)
		vertex[34] = @nscale1 * (0.0583022, -0.0931852)
		vertex[35] = @nscale1 * (0.00653841, 0.1)
		vertex[36] = @nscale1 * (-0.166667, 0.2)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 179 ; "1,6,6,1;3/4,-1/4,-1/6"
		cursality = 1
		numbervertices = 37 ; n + cursality for closed curves
		cincrement = 37 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.235294, -0.470588)
		vertex[1] = @nscale1 * (-0.176471, -0.470588)
		vertex[2] = @nscale1 * (-0.426038, -0.221021)
		vertex[3] = @nscale1 * (-0.426038, 0.13192)
		vertex[4] = @nscale1 * (-0.484861, 0.0300347)
		vertex[5] = @nscale1 * (-0.428042, 0.0452593)
		vertex[6] = @nscale1 * (-0.122386, -0.131211)
		vertex[7] = @nscale1 * (-0.298857, 0.174445)
		vertex[8] = @nscale1 * (-0.329306, 0.0608065)
		vertex[9] = @nscale1 * (-0.380249, 0.0313947)
		vertex[10] = @nscale1 * (-0.0273074, 0.0313947)
		vertex[11] = @nscale1 * (-0.276875, 0.280962)
		vertex[12] = @nscale1 * (-0.276875, 0.398609)
		vertex[13] = @nscale1 * (-0.306286, 0.347666)
		vertex[14] = @nscale1 * (0.0346287, 0.439014)
		vertex[15] = @nscale1 * (0.340285, 0.262543)
		vertex[16] = @nscale1 * (0.281461, 0.364429)
		vertex[17] = @nscale1 * (0.266237, 0.30761)
		vertex[18] = @nscale1 * (-0.0394195, 0.131139)
		vertex[19] = @nscale1 * (0.313522, 0.131139)
		vertex[20] = @nscale1 * (0.230333, 0.214328)
		vertex[21] = @nscale1 * (0.230333, 0.273152)
		vertex[22] = @nscale1 * (0.0538621, -0.0325044)
		vertex[23] = @nscale1 * (0.394777, 0.0588435)
		vertex[24] = @nscale1 * (0.496662, 0.0000199788)
		vertex[25] = @nscale1 * (0.467251, 0.0509626)
		vertex[26] = @nscale1 * (0.375903, -0.289952)
		vertex[27] = @nscale1 * (0.0702468, -0.466423)
		vertex[28] = @nscale1 * (0.187894, -0.466423)
		vertex[29] = @nscale1 * (0.146299, -0.424828)
		vertex[30] = @nscale1 * (0.146299, -0.0718872)
		vertex[31] = @nscale1 * (-0.0301713, -0.377543)
		vertex[32] = @nscale1 * (0.083467, -0.347094)
		vertex[33] = @nscale1 * (0.13441, -0.376506)
		vertex[34] = @nscale1 * (-0.0420609, -0.0708497)
		vertex[35] = @nscale1 * (-0.133409, -0.411765)
		vertex[36] = @nscale1 * (-0.235294, -0.470588)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 180 ; "1,2,1,3;-4/5"
		cursality = 1
		numbervertices = 21 ; n + cursality for closed curves
		cincrement = 21 ; numbervertices/cursality
		scratchfloat = 1/3
		; initialize arrays
		vertex[0] = @nscale1 * (-0.8, 1.5) * scratchfloat
		vertex[1] = @nscale1 * (0.2, 1.5) * scratchfloat
		vertex[2] = @nscale1 * (-1.41803, 0.324429) * scratchfloat
		vertex[3] = @nscale1 * (-1.10902, 1.27549) * scratchfloat
		vertex[4] = @nscale1 * (-0.181966, -1.57768) * scratchfloat
		vertex[5] = @nscale1 * (-0.990983, -0.989898) * scratchfloat
		vertex[6] = @nscale1 * (1.00902, -0.989898) * scratchfloat
		vertex[7] = @nscale1 * (0.2, -1.57768) * scratchfloat
		vertex[8] = @nscale1 * (1.12705, 1.27549) * scratchfloat
		vertex[9] = @nscale1 * (1.43607, 0.324429) * scratchfloat
		vertex[10] = @nscale1 * (-0.181966, 1.5) * scratchfloat
		vertex[11] = @nscale1 * (0.818034, 1.5) * scratchfloat
		vertex[12] = @nscale1 * (-1.60902, -0.263356) * scratchfloat
		vertex[13] = @nscale1 * (-1.3, 0.687701) * scratchfloat
		vertex[14] = @nscale1 * (-0.681966, -1.21441) * scratchfloat
		vertex[15] = @nscale1 * (-1.49098, -0.626627) * scratchfloat
		vertex[16] = @nscale1 * (1.50902, -0.626627) * scratchfloat
		vertex[17] = @nscale1 * (0.7, -1.21441) * scratchfloat
		vertex[18] = @nscale1 * (1.31803, 0.687701) * scratchfloat
		vertex[19] = @nscale1 * (1.62705, -0.263356) * scratchfloat
		vertex[20] = @nscale1 * (-0.8, 1.5) * scratchfloat
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 181 ; "1,2,1,3;-4/5,-4/5,0"
		cursality = 1
		numbervertices = 61 ; n + cursality for closed curves
		cincrement = 61 ; numbervertices/cursality
		scratchfloat = 1/6
		; initialize arrays
		vertex[0] = @nscale1 * (0.0, 0.1) * scratchfloat
		vertex[1] = @nscale1 * (1, 0.1) * scratchfloat
		vertex[2] = @nscale1 * (-0.618034, -1.07557) * scratchfloat
		vertex[3] = @nscale1 * (-0.309017, -0.124514) * scratchfloat
		vertex[4] = @nscale1 * (0.618034, 2.72866) * scratchfloat
		vertex[5] = @nscale1 * (0.927051, 1.7776) * scratchfloat
		vertex[6] = @nscale1 * (-0.690983, 2.95317) * scratchfloat
		vertex[7] = @nscale1 * (-1.5, 3.54095) * scratchfloat
		vertex[8] = @nscale1 * (1.5, 3.54095) * scratchfloat
		vertex[9] = @nscale1 * (0.690983, 2.95317) * scratchfloat
		vertex[10] = @nscale1 * (-0.927051, 1.7776) * scratchfloat
		vertex[11] = @nscale1 * (-0.618034, 2.72866) * scratchfloat
		vertex[12] = @nscale1 * (0.309017, -0.124514) * scratchfloat
		vertex[13] = @nscale1 * (0.618034, -1.07557) * scratchfloat
		vertex[14] = @nscale1 * (-1., 0.1) * scratchfloat
		vertex[15] = @nscale1 * (0., 0.1) * scratchfloat
		vertex[16] = @nscale1 * (3., 0.1) * scratchfloat
		vertex[17] = @nscale1 * (2.19098, -0.487785) * scratchfloat
		vertex[18] = @nscale1 * (2.80902, 1.41433) * scratchfloat
		vertex[19] = @nscale1 * (3.11803, 2.36538) * scratchfloat
		vertex[20] = @nscale1 * (4.04508, -0.487785) * scratchfloat
		vertex[21] = @nscale1 * (3.23607, 0.1) * scratchfloat
		vertex[22] = @nscale1 * (1.61803, 1.27557) * scratchfloat
		vertex[23] = @nscale1 * (2.61803, 1.27557) * scratchfloat
		vertex[24] = @nscale1 * (0.190983, -0.487785) * scratchfloat
		vertex[25] = @nscale1 * (-0.618034, -1.07557) * scratchfloat
		vertex[26] = @nscale1 * (0., 0.826543) * scratchfloat
		vertex[27] = @nscale1 * (0.309017, -0.124514) * scratchfloat
		vertex[28] = @nscale1 * (1.23607, -2.97768) * scratchfloat
		vertex[29] = @nscale1 * (0.427051, -2.3899) * scratchfloat
		vertex[30] = @nscale1 * (2.42705, -2.3899) * scratchfloat
		vertex[31] = @nscale1 * (3.42705, -2.3899) * scratchfloat
		vertex[32] = @nscale1 * (1., -4.15325) * scratchfloat
		vertex[33] = @nscale1 * (1.30902, -3.2022) * scratchfloat
		vertex[34] = @nscale1 * (1.92705, -1.30008) * scratchfloat
		vertex[35] = @nscale1 * (2.23607, -2.25114) * scratchfloat
		vertex[36] = @nscale1 * (-0.190983, -0.487785) * scratchfloat
		vertex[37] = @nscale1 * (-1., 0.1) * scratchfloat
		vertex[38] = @nscale1 * (1., 0.1) * scratchfloat
		vertex[39] = @nscale1 * (0.190983, -0.487785) * scratchfloat
		vertex[40] = @nscale1 * (-2.23607, -2.25114) * scratchfloat
		vertex[41] = @nscale1 * (-1.92705, -1.30008) * scratchfloat
		vertex[42] = @nscale1 * (-1.30902, -3.2022) * scratchfloat
		vertex[43] = @nscale1 * (-1., -4.15325) * scratchfloat
		vertex[44] = @nscale1 * (-3.42705, -2.3899) * scratchfloat
		vertex[45] = @nscale1 * (-2.42705, -2.3899) * scratchfloat
		vertex[46] = @nscale1 * (-0.427051, -2.3899) * scratchfloat
		vertex[47] = @nscale1 * (-1.23607, -2.97768) * scratchfloat
		vertex[48] = @nscale1 * (-0.309017, -0.124514) * scratchfloat
		vertex[49] = @nscale1 * (0, 0.826543) * scratchfloat
		vertex[50] = @nscale1 * (0.618034, -1.07557) * scratchfloat
		vertex[51] = @nscale1 * (-0.190983, -0.487785) * scratchfloat
		vertex[52] = @nscale1 * (-2.61803, 1.27557) * scratchfloat
		vertex[53] = @nscale1 * (-1.61803, 1.27557) * scratchfloat
		vertex[54] = @nscale1 * (-3.23607, 0.1) * scratchfloat
		vertex[55] = @nscale1 * (-4.04508, -0.487785) * scratchfloat
		vertex[56] = @nscale1 * (-3.11803, 2.36538) * scratchfloat
		vertex[57] = @nscale1 * (-2.80902, 1.41433) * scratchfloat
		vertex[58] = @nscale1 * (-2.19098, -0.487785) * scratchfloat
		vertex[59] = @nscale1 * (-3., 0.1) * scratchfloat
		vertex[60] = @nscale1 * (0,0.1) * scratchfloat
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 182 ; "1,2,1,3;-4/5,-1/5,-4/5"
		cursality = 1
		numbervertices = 61 ; n + cursality for closed curves
		cincrement = 61 ; numbervertices/cursality
		scratchfloat = 0.2
		; initialize arrays
		vertex[0] = @nscale1 * (-1.5, 2.6) * scratchfloat
		vertex[1] = @nscale1 * (-0.5, 2.6) * scratchfloat
		vertex[2] = @nscale1 * (-2.11803, 1.42443) * scratchfloat
		vertex[3] = @nscale1 * (-3.11803, 1.42443) * scratchfloat
		vertex[4] = @nscale1 * (-0.690983, 3.18779) * scratchfloat
		vertex[5] = @nscale1 * (-1., 2.23673) * scratchfloat
		vertex[6] = @nscale1 * (-2.61803, 1.06116) * scratchfloat
		vertex[7] = @nscale1 * (-2.30902, 2.01221) * scratchfloat
		vertex[8] = @nscale1 * (-1.38197, -0.840955) * scratchfloat
		vertex[9] = @nscale1 * (-1.69098, -1.79201) * scratchfloat
		vertex[10] = @nscale1 * (-2.30902, 0.110102) * scratchfloat
		vertex[11] = @nscale1 * (-1.5, -0.477684) * scratchfloat
		vertex[12] = @nscale1 * (-0.572949, -3.33085) * scratchfloat
		vertex[13] = @nscale1 * (-1.38197, -2.74307) * scratchfloat
		vertex[14] = @nscale1 * (0.618034, -2.74307) * scratchfloat
		vertex[15] = @nscale1 * (1.42705, -3.33085) * scratchfloat
		vertex[16] = @nscale1 * (-1.57295, -3.33085) * scratchfloat
		vertex[17] = @nscale1 * (-0.763932, -2.74307) * scratchfloat
		vertex[18] = @nscale1 * (1.23607, -2.74307) * scratchfloat
		vertex[19] = @nscale1 * (0.427051, -3.33085) * scratchfloat
		vertex[20] = @nscale1 * (1.3541, -0.477684) * scratchfloat
		vertex[21] = @nscale1 * (2.16312, 0.110102) * scratchfloat
		vertex[22] = @nscale1 * (1.54508, -1.79201) * scratchfloat
		vertex[23] = @nscale1 * (1.23607, -0.840955) * scratchfloat
		vertex[24] = @nscale1 * (2.16312, 2.01221) * scratchfloat
		vertex[25] = @nscale1 * (2.47214, 1.06116) * scratchfloat
		vertex[26] = @nscale1 * (0.854102, 2.23673) * scratchfloat
		vertex[27] = @nscale1 * (0.545085, 3.18779) * scratchfloat
		vertex[28] = @nscale1 * (2.97214, 1.42443) * scratchfloat
		vertex[29] = @nscale1 * (1.97214, 1.42443) * scratchfloat
		vertex[30] = @nscale1 * (0.354102, 2.6) * scratchfloat
		vertex[31] = @nscale1 * (1.3541, 2.6) * scratchfloat
		vertex[32] = @nscale1 * (-1.07295, 0.836644) * scratchfloat
		vertex[33] = @nscale1 * (-2.07295, 0.836644) * scratchfloat
		vertex[34] = @nscale1 * (-0.454915, 2.01221) * scratchfloat
		vertex[35] = @nscale1 * (-0.763932, 1.06116) * scratchfloat
		vertex[36] = @nscale1 * (-3.19098, -0.702198) * scratchfloat
		vertex[37] = @nscale1 * (-2.88197, 0.248859) * scratchfloat
		vertex[38] = @nscale1 * (-2.26393, -1.65325) * scratchfloat
		vertex[39] = @nscale1 * (-2.57295, -2.60431) * scratchfloat
		vertex[40] = @nscale1 * (-3.5, 0.248859) * scratchfloat
		vertex[41] = @nscale1 * (-2.69098, -0.338926) * scratchfloat
		vertex[42] = @nscale1 * (-2.07295, -2.24104) * scratchfloat
		vertex[43] = @nscale1 * (-2.88197, -1.65325) * scratchfloat
		vertex[44] = @nscale1 * (0.118034, -1.65325) * scratchfloat
		vertex[45] = @nscale1 * (0.927051, -2.24104) * scratchfloat
		vertex[46] = @nscale1 * (-1.07295, -2.24104) * scratchfloat
		vertex[47] = @nscale1 * (-0.263932, -1.65325) * scratchfloat
		vertex[48] = @nscale1 * (2.73607, -1.65325) * scratchfloat
		vertex[49] = @nscale1 * (1.92705, -2.24104) * scratchfloat
		vertex[50] = @nscale1 * (2.54508, -0.338926) * scratchfloat
		vertex[51] = @nscale1 * (3.3541, 0.248859) * scratchfloat
		vertex[52] = @nscale1 * (2.42705, -2.60431) * scratchfloat
		vertex[53] = @nscale1 * (2.11803, -1.65325) * scratchfloat
		vertex[54] = @nscale1 * (2.73607, 0.248859) * scratchfloat
		vertex[55] = @nscale1 * (3.04508, -0.702198) * scratchfloat
		vertex[56] = @nscale1 * (0.618034, 1.06116) * scratchfloat
		vertex[57] = @nscale1 * (0.309017, 2.01221) * scratchfloat
		vertex[58] = @nscale1 * (1.92705, 0.836644) * scratchfloat
		vertex[59] = @nscale1 * (0.927051, 0.836644) * scratchfloat
		vertex[60] = @nscale1 * (-1.5, 2.6) * scratchfloat
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 183 ; "1,3;1/5,3/5,-1/5"
		cursality = 1
		numbervertices = 31 ; n + cursality for closed curves
		cincrement = 31 ; numbervertices/cursality
		scratchfloat = 0.2
		; initialize arrays
		vertex[0] = @nscale1 * (-0.5, -1.75) * scratchfloat
		vertex[1] = @nscale1 * (0.5, -1.75) * scratchfloat
		vertex[2] = @nscale1 * (2.92705, 0.0133558) * scratchfloat
		vertex[3] = @nscale1 * (2.11803, 0.601141) * scratchfloat
		vertex[4] = @nscale1 * (1.19098, 3.45431) * scratchfloat
		vertex[5] = @nscale1 * (0.381966, 4.0421) * scratchfloat
		vertex[6] = @nscale1 * (-0.545085, 1.18893) * scratchfloat
		vertex[7] = @nscale1 * (-1.3541, 0.601141) * scratchfloat
		vertex[8] = @nscale1 * (-2.28115, -2.25203) * scratchfloat
		vertex[9] = @nscale1 * (-1.28115, -2.25203) * scratchfloat
		vertex[10] = @nscale1 * (1.1459, -4.01538) * scratchfloat
		vertex[11] = @nscale1 * (2.1459, -4.01538) * scratchfloat
		vertex[12] = @nscale1 * (1.21885, -1.16221) * scratchfloat
		vertex[13] = @nscale1 * (1.52786, -0.211158) * scratchfloat
		vertex[14] = @nscale1 * (0.600813, 2.64201) * scratchfloat
		vertex[15] = @nscale1 * (-0.208204, 2.05423) * scratchfloat
		vertex[16] = @nscale1 * (-3.2082, 2.05423) * scratchfloat
		vertex[17] = @nscale1 * (-4.01722, 1.46644) * scratchfloat
		vertex[18] = @nscale1 * (-1.59017, -0.296915) * scratchfloat
		vertex[19] = @nscale1 * (-1.28115, -1.24797) * scratchfloat
		vertex[20] = @nscale1 * (1.1459, -3.01133) * scratchfloat
		vertex[21] = @nscale1 * (1.45492, -2.06027) * scratchfloat
		vertex[22] = @nscale1 * (3.88197, -0.296915) * scratchfloat
		vertex[23] = @nscale1 * (4.19098, 0.654142) * scratchfloat
		vertex[24] = @nscale1 * (1.19098, 0.654142) * scratchfloat
		vertex[25] = @nscale1 * (0.381966, 1.24193) * scratchfloat
		vertex[26] = @nscale1 * (-2.61803, 1.24193) * scratchfloat
		vertex[27] = @nscale1 * (-2.30902, 0.29087) * scratchfloat
		vertex[28] = @nscale1 * (-3.23607, -2.5623) * scratchfloat
		vertex[29] = @nscale1 * (-2.92705, -3.51336) * scratchfloat
		vertex[30] = @nscale1 * (-0.5, -1.75) * scratchfloat
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 184 ; "1,2,3,3,2,1;5/6,1/6,1/6"
		cursality = 1
		numbervertices = 37 ; n + cursality for closed curves
		cincrement = 37 ; numbervertices/cursality
		; initialize arrays
		scratchfloat = 2/3
		vertex[0] = @nscale1 * (0.333333, 0.638889) * scratchfloat
		vertex[1] = @nscale1 * (0.555556, 0.638889) * scratchfloat
		vertex[2] = @nscale1 * (0.170655, 0.861111) * scratchfloat
		vertex[3] = @nscale1 * (-0.496011, 0.861111) * scratchfloat
		vertex[4] = @nscale1 * (-1.07336, 0.527778) * scratchfloat
		vertex[5] = @nscale1 * (-0.628917, 0.527778) * scratchfloat
		vertex[6] = @nscale1 * (-0.436467, 0.638889) * scratchfloat
		vertex[7] = @nscale1 * (-0.325356, 0.831339) * scratchfloat
		vertex[8] = @nscale1 * (-0.710256, 0.609117) * scratchfloat
		vertex[9] = @nscale1 * (-1.04359, 0.0317665) * scratchfloat
		vertex[10] = @nscale1 * (-1.04359, -0.6349) * scratchfloat
		vertex[11] = @nscale1 * (-0.821367, -0.25) * scratchfloat
		vertex[12] = @nscale1 * (-0.821367, -0.0277778) * scratchfloat
		vertex[13] = @nscale1 * (-0.932478, 0.164672) * scratchfloat
		vertex[14] = @nscale1 * (-0.932478, -0.279772) * scratchfloat
		vertex[15] = @nscale1 * (-0.599145, -0.857122) * scratchfloat
		vertex[16] = @nscale1 * (-0.0217947, -1.19046) * scratchfloat
		vertex[17] = @nscale1 * (-0.244017, -0.805556) * scratchfloat
		vertex[18] = @nscale1 * (-0.436467, -0.694444) * scratchfloat
		vertex[19] = @nscale1 * (-0.658689, -0.694444) * scratchfloat
		vertex[20] = @nscale1 * (-0.273789, -0.916667) * scratchfloat
		vertex[21] = @nscale1 * (0.392878, -0.916667) * scratchfloat
		vertex[22] = @nscale1 * (0.970228, -0.583333) * scratchfloat
		vertex[23] = @nscale1 * (0.525783, -0.583333) * scratchfloat
		vertex[24] = @nscale1 * (0.333333, -0.694444) * scratchfloat
		vertex[25] = @nscale1 * (0.222222, -0.886895) * scratchfloat
		vertex[26] = @nscale1 * (0.607122, -0.664672) * scratchfloat
		vertex[27] = @nscale1 * (0.940456, -0.087322) * scratchfloat
		vertex[28] = @nscale1 * (0.940456, 0.579345) * scratchfloat
		vertex[29] = @nscale1 * (0.718234, 0.194444) * scratchfloat
		vertex[30] = @nscale1 * (0.718234, -0.0277778) * scratchfloat
		vertex[31] = @nscale1 * (0.829345, -0.220228) * scratchfloat
		vertex[32] = @nscale1 * (0.829345, 0.224217) * scratchfloat
		vertex[33] = @nscale1 * (0.496011, 0.801567) * scratchfloat
		vertex[34] = @nscale1 * (-0.081339, 1.1349) * scratchfloat
		vertex[35] = @nscale1 * (0.140883, 0.75) * scratchfloat
		vertex[36] = @nscale1 * (0.333333, 0.638889) * scratchfloat
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 185 ; "1,1,3,1;-5/6,-1/6,3/7"
		cursality = 1
		numbervertices = 85 ; n + cursality for closed curves
		cincrement = 85 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.625, -0.625)
		vertex[1] = @nscale1 * (0.791667, -0.625)
		vertex[2] = @nscale1 * (0.647329, -0.708333)
		vertex[3] = @nscale1 * (0.147329, -0.708333)
		vertex[4] = @nscale1 * (0.110242, -0.870821)
		vertex[5] = @nscale1 * (0.0611164, -0.711559)
		vertex[6] = @nscale1 * (0.0982032, -0.549071)
		vertex[7] = @nscale1 * (-0.352281, -0.332129)
		vertex[8] = @nscale1 * (-0.186081, -0.319674)
		vertex[9] = @nscale1 * (-0.0359191, -0.391988)
		vertex[10] = @nscale1 * (0.0679959, -0.261683)
		vertex[11] = @nscale1 * (-0.00652525, -0.756098)
		vertex[12] = @nscale1 * (-0.11044, -0.886404)
		vertex[13] = @nscale1 * (-0.00652525, -1.01671)
		vertex[14] = @nscale1 * (-0.161671, -0.955819)
		vertex[15] = @nscale1 * (-0.473416, -0.564903)
		vertex[16] = @nscale1 * (-0.623577, -0.637217)
		vertex[17] = @nscale1 * (-0.529691, -0.499511)
		vertex[18] = @nscale1 * (-0.379529, -0.427197)
		vertex[19] = @nscale1 * (-0.49079, 0.0602674)
		vertex[20] = @nscale1 * (-0.377427, -0.0619079)
		vertex[21] = @nscale1 * (-0.340341, -0.224396)
		vertex[22] = @nscale1 * (-0.173674, -0.224396)
		vertex[23] = @nscale1 * (-0.606687, -0.474396)
		vertex[24] = @nscale1 * (-0.773353, -0.474396)
		vertex[25] = @nscale1 * (-0.81044, -0.636884)
		vertex[26] = @nscale1 * (-0.859566, -0.477622)
		vertex[27] = @nscale1 * (-0.748306, 0.00984221)
		vertex[28] = @nscale1 * (-0.898467, 0.0821562)
		vertex[29] = @nscale1 * (-0.732266, 0.0946112)
		vertex[30] = @nscale1 * (-0.582105, 0.0222972)
		vertex[31] = @nscale1 * (-0.27036, 0.413213)
		vertex[32] = @nscale1 * (-0.2952, 0.248408)
		vertex[33] = @nscale1 * (-0.399115, 0.118103)
		vertex[34] = @nscale1 * (-0.2952, -0.0122027)
		vertex[35] = @nscale1 * (-0.760637, 0.170468)
		vertex[36] = @nscale1 * (-0.864552, 0.300773)
		vertex[37] = @nscale1 * (-1.01471, 0.228459)
		vertex[38] = @nscale1 * (-0.920827, 0.366166)
		vertex[39] = @nscale1 * (-0.470343, 0.583107)
		vertex[40] = @nscale1 * (-0.507429, 0.745595)
		vertex[41] = @nscale1 * (-0.394067, 0.62342)
		vertex[42] = @nscale1 * (-0.35698, 0.460932)
		vertex[43] = @nscale1 * (0.14302, 0.460932)
		vertex[44] = @nscale1 * (-0.00131804, 0.377599)
		vertex[45] = @nscale1 * (-0.167985, 0.377599)
		vertex[46] = @nscale1 * (-0.205072, 0.215111)
		vertex[47] = @nscale1 * (-0.352449, 0.692897)
		vertex[48] = @nscale1 * (-0.315362, 0.855385)
		vertex[49] = @nscale1 * (-0.465524, 0.927699)
		vertex[50] = @nscale1 * (-0.299323, 0.940154)
		vertex[51] = @nscale1 * (0.151161, 0.723212)
		vertex[52] = @nscale1 * (0.255076, 0.853518)
		vertex[53] = @nscale1 * (0.230236, 0.688712)
		vertex[54] = @nscale1 * (0.126321, 0.558407)
		vertex[55] = @nscale1 * (0.438066, 0.167491)
		vertex[56] = @nscale1 * (0.28292, 0.228382)
		vertex[57] = @nscale1 * (0.179005, 0.358687)
		vertex[58] = @nscale1 * (0.0288437, 0.286373)
		vertex[59] = @nscale1 * (0.310504, 0.699492)
		vertex[60] = @nscale1 * (0.460665, 0.771806)
		vertex[61] = @nscale1 * (0.423578, 0.934294)
		vertex[62] = @nscale1 * (0.536941, 0.812119)
		vertex[63] = @nscale1 * (0.648201, 0.324655)
		vertex[64] = @nscale1 * (0.814868, 0.324655)
		vertex[65] = @nscale1 * (0.67053, 0.241322)
		vertex[66] = @nscale1 * (0.503863, 0.241322)
		vertex[67] = @nscale1 * (0.392603, -0.246142)
		vertex[68] = @nscale1 * (0.343477, -0.0868802)
		vertex[69] = @nscale1 * (0.380564, 0.0756078)
		vertex[70] = @nscale1 * (0.230402, 0.147922)
		vertex[71] = @nscale1 * (0.729004, 0.185287)
		vertex[72] = @nscale1 * (0.879166, 0.112973)
		vertex[73] = @nscale1 * (0.983081, 0.243278)
		vertex[74] = @nscale1 * (0.95824, 0.078473)
		vertex[75] = @nscale1 * (0.646496, -0.312443)
		vertex[76] = @nscale1 * (0.750411, -0.442748)
		vertex[77] = @nscale1 * (0.595265, -0.381858)
		vertex[78] = @nscale1 * (0.49135, -0.251553)
		vertex[79] = @nscale1 * (0.0408655, -0.468494)
		vertex[80] = @nscale1 * (0.134752, -0.330788)
		vertex[81] = @nscale1 * (0.284914, -0.258474)
		vertex[82] = @nscale1 * (0.247827, -0.0959861)
		vertex[83] = @nscale1 * (0.587913, -0.462512)
		vertex[84] = @nscale1 * (0.625, -0.625)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 186 ; "1,1,3,1;-1/6,1/6,-3/7"
		cursality = 1
		numbervertices = 85 ; n + cursality for closed curves
		cincrement = 85 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0., 0.183333)
		vertex[1] = @nscale1 * (0.133333, 0.183333)
		vertex[2] = @nscale1 * (0.248803, 0.116667)
		vertex[3] = @nscale1 * (0.648803, 0.116667)
		vertex[4] = @nscale1 * (0.678473, -0.0133237)
		vertex[5] = @nscale1 * (0.639172, -0.140733)
		vertex[6] = @nscale1 * (0.668842, -0.270724)
		vertex[7] = @nscale1 * (0.308454, -0.444277)
		vertex[8] = @nscale1 * (0.175494, -0.434313)
		vertex[9] = @nscale1 * (0.0553644, -0.492164)
		vertex[10] = @nscale1 * (-0.0277676, -0.38792)
		vertex[11] = @nscale1 * (-0.0873845, 0.00761206)
		vertex[12] = @nscale1 * (-0.170516, 0.111856)
		vertex[13] = @nscale1 * (-0.0873845, 0.2161)
		vertex[14] = @nscale1 * (0.036732, 0.264813)
		vertex[15] = @nscale1 * (0.286128, 0.577545)
		vertex[16] = @nscale1 * (0.406257, 0.519694)
		vertex[17] = @nscale1 * (0.481366, 0.409529)
		vertex[18] = @nscale1 * (0.601496, 0.351678)
		vertex[19] = @nscale1 * (0.512487, -0.0382935)
		vertex[20] = @nscale1 * (0.421798, -0.136034)
		vertex[21] = @nscale1 * (0.392128, -0.266024)
		vertex[22] = @nscale1 * (0.258795, -0.266024)
		vertex[23] = @nscale1 * (-0.0876154, -0.0660241)
		vertex[24] = @nscale1 * (-0.220949, -0.0660241)
		vertex[25] = @nscale1 * (-0.250618, 0.0639663)
		vertex[26] = @nscale1 * (-0.211318, 0.191376)
		vertex[27] = @nscale1 * (-0.300326, 0.581347)
		vertex[28] = @nscale1 * (-0.180197, 0.639198)
		vertex[29] = @nscale1 * (-0.0472362, 0.629234)
		vertex[30] = @nscale1 * (0.072893, 0.687085)
		vertex[31] = @nscale1 * (0.322289, 0.374353)
		vertex[32] = @nscale1 * (0.342161, 0.242509)
		vertex[33] = @nscale1 * (0.425293, 0.138265)
		vertex[34] = @nscale1 * (0.342161, 0.0340204)
		vertex[35] = @nscale1 * (-0.0301883, -0.112116)
		vertex[36] = @nscale1 * (-0.11332, -0.21636)
		vertex[37] = @nscale1 * (-0.233449, -0.158509)
		vertex[38] = @nscale1 * (-0.308559, -0.0483439)
		vertex[39] = @nscale1 * (-0.668946, 0.12521)
		vertex[40] = @nscale1 * (-0.639277, 0.2552)
		vertex[41] = @nscale1 * (-0.548587, 0.35294)
		vertex[42] = @nscale1 * (-0.518918, 0.482931)
		vertex[43] = @nscale1 * (-0.118918, 0.482931)
		vertex[44] = @nscale1 * (-0.00344766, 0.416264)
		vertex[45] = @nscale1 * (0.129886, 0.416264)
		vertex[46] = @nscale1 * (0.159555, 0.286274)
		vertex[47] = @nscale1 * (0.0416531, -0.0959556)
		vertex[48] = @nscale1 * (0.0713225, -0.225946)
		vertex[49] = @nscale1 * (-0.0488067, -0.283797)
		vertex[50] = @nscale1 * (-0.181767, -0.273833)
		vertex[51] = @nscale1 * (-0.542155, -0.447387)
		vertex[52] = @nscale1 * (-0.625287, -0.343142)
		vertex[53] = @nscale1 * (-0.645159, -0.211298)
		vertex[54] = @nscale1 * (-0.728291, -0.107054)
		vertex[55] = @nscale1 * (-0.478895, 0.205678)
		vertex[56] = @nscale1 * (-0.354779, 0.254391)
		vertex[57] = @nscale1 * (-0.271647, 0.358635)
		vertex[58] = @nscale1 * (-0.151517, 0.300784)
		vertex[59] = @nscale1 * (0.0738106, -0.0297118)
		vertex[60] = @nscale1 * (0.19394, -0.087563)
		vertex[61] = @nscale1 * (0.16427, -0.217553)
		vertex[62] = @nscale1 * (0.0735807, -0.315294)
		vertex[63] = @nscale1 * (-0.0154277, -0.705265)
		vertex[64] = @nscale1 * (-0.148761, -0.705265)
		vertex[65] = @nscale1 * (-0.264231, -0.638598)
		vertex[66] = @nscale1 * (-0.397564, -0.638598)
		vertex[67] = @nscale1 * (-0.486573, -0.248627)
		vertex[68] = @nscale1 * (-0.447272, -0.121217)
		vertex[69] = @nscale1 * (-0.476942, 0.00877312)
		vertex[70] = @nscale1 * (-0.356812, 0.0666243)
		vertex[71] = @nscale1 * (0.0420691, 0.0367322)
		vertex[72] = @nscale1 * (0.162198, 0.0945834)
		vertex[73] = @nscale1 * (0.24533, -0.00966079)
		vertex[74] = @nscale1 * (0.265203, -0.141505)
		vertex[75] = @nscale1 * (0.514599, -0.454237)
		vertex[76] = @nscale1 * (0.431467, -0.558482)
		vertex[77] = @nscale1 * (0.30735, -0.607194)
		vertex[78] = @nscale1 * (0.224218, -0.711438)
		vertex[79] = @nscale1 * (-0.136169, -0.537885)
		vertex[80] = @nscale1 * (-0.211279, -0.427719)
		vertex[81] = @nscale1 * (-0.331408, -0.369868)
		vertex[82] = @nscale1 * (-0.301739, -0.239878)
		vertex[83] = @nscale1 * (-0.0296695, 0.0533429)
		vertex[84] = @nscale1 * (0., 0.183333)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 187 ; "1,1,3,1;5/6,1/6,4/7"
		cursality = 1
		numbervertices = 85 ; n + cursality for closed curves
		cincrement = 85 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (-0.15625, 0.46875)
		vertex[1] = @nscale1 * (-0.03125, 0.46875)
		vertex[2] = @nscale1 * (-0.139503, 0.53125)
		vertex[3] = @nscale1 * (-0.514503, 0.53125)
		vertex[4] = @nscale1 * (-0.486688, 0.409384)
		vertex[5] = @nscale1 * (-0.449844, 0.528831)
		vertex[6] = @nscale1 * (-0.477659, 0.650697)
		vertex[7] = @nscale1 * (-0.815522, 0.48799)
		vertex[8] = @nscale1 * (-0.690872, 0.478649)
		vertex[9] = @nscale1 * (-0.578251, 0.532884)
		vertex[10] = @nscale1 * (-0.656187, 0.630613)
		vertex[11] = @nscale1 * (-0.600296, 0.259802)
		vertex[12] = @nscale1 * (-0.52236, 0.162073)
		vertex[13] = @nscale1 * (-0.444423, 0.259802)
		vertex[14] = @nscale1 * (-0.560783, 0.214134)
		vertex[15] = @nscale1 * (-0.794591, -0.0790527)
		vertex[16] = @nscale1 * (-0.68197, -0.133288)
		vertex[17] = @nscale1 * (-0.752385, -0.0300083)
		vertex[18] = @nscale1 * (-0.865006, 0.0242272)
		vertex[19] = @nscale1 * (-0.948452, -0.341371)
		vertex[20] = @nscale1 * (-0.86343, -0.249739)
		vertex[21] = @nscale1 * (-0.835615, -0.127873)
		vertex[22] = @nscale1 * (-0.960615, -0.127873)
		vertex[23] = @nscale1 * (-0.635855, -0.315373)
		vertex[24] = @nscale1 * (-0.510855, -0.315373)
		vertex[25] = @nscale1 * (-0.538671, -0.193507)
		vertex[26] = @nscale1 * (-0.575515, -0.312954)
		vertex[27] = @nscale1 * (-0.49207, -0.678552)
		vertex[28] = @nscale1 * (-0.379449, -0.624316)
		vertex[29] = @nscale1 * (-0.504099, -0.614975)
		vertex[30] = @nscale1 * (-0.61672, -0.669211)
		vertex[31] = @nscale1 * (-0.382911, -0.962397)
		vertex[32] = @nscale1 * (-0.401542, -0.838794)
		vertex[33] = @nscale1 * (-0.479478, -0.741065)
		vertex[34] = @nscale1 * (-0.557414, -0.838794)
		vertex[35] = @nscale1 * (-0.208337, -0.701791)
		vertex[36] = @nscale1 * (-0.1304, -0.604062)
		vertex[37] = @nscale1 * (-0.243021, -0.549826)
		vertex[38] = @nscale1 * (-0.172606, -0.653106)
		vertex[39] = @nscale1 * (0.165257, -0.815813)
		vertex[40] = @nscale1 * (0.193072, -0.693947)
		vertex[41] = @nscale1 * (0.10805, -0.785578)
		vertex[42] = @nscale1 * (0.0802354, -0.907444)
		vertex[43] = @nscale1 * (0.455235, -0.907444)
		vertex[44] = @nscale1 * (0.346982, -0.844944)
		vertex[45] = @nscale1 * (0.221982, -0.844944)
		vertex[46] = @nscale1 * (0.249797, -0.96681)
		vertex[47] = @nscale1 * (0.36033, -0.60847)
		vertex[48] = @nscale1 * (0.332515, -0.486604)
		vertex[49] = @nscale1 * (0.219894, -0.54084)
		vertex[50] = @nscale1 * (0.344545, -0.550181)
		vertex[51] = @nscale1 * (0.682408, -0.387475)
		vertex[52] = @nscale1 * (0.604472, -0.289746)
		vertex[53] = @nscale1 * (0.623102, -0.413349)
		vertex[54] = @nscale1 * (0.701038, -0.511078)
		vertex[55] = @nscale1 * (0.934847, -0.217892)
		vertex[56] = @nscale1 * (0.818488, -0.263559)
		vertex[57] = @nscale1 * (0.740552, -0.361288)
		vertex[58] = @nscale1 * (0.853173, -0.415524)
		vertex[59] = @nscale1 * (0.641928, -0.105684)
		vertex[60] = @nscale1 * (0.529307, -0.0514486)
		vertex[61] = @nscale1 * (0.501491, -0.173315)
		vertex[62] = @nscale1 * (0.586513, -0.0816831)
		vertex[63] = @nscale1 * (0.669958, 0.283915)
		vertex[64] = @nscale1 * (0.544958, 0.283915)
		vertex[65] = @nscale1 * (0.653212, 0.221415)
		vertex[66] = @nscale1 * (0.778212, 0.221415)
		vertex[67] = @nscale1 * (0.694766, 0.587013)
		vertex[68] = @nscale1 * (0.657922, 0.467566)
		vertex[69] = @nscale1 * (0.685737, 0.3457)
		vertex[70] = @nscale1 * (0.798358, 0.399936)
		vertex[71] = @nscale1 * (0.424407, 0.427959)
		vertex[72] = @nscale1 * (0.311786, 0.373724)
		vertex[73] = @nscale1 * (0.389722, 0.275995)
		vertex[74] = @nscale1 * (0.371091, 0.399599)
		vertex[75] = @nscale1 * (0.137283, 0.692786)
		vertex[76] = @nscale1 * (0.0593465, 0.595057)
		vertex[77] = @nscale1 * (0.175706, 0.640724)
		vertex[78] = @nscale1 * (0.253642, 0.738453)
		vertex[79] = @nscale1 * (-0.0842213, 0.90116)
		vertex[80] = @nscale1 * (-0.0138063, 0.79788)
		vertex[81] = @nscale1 * (0.0988148, 0.743644)
		vertex[82] = @nscale1 * (0.12663, 0.86551)
		vertex[83] = @nscale1 * (-0.128435, 0.590616)
		vertex[84] = @nscale1 * (-0.15625, 0.46875)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 188 ; "1,3,1,4,2;-1/2,1/6"
		cursality = 1
		numbervertices = 73 ; n + cursality for closed curves
		cincrement = 73 ; numbervertices/cursality
		; initialize arrays
		vertex[0] = @nscale1 * (0.290323, 0.870968)
		vertex[1] = @nscale1 * (0.419355, 0.870968)
		vertex[2] = @nscale1 * (0.419355, 0.483871)
		vertex[3] = @nscale1 * (0.483871, 0.372126)
		vertex[4] = @nscale1 * (0.0368901, 0.114061)
		vertex[5] = @nscale1 * (-0.0921421, -0.109429)
		vertex[6] = @nscale1 * (-0.203887, -0.0449131)
		vertex[7] = @nscale1 * (-0.590984, -0.0449131)
		vertex[8] = @nscale1 * (-0.590984, 0.0841192)
		vertex[9] = @nscale1 * (-0.849049, 0.5311)
		vertex[10] = @nscale1 * (-0.625558, 0.660132)
		vertex[11] = @nscale1 * (-0.561042, 0.771878)
		vertex[12] = @nscale1 * (-0.225806, 0.578329)
		vertex[13] = @nscale1 * (-0.0967742, 0.578329)
		vertex[14] = @nscale1 * (-0.0967742, 0.0622001)
		vertex[15] = @nscale1 * (0.0322581, -0.16129)
		vertex[16] = @nscale1 * (-0.0794871, -0.225806)
		vertex[17] = @nscale1 * (-0.273036, -0.561042)
		vertex[18] = @nscale1 * (-0.384781, -0.496526)
		vertex[19] = @nscale1 * (-0.90091, -0.496526)
		vertex[20] = @nscale1 * (-0.90091, -0.238461)
		vertex[21] = @nscale1 * (-0.965426, -0.126716)
		vertex[22] = @nscale1 * (-0.63019, 0.0668322)
		vertex[23] = @nscale1 * (-0.565674, 0.178577)
		vertex[24] = @nscale1 * (-0.118693, -0.0794871)
		vertex[25] = @nscale1 * (0.139371, -0.0794871)
		vertex[26] = @nscale1 * (0.139371, -0.208519)
		vertex[27] = @nscale1 * (0.33292, -0.543755)
		vertex[28] = @nscale1 * (0.221174, -0.608271)
		vertex[29] = @nscale1 * (-0.0368901, -1.05525)
		vertex[30] = @nscale1 * (-0.260381, -0.92622)
		vertex[31] = @nscale1 * (-0.389413, -0.92622)
		vertex[32] = @nscale1 * (-0.389413, -0.539123)
		vertex[33] = @nscale1 * (-0.453929, -0.427378)
		vertex[34] = @nscale1 * (-0.00694807, -0.169313)
		vertex[35] = @nscale1 * (0.122084, 0.0541772)
		vertex[36] = @nscale1 * (0.233829, -0.010339)
		vertex[37] = @nscale1 * (0.620926, -0.010339)
		vertex[38] = @nscale1 * (0.620926, -0.139371)
		vertex[39] = @nscale1 * (0.878991, -0.586352)
		vertex[40] = @nscale1 * (0.6555, -0.715384)
		vertex[41] = @nscale1 * (0.590984, -0.82713)
		vertex[42] = @nscale1 * (0.255748, -0.633581)
		vertex[43] = @nscale1 * (0.126716, -0.633581)
		vertex[44] = @nscale1 * (0.126716, -0.117452)
		vertex[45] = @nscale1 * (-0.00231602, 0.106038)
		vertex[46] = @nscale1 * (0.109429, 0.170554)
		vertex[47] = @nscale1 * (0.302978, 0.50579)
		vertex[48] = @nscale1 * (0.414723, 0.441274)
		vertex[49] = @nscale1 * (0.930852, 0.441274)
		vertex[50] = @nscale1 * (0.930852, 0.183209)
		vertex[51] = @nscale1 * (0.995368, 0.0714642)
		vertex[52] = @nscale1 * (0.660132, -0.122084)
		vertex[53] = @nscale1 * (0.595616, -0.233829)
		vertex[54] = @nscale1 * (0.148635, 0.0242351)
		vertex[55] = @nscale1 * (-0.109429, 0.0242351)
		vertex[56] = @nscale1 * (-0.109429, 0.153267)
		vertex[57] = @nscale1 * (-0.302978, 0.488503)
		vertex[58] = @nscale1 * (-0.191232, 0.553019)
		vertex[59] = @nscale1 * (0.0668322, 1.)
		vertex[60] = @nscale1 * (0.290323, 0.870968)
		vertex[61] = @nscale1 * (0.419355, 0.870968)
		vertex[62] = @nscale1 * (0.419355, 0.483871)
		vertex[63] = @nscale1 * (0.483871, 0.372126)
		vertex[64] = @nscale1 * (0.0368901, 0.114061)
		vertex[65] = @nscale1 * (-0.0921421, -0.109429)
		vertex[66] = @nscale1 * (-0.203887, -0.0449131)
		vertex[67] = @nscale1 * (-0.590984, -0.0449131)
		vertex[68] = @nscale1 * (-0.590984, 0.0841192)
		vertex[69] = @nscale1 * (-0.849049, 0.5311)
		vertex[70] = @nscale1 * (-0.625558, 0.660132)
		vertex[71] = @nscale1 * (-0.561042, 0.771878)
		vertex[72] = @nscale1 * (-0.225806, 0.578329)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 189 ; "13-gon"
		cursality = 1
		numbervertices = 14 ; vertices + cursality for closed curves
		cincrement = 14 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(glindex * twopi / 13)
			ycoord[glindex] = @nscale1 * sin(glindex * twopi / 13)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 190 ; "14-gon"
		cursality = 1
		numbervertices = 15 ; vertices + cursality for closed curves
		cincrement = 15 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(glindex * twopi / 14)
			ycoord[glindex] = @nscale1 * sin(glindex * twopi / 14)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 191 ; "15-gon"
		cursality = 1
		numbervertices = 16 ; vertices + cursality for closed curves
		cincrement = 16 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(glindex * twopi / 15)
			ycoord[glindex] = @nscale1 * sin(glindex * twopi / 15)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 192 ; "16-gon"
		cursality = 1
		numbervertices = 17 ; vertices + cursality for closed curves
		cincrement = 17 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = @nscale1 * cos(glindex * twopi / 16)
			ycoord[glindex] = @nscale1 * sin(glindex * twopi / 16)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 193 ; "13-asterisk"
		cursality = 13
		numbervertices = 26 ; vertices only for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			vertex[glindex] = (0,0)
			xcoord[glindex + 1] = @nscale1 * cos(glindex * #pi / 13)
			ycoord[glindex + 1] = @nscale1 * sin(glindex * #pi / 13)
			glindex = glindex + 1
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		vertex[1] = @leafAlength * vertex[1]
		xcoord[1] = real(vertex[1])
		ycoord[1] = imag(vertex[1])
	elseif traparray == 194 ; "14-asterisk"
		cursality = 14
		numbervertices = 28 ; vertices only for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			vertex[glindex] = (0,0)
			xcoord[glindex + 1] = @nscale1 * cos(glindex * #pi / 14)
			ycoord[glindex + 1] = @nscale1 * sin(glindex * #pi / 14)
			glindex = glindex + 1
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		vertex[1] = @leafAlength * vertex[1]
		xcoord[1] = real(vertex[1])
		ycoord[1] = imag(vertex[1])
	elseif traparray == 195 ; "15-asterisk"
		cursality = 15
		numbervertices = 30 ; vertices only for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			vertex[glindex] = (0,0)
			xcoord[glindex + 1] = @nscale1 * cos(glindex * #pi / 15)
			ycoord[glindex + 1] = @nscale1 * sin(glindex * #pi / 15)
			glindex = glindex + 1
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		vertex[1] = @leafAlength * vertex[1]
		xcoord[1] = real(vertex[1])
		ycoord[1] = imag(vertex[1])
	elseif traparray == 196 ; "16-asterisk"
		cursality = 16
		numbervertices = 32 ; vertices only for open curves
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		while glindex < numbervertices
			vertex[glindex] = (0,0)
			xcoord[glindex + 1] = @nscale1 * cos(glindex * #pi / 16)
			ycoord[glindex + 1] = @nscale1 * sin(glindex * #pi / 16)
			glindex = glindex + 1
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		vertex[1] = @leafAlength * vertex[1]
		xcoord[1] = real(vertex[1])
		ycoord[1] = imag(vertex[1])
	elseif traparray == 197 ; "13-star"
		cursality = 1
		numbervertices = 27 ; n + cursality for closed curves
		cincrement = 27 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = @nscale1 * (0.5, 0.)
		vertex[ 1] = @starspikiness * @nscale1 * (0.970942, 0.239316)
		vertex[ 2] = @nscale1 * (0.442728, 0.232362)
		vertex[ 3] = @starspikiness * @nscale1 * (0.748511, 0.663123)
		vertex[ 4] = @nscale1 * (0.284032, 0.411492)
		vertex[ 5] = @starspikiness * @nscale1 * (0.354605, 0.935016)
		vertex[ 6] = @nscale1 * (0.0602683, 0.496354)
		vertex[ 7] = @starspikiness * @nscale1 * (-0.120537, 0.992709)
		vertex[ 8] = @nscale1 * (-0.177302, 0.467508)
		vertex[ 9] = @starspikiness * @nscale1 * (-0.568065, 0.822984)
		vertex[ 10] = @nscale1 * (-0.374255, 0.331561)
		vertex[ 11] = @starspikiness * @nscale1 * (-0.885456, 0.464723)
		vertex[ 12] = @nscale1 * (-0.485471, 0.119658)
		vertex[ 13] = @starspikiness * @nscale1 * (-1., 0.)
		vertex[ 14] = @nscale1 * (-0.485471, -0.119658)
		vertex[ 15] = @starspikiness * @nscale1 * (-0.885456, -0.464723)
		vertex[ 16] = @nscale1 * (-0.374255, -0.331561)
		vertex[ 17] = @starspikiness * @nscale1 * (-0.568065, -0.822984)
		vertex[ 18] = @nscale1 * (-0.177302, -0.467508)
		vertex[ 19] = @starspikiness * @nscale1 * (-0.120537, -0.992709)
		vertex[ 20] = @nscale1 * (0.0602683, -0.496354)
		vertex[ 21] = @starspikiness * @nscale1 * (0.354605, -0.935016)
		vertex[ 22] = @nscale1 * (0.284032, -0.411492)
		vertex[ 23] = @starspikiness * @nscale1 * (0.748511, -0.663123)
		vertex[ 24] = @nscale1 * (0.442728, -0.232362)
		vertex[ 25] = @starspikiness * @nscale1 * (0.970942, -0.239316)
		vertex[ 26] = @nscale1 * (0.5, 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 198 ; "14-star"
		cursality = 1
		numbervertices = 29 ; n + cursality for closed curves
		cincrement = 29 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = @nscale1 * (0.5, 0.)
		vertex[ 1] = @starspikiness * @nscale1 * (0.974928, 0.222521)
		vertex[ 2] = @nscale1 * (0.450484, 0.216942)
		vertex[ 3] = @starspikiness * @nscale1 * (0.781831, 0.62349)
		vertex[ 4] = @nscale1 * (0.311745, 0.390916)
		vertex[ 5] = @starspikiness * @nscale1 * (0.433884, 0.900969)
		vertex[ 6] = @nscale1 * (0.11126, 0.487464)
		vertex[ 7] = @starspikiness * @nscale1 * (0., 1.)
		vertex[ 8] = @nscale1 * (-0.11126, 0.487464)
		vertex[ 9] = @starspikiness * @nscale1 * (-0.433884, 0.900969)
		vertex[ 10] = @nscale1 * (-0.311745, 0.390916)
		vertex[ 11] = @starspikiness * @nscale1 * (-0.781831, 0.62349)
		vertex[ 12] = @nscale1 * (-0.450484, 0.216942)
		vertex[ 13] = @starspikiness * @nscale1 * (-0.974928, 0.222521)
		vertex[ 14] = @nscale1 * (-0.5,  0.)
		vertex[ 15] = @starspikiness * @nscale1 * (-0.974928, -0.222521)
		vertex[ 16] = @nscale1 * (-0.450484, -0.216942)
		vertex[ 17] = @starspikiness * @nscale1 * (-0.781831, -0.62349)
		vertex[ 18] = @nscale1 * (-0.311745, -0.390916)
		vertex[ 19] = @starspikiness * @nscale1 * (-0.433884, -0.900969)
		vertex[ 20] = @nscale1 * (-0.11126, -0.487464)
		vertex[ 21] = @starspikiness * @nscale1 * (0., -1.)
		vertex[ 22] = @nscale1 * (0.11126, -0.487464)
		vertex[ 23] = @starspikiness * @nscale1 * (0.433884, -0.900969)
		vertex[ 24] = @nscale1 * (0.311745, -0.390916)
		vertex[ 25] = @starspikiness * @nscale1 * (0.781831, -0.62349)
		vertex[ 26] = @nscale1 * (0.450484, -0.216942)
		vertex[ 27] = @starspikiness * @nscale1 * (0.974928, -0.222521)
		vertex[ 28] = @nscale1 * (0.5, 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 199 ; "15-star"
		cursality = 1
		numbervertices = 31 ; n + cursality for closed curves
		cincrement = 31 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = @nscale1 * (0.5, 0.)
		vertex[ 1] = @starspikiness * @nscale1 * (0.978148, 0.207912)
		vertex[ 2] = @nscale1 * (0.456773, 0.203368)
		vertex[ 3] = @starspikiness * @nscale1 * (0.809017, 0.587785)
		vertex[ 4] = @nscale1 * (0.334565, 0.371572)
		vertex[ 5] = @starspikiness * @nscale1 * (0.5, 0.866025)
		vertex[ 6] = @nscale1 * (0.154508, 0.475528)
		vertex[ 7] = @starspikiness * @nscale1 * (0.104528, 0.994522)
		vertex[ 8] = @nscale1 * (-0.0522642, 0.497261)
		vertex[ 9] = @starspikiness * @nscale1 * (-0.309017, 0.951057)
		vertex[ 10] = @nscale1 * (-0.25, 0.433013)
		vertex[ 11] = @starspikiness * @nscale1 * (-0.669131, 0.743145)
		vertex[ 12] = @nscale1 * (-0.404508, 0.293893)
		vertex[ 13] = @starspikiness * @nscale1 * (-0.913545, 0.406737)
		vertex[ 14] = @nscale1 * (-0.489074, 0.103956)
		vertex[ 15] = @starspikiness * @nscale1 * (-1., 0.)
		vertex[ 16] = @nscale1 * (-0.489074, -0.103956)
		vertex[ 17] = @starspikiness * @nscale1 * (-0.913545, -0.406737)
		vertex[ 18] = @nscale1 * (-0.404508, -0.293893)
		vertex[ 19] = @starspikiness * @nscale1 * (-0.669131, -0.743145)
		vertex[ 20] = @nscale1 * (-0.25, -0.433013)
		vertex[ 21] = @starspikiness * @nscale1 * (-0.309017, -0.951057)
		vertex[ 22] = @nscale1 * (-0.0522642, -0.497261)
		vertex[ 23] = @starspikiness * @nscale1 * (0.104528, -0.994522)
		vertex[ 24] = @nscale1 * (0.154508, -0.475528)
		vertex[ 25] = @starspikiness * @nscale1 * (0.5, -0.866025)
		vertex[ 26] = @nscale1 * (0.334565, -0.371572)
		vertex[ 27] = @starspikiness * @nscale1 * (0.809017, -0.587785)
		vertex[ 28] = @nscale1 * (0.456773, -0.203368)
		vertex[ 29] = @starspikiness * @nscale1 * (0.978148, -0.207912)
		vertex[ 30] = @nscale1 * (0.5, 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 200 ; "16-star"
		cursality = 1
		numbervertices = 33 ; n + cursality for closed curves
		cincrement = 33 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = @nscale1 * (0.5, 0.)
		vertex[ 1] = @starspikiness * @nscale1 * (0.980785, 0.19509)
		vertex[ 2] = @nscale1 * (0.46194, 0.191342)
		vertex[ 3] = @starspikiness * @nscale1 * (0.83147, 0.55557)
		vertex[ 4] = @nscale1 * (0.353553, 0.353553)
		vertex[ 5] = @starspikiness * @nscale1 * (0.55557, 0.83147)
		vertex[ 6] = @nscale1 * (0.191342, 0.46194)
		vertex[ 7] = @starspikiness * @nscale1 * (0.19509, 0.980785)
		vertex[ 8] = @nscale1 * (0., 0.5)
		vertex[ 9] = @starspikiness * @nscale1 * (-0.19509, 0.980785)
		vertex[ 10] = @nscale1 * (-0.191342, 0.46194)
		vertex[ 11] = @starspikiness * @nscale1 * (-0.55557, 0.83147)
		vertex[ 12] = @nscale1 * (-0.353553, 0.353553)
		vertex[ 13] = @starspikiness * @nscale1 * (-0.83147, 0.55557)
		vertex[ 14] = @nscale1 * (-0.46194, 0.191342)
		vertex[ 15] = @starspikiness * @nscale1 * (-0.980785, 0.19509)
		vertex[ 16] = @nscale1 * (-0.5, 0.)
		vertex[ 17] = @starspikiness * @nscale1 * (-0.980785, -0.19509)
		vertex[ 18] = @nscale1 * (-0.46194, -0.191342)
		vertex[ 19] = @starspikiness * @nscale1 * (-0.83147, -0.55557)
		vertex[ 20] = @nscale1 * (-0.353553, -0.353553)
		vertex[ 21] = @starspikiness * @nscale1 * (-0.55557, -0.83147)
		vertex[ 22] = @nscale1 * (-0.191342, -0.46194)
		vertex[ 23] = @starspikiness * @nscale1 * (-0.19509, -0.980785)
		vertex[ 24] = @nscale1 * (0., -0.5)
		vertex[ 25] = @starspikiness * @nscale1 * (0.19509, -0.980785)
		vertex[ 26] = @nscale1 * (0.191342, -0.46194)
		vertex[ 27] = @starspikiness * @nscale1 * (0.55557, -0.83147)
		vertex[ 28] = @nscale1 * (0.353553, -0.353553)
		vertex[ 29] = @starspikiness * @nscale1 * (0.83147, -0.55557)
		vertex[ 30] = @nscale1 * (0.46194, -0.191342)
		vertex[ 31] = @starspikiness * @nscale1 * (0.980785, -0.19509)
		vertex[ 32] = @nscale1 * (0.5, 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 201 ; "3-rhombstar"
		cursality = 3
		numbervertices = 12 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.75 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.75 * @nscale1 * (0.5, 0.866025)
		vertex[ 2] = 0.75 * @nscale1 * (-0.5, 0.866025)
		vertex[ 3] = 0.75 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.75 * @nscale1 * (-0.5, -0.866025)
		vertex[ 5] = 0.75 * @nscale1 * (0.5, -0.866025)
		vertex[ 6] = 0.75 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.75 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.75 * @nscale1 * (-0.5, 0.866025)
		vertex[ 9] = 0.75 * @nscale1 * (-1., 0.)
		vertex[ 10] =0.75 *  @nscale1 * (-0.5, -0.866025)
		vertex[ 11] = 0.75 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 202 ; "5-rhombstar"
		cursality = 5
		numbervertices = 20 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.5 * @nscale1 * (1.15, 0.)
		vertex[ 1] = 0.5 * @nscale1 * (1.45902, 0.951057)
		vertex[ 2] = 0.5 * @nscale1 * (0.459017, 0.951057)
		vertex[ 3] = 0.5 * @nscale1 * (0.15, 0.)
		vertex[ 4] = 0.5 * @nscale1 * (0.459017, -0.951057)
		vertex[ 5] = 0.5 * @nscale1 * (1.45902, -0.951057)
		vertex[ 6] = 0.5 * @nscale1 * (1.15, 0.)
		vertex[ 7] = 0.5 * @nscale1 * (0.15, 0.)
		vertex[ 8] = 0.5 * @nscale1 * (-0.659017, -0.587785)
		vertex[ 9] = 0.5 * @nscale1 * (-0.35, -1.53884)
		vertex[ 10] = 0.5 * @nscale1 * (0.459017, -0.951057)
		vertex[ 11] = 0.5 * @nscale1 * (0.15, 0.)
		vertex[ 12] = 0.5 * @nscale1 * (-0.659017, 0.587785)
		vertex[ 13] = 0.5 * @nscale1 * (-1.46803, 0.)
		vertex[ 14] = 0.5 * @nscale1 * (-0.659017, -0.587785)
		vertex[ 15] = 0.5 * @nscale1 * (0.15, 0.)
		vertex[ 16] = 0.5 * @nscale1 * (0.459017, 0.951057)
		vertex[ 17] = 0.5 * @nscale1 * (-0.35, 1.53884)
		vertex[ 18] = 0.5 * @nscale1 * (-0.659017, 0.587785)
		vertex[ 19] = 0.5 * @nscale1 * (0.15, 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 203 ; "6-rhombstar"
		cursality = 6
		numbervertices = 24 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.5 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.5 * @nscale1 * (1.5, 0.866025)
		vertex[ 2] = 0.5 * @nscale1 * (0.5, 0.866025)
		vertex[ 3] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.5 * @nscale1 * (0.5, -0.866025)
		vertex[ 5] = 0.5 * @nscale1 * (1.5, -0.866025)
		vertex[ 6] = 0.5 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.5 * @nscale1 * (-0.5, -0.866025)
		vertex[ 9] = 0.5 * @nscale1 * (0., -1.73205)
		vertex[ 10] = 0.5 * @nscale1 * (0.5, -0.866025)
		vertex[ 11] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.5 * @nscale1 * (-1., 0.)
		vertex[ 13] = 0.5 * @nscale1 * (-1.5, -0.866025)
		vertex[ 14] = 0.5 * @nscale1 * (-0.5, -0.866025)
		vertex[ 15] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.5 * @nscale1 * (-0.5, 0.866025)
		vertex[ 17] = 0.5 * @nscale1 * (-1.5, 0.866025)
		vertex[ 18] = 0.5 * @nscale1 * (-1., 0.)
		vertex[ 19] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.5 * @nscale1 * (0.5, 0.866025)
		vertex[ 21] = 0.5 * @nscale1 * (0., 1.73205)
		vertex[ 22] = 0.5 * @nscale1 * (-0.5, 0.866025)
		vertex[ 23] = 0.5 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 204 ; "7-rhombstar"
		cursality = 7
		numbervertices = 28 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.5 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.5 * @nscale1 * (1.62349, 0.781831)
		vertex[ 2] = 0.5 * @nscale1 * (0.62349, 0.781831)
		vertex[ 3] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.5 * @nscale1 * (0.62349, -0.781831)
		vertex[ 5] = 0.5 * @nscale1 * (1.62349, -0.781831)
		vertex[ 6] = 0.5 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.5 * @nscale1 * (-0.222521, -0.974928)
		vertex[ 9] = 0.5 * @nscale1 * (0.400969, -1.75676)
		vertex[ 10] = 0.5 * @nscale1 * (0.62349, -0.781831)
		vertex[ 11] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.5 * @nscale1 * (-0.900969, -0.433884)
		vertex[ 13] = 0.5 * @nscale1 * (-1.12349, -1.40881)
		vertex[ 14] = 0.5 * @nscale1 * (-0.222521, -0.974928)
		vertex[ 15] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.5 * @nscale1 * (-0.900969, 0.433884)
		vertex[ 17] = 0.5 * @nscale1 * (-1.80194, 0.)
		vertex[ 18] = 0.5 * @nscale1 * (-0.900969, -0.433884)
		vertex[ 19] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.5 * @nscale1 * (-0.222521, 0.974928)
		vertex[ 21] = 0.5 * @nscale1 * (-1.12349, 1.40881)
		vertex[ 22] = 0.5 * @nscale1 * (-0.900969, 0.433884)
		vertex[ 23] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.5 * @nscale1 * (0.62349, 0.781831)
		vertex[ 25] = 0.5 * @nscale1 * (0.400969, 1.75676)
		vertex[ 26] = 0.5 * @nscale1 * (-0.222521, 0.974928)
		vertex[ 27] = 0.5 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 205 ; "8-rhombstar"
		cursality = 8
		numbervertices = 32 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.5 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.5 * @nscale1 * (1.70711, 0.707107)
		vertex[ 2] = 0.5 * @nscale1 * (0.707107, 0.707107)
		vertex[ 3] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.5 * @nscale1 * (0.707107, -0.707107)
		vertex[ 5] = 0.5 * @nscale1 * (1.70711, -0.707107)
		vertex[ 6] = 0.5 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.5 * @nscale1 * (0., -1.)
		vertex[ 9] = 0.5 * @nscale1 * (0.707107, -1.70711)
		vertex[ 10] = 0.5 * @nscale1 * (0.707107, -0.707107)
		vertex[ 11] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.5 * @nscale1 * (-0.707107, -0.707107)
		vertex[ 13] = 0.5 * @nscale1 * (-0.707107, -1.70711)
		vertex[ 14] = 0.5 * @nscale1 * (0., -1.)
		vertex[ 15] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.5 * @nscale1 * (-1., 0.)
		vertex[ 17] = 0.5 * @nscale1 * (-1.70711, -0.707107)
		vertex[ 18] = 0.5 * @nscale1 * (-0.707107, -0.707107)
		vertex[ 19] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.5 * @nscale1 * (-0.707107, 0.707107)
		vertex[ 21] = 0.5 * @nscale1 * (-1.70711, 0.707107)
		vertex[ 22] = 0.5 * @nscale1 * (-1., 0.)
		vertex[ 23] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.5 * @nscale1 * (0., 1.)
		vertex[ 25] = 0.5 * @nscale1 * (-0.707107, 1.70711)
		vertex[ 26] = 0.5 * @nscale1 * (-0.707107, 0.707107)
		vertex[ 27] = 0.5 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.5 * @nscale1 * (0.707107, 0.707107)
		vertex[ 29] = 0.5 * @nscale1 * (0.707107, 1.70711)
		vertex[ 30] = 0.5 * @nscale1 * (0., 1.)
		vertex[ 31] = 0.5 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 206 ; "9-rhombstar"
		cursality = 9
		numbervertices = 36 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.4 * @nscale1 * (1.76604, 0.642788)
		vertex[ 2] = 0.4 * @nscale1 * (0.766044, 0.642788)
		vertex[ 3] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.4 * @nscale1 * (0.766044, -0.642788)
		vertex[ 5] = 0.4 * @nscale1 * (1.76604, -0.642788)
		vertex[ 6] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.4 * @nscale1 * (0.173648, -0.984808)
		vertex[ 9] = 0.4 * @nscale1 * (0.939693, -1.6276)
		vertex[ 10] = 0.4 * @nscale1 * (0.766044, -0.642788)
		vertex[ 11] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.4 * @nscale1 * (-0.5, -0.866025)
		vertex[ 13] = 0.4 * @nscale1 * (-0.326352, -1.85083)
		vertex[ 14] = 0.4 * @nscale1 * (0.173648, -0.984808)
		vertex[ 15] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.4 * @nscale1 * (-0.939693, -0.34202)
		vertex[ 17] = 0.4 * @nscale1 * (-1.43969, -1.20805)
		vertex[ 18] = 0.4 * @nscale1 * (-0.5, -0.866025)
		vertex[ 19] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.4 * @nscale1 * (-0.939693, 0.34202)
		vertex[ 21] = 0.4 * @nscale1 * (-1.87939, 0.)
		vertex[ 22] = 0.4 * @nscale1 * (-0.939693, -0.34202)
		vertex[ 23] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.4 * @nscale1 * (-0.5, 0.866025)
		vertex[ 25] = 0.4 * @nscale1 * (-1.43969, 1.20805)
		vertex[ 26] = 0.4 * @nscale1 * (-0.939693, 0.34202)
		vertex[ 27] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.4 * @nscale1 * (0.173648, 0.984808)
		vertex[ 29] = 0.4 * @nscale1 * (-0.326352, 1.85083)
		vertex[ 30] = 0.4 * @nscale1 * (-0.5, 0.866025)
		vertex[ 31] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 32] = 0.4 * @nscale1 * (0.766044, 0.642788)
		vertex[ 33] = 0.4 * @nscale1 * (0.939693, 1.6276)
		vertex[ 34] = 0.4 * @nscale1 * (0.173648, 0.984808)
		vertex[ 35] = 0.4 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 207 ; "10-rhombstar"
		cursality = 10
		numbervertices = 40 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.4 * @nscale1 * (1.80902, 0.587785)
		vertex[ 2] = 0.4 * @nscale1 * (0.809017, 0.587785)
		vertex[ 3] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.4 * @nscale1 * (0.809017, -0.587785)
		vertex[ 5] = 0.4 * @nscale1 * (1.80902, -0.587785)
		vertex[ 6] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.4 * @nscale1 * (0.309017, -0.951057)
		vertex[ 9] = 0.4 * @nscale1 * (1.11803, -1.53884)
		vertex[ 10] = 0.4 * @nscale1 * (0.809017, -0.587785)
		vertex[ 11] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.4 * @nscale1 * (-0.309017, -0.951057)
		vertex[ 13] = 0.4 * @nscale1 * (0., -1.90211)
		vertex[ 14] = 0.4 * @nscale1 * (0.309017, -0.951057)
		vertex[ 15] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.4 * @nscale1 * (-0.809017, -0.587785)
		vertex[ 17] = 0.4 * @nscale1 * (-1.11803, -1.53884)
		vertex[ 18] = 0.4 * @nscale1 * (-0.309017, -0.951057)
		vertex[ 19] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.4 * @nscale1 * (-1., 0.)
		vertex[ 21] = 0.4 * @nscale1 * (-1.80902, -0.587785)
		vertex[ 22] = 0.4 * @nscale1 * (-0.809017, -0.587785)
		vertex[ 23] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.4 * @nscale1 * (-0.809017, 0.587785)
		vertex[ 25] = 0.4 * @nscale1 * (-1.80902, 0.587785)
		vertex[ 26] = 0.4 * @nscale1 * (-1., 0.)
		vertex[ 27] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.4 * @nscale1 * (-0.309017, 0.951057)
		vertex[ 29] = 0.4 * @nscale1 * (-1.11803, 1.53884)
		vertex[ 30] = 0.4 * @nscale1 * (-0.809017, 0.587785)
		vertex[ 31] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 32] = 0.4 * @nscale1 * (0.309017, 0.951057)
		vertex[ 33] = 0.4 * @nscale1 * (0., 1.90211)
		vertex[ 34] = 0.4 * @nscale1 * (-0.309017, 0.951057)
		vertex[ 35] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 36] = 0.4 * @nscale1 * (0.809017, 0.587785)
		vertex[ 37] = 0.4 * @nscale1 * (1.11803, 1.53884)
		vertex[ 38] = 0.4 * @nscale1 * (0.309017, 0.951057)
		vertex[ 39] = 0.4 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 208 ; "11-rhombstar"
		cursality = 11
		numbervertices = 44 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.4 * @nscale1 * (1.84125, 0.540641)
		vertex[ 2] = 0.4 * @nscale1 * (0.841254, 0.540641)
		vertex[ 3] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.4 * @nscale1 * (0.841254, -0.540641)
		vertex[ 5] = 0.4 * @nscale1 * (1.84125, -0.540641)
		vertex[ 6] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.4 * @nscale1 * (0.415415, -0.909632)
		vertex[ 9] = 0.4 * @nscale1 * (1.25667, -1.45027)
		vertex[ 10] = 0.4 * @nscale1 * (0.841254, -0.540641)
		vertex[ 11] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.4 * @nscale1 * (-0.142315, -0.989821)
		vertex[ 13] = 0.4 * @nscale1 * (0.2731, -1.89945)
		vertex[ 14] = 0.4 * @nscale1 * (0.415415, -0.909632)
		vertex[ 15] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.4 * @nscale1 * (-0.654861, -0.75575)
		vertex[ 17] = 0.4 * @nscale1 * (-0.797176, -1.74557)
		vertex[ 18] = 0.4 * @nscale1 * (-0.142315, -0.989821)
		vertex[ 19] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.4 * @nscale1 * (-0.959493, -0.281733)
		vertex[ 21] = 0.4 * @nscale1 * (-1.61435, -1.03748)
		vertex[ 22] = 0.4 * @nscale1 * (-0.654861, -0.75575)
		vertex[ 23] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.4 * @nscale1 * (-0.959493, 0.281733)
		vertex[ 25] = 0.4 * @nscale1 * (-1.91899, 0.)
		vertex[ 26] = 0.4 * @nscale1 * (-0.959493, -0.281733)
		vertex[ 27] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.4 * @nscale1 * (-0.654861, 0.75575)
		vertex[ 29] = 0.4 * @nscale1 * (-1.61435, 1.03748)
		vertex[ 30] = 0.4 * @nscale1 * (-0.959493, 0.281733)
		vertex[ 31] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 32] = 0.4 * @nscale1 * (-0.142315, 0.989821)
		vertex[ 33] = 0.4 * @nscale1 * (-0.797176, 1.74557)
		vertex[ 34] = 0.4 * @nscale1 * (-0.654861, 0.75575)
		vertex[ 35] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 36] = 0.4 * @nscale1 * (0.415415, 0.909632)
		vertex[ 37] = 0.4 * @nscale1 * (0.2731, 1.89945)
		vertex[ 38] = 0.4 * @nscale1 * (-0.142315, 0.989821)
		vertex[ 39] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 40] = 0.4 * @nscale1 * (0.841254, 0.540641)
		vertex[ 41] = 0.4 * @nscale1 * (1.25667, 1.45027)
		vertex[ 42] = 0.4 * @nscale1 * (0.415415, 0.909632)
		vertex[ 43] = 0.4 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 209 ; "12-rhombstar"
		cursality = 12
		numbervertices = 48 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.4 * @nscale1 * (1.86603, 0.5)
		vertex[ 2] = 0.4 * @nscale1 * (0.866025, 0.5)
		vertex[ 3] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.4 * @nscale1 * (0.866025, -0.5)
		vertex[ 5] = 0.4 * @nscale1 * (1.86603, -0.5)
		vertex[ 6] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.4 * @nscale1 * (0.5, -0.866025)
		vertex[ 9] = 0.4 * @nscale1 * (1.36603, -1.36603)
		vertex[ 10] = 0.4 * @nscale1 * (0.866025, -0.5)
		vertex[ 11] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.4 * @nscale1 * (0., -1.)
		vertex[ 13] = 0.4 * @nscale1 * (0.5, -1.86603)
		vertex[ 14] = 0.4 * @nscale1 * (0.5, -0.866025)
		vertex[ 15] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.4 * @nscale1 * (-0.5, -0.866025)
		vertex[ 17] = 0.4 * @nscale1 * (-0.5, -1.86603)
		vertex[ 18] = 0.4 * @nscale1 * (0., -1.)
		vertex[ 19] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.4 * @nscale1 * (-0.866025, -0.5)
		vertex[ 21] = 0.4 * @nscale1 * (-1.36603, -1.36603)
		vertex[ 22] = 0.4 * @nscale1 * (-0.5, -0.866025)
		vertex[ 23] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.4 * @nscale1 * (-1., 0.)
		vertex[ 25] = 0.4 * @nscale1 * (-1.86603, -0.5)
		vertex[ 26] = 0.4 * @nscale1 * (-0.866025, -0.5)
		vertex[ 27] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.4 * @nscale1 * (-0.866025, 0.5)
		vertex[ 29] = 0.4 * @nscale1 * (-1.86603, 0.5)
		vertex[ 30] = 0.4 * @nscale1 * (-1., 0.)
		vertex[ 31] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 32] = 0.4 * @nscale1 * (-0.5, 0.866025)
		vertex[ 33] = 0.4 * @nscale1 * (-1.36603, 1.36603)
		vertex[ 34] = 0.4 * @nscale1 * (-0.866025, 0.5)
		vertex[ 35] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 36] = 0.4 * @nscale1 * (0., 1.)
		vertex[ 37] = 0.4 * @nscale1 * (-0.5, 1.86603)
		vertex[ 38] = 0.4 * @nscale1 * (-0.5, 0.866025)
		vertex[ 39] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 40] = 0.4 * @nscale1 * (0.5, 0.866025)
		vertex[ 41] = 0.4 * @nscale1 * (0.5, 1.86603)
		vertex[ 42] = 0.4 * @nscale1 * (0., 1.)
		vertex[ 43] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 44] = 0.4 * @nscale1 * (0.866025, 0.5)
		vertex[ 45] = 0.4 * @nscale1 * (1.36603, 1.36603)
		vertex[ 46] = 0.4 * @nscale1 * (0.5, 0.866025)
		vertex[ 47] = 0.4 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 210 ; "13-rhombstar"
		cursality = 13
		numbervertices = 52 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.4 * @nscale1 * (1.88546, 0.464723)
		vertex[ 2] = 0.4 * @nscale1 * (0.885456, 0.464723)
		vertex[ 3] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.4 * @nscale1 * (0.885456, -0.464723)
		vertex[ 5] = 0.4 * @nscale1 * (1.88546, -0.464723)
		vertex[ 6] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.4 * @nscale1 * (0.568065, -0.822984)
		vertex[ 9] = 0.4 * @nscale1 * (1.45352, -1.28771)
		vertex[ 10] = 0.4 * @nscale1 * (0.885456, -0.464723)
		vertex[ 11] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.4 * @nscale1 * (0.120537, -0.992709)
		vertex[ 13] = 0.4 * @nscale1 * (0.688601, -1.81569)
		vertex[ 14] = 0.4 * @nscale1 * (0.568065, -0.822984)
		vertex[ 15] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.4 * @nscale1 * (-0.354605, -0.935016)
		vertex[ 17] = 0.4 * @nscale1 * (-0.234068, -1.92773)
		vertex[ 18] = 0.4 * @nscale1 * (0.120537, -0.992709)
		vertex[ 19] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.4 * @nscale1 * (-0.748511, -0.663123)
		vertex[ 21] = 0.4 * @nscale1 * (-1.10312, -1.59814)
		vertex[ 22] = 0.4 * @nscale1 * (-0.354605, -0.935016)
		vertex[ 23] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.4 * @nscale1 * (-0.970942, -0.239316)
		vertex[ 25] = 0.4 * @nscale1 * (-1.71945, -0.902438)
		vertex[ 26] = 0.4 * @nscale1 * (-0.748511, -0.663123)
		vertex[ 27] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.4 * @nscale1 * (-0.970942, 0.239316)
		vertex[ 29] = 0.4 * @nscale1 * (-1.94188, 0.)
		vertex[ 30] = 0.4 * @nscale1 * (-0.970942, -0.239316)
		vertex[ 31] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 32] = 0.4 * @nscale1 * (-0.748511, 0.663123)
		vertex[ 33] = 0.4 * @nscale1 * (-1.71945, 0.902438)
		vertex[ 34] = 0.4 * @nscale1 * (-0.970942, 0.239316)
		vertex[ 35] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 36] = 0.4 * @nscale1 * (-0.354605, 0.935016)
		vertex[ 37] = 0.4 * @nscale1 * (-1.10312, 1.59814)
		vertex[ 38] = 0.4 * @nscale1 * (-0.748511, 0.663123)
		vertex[ 39] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 40] = 0.4 * @nscale1 * (0.120537, 0.992709)
		vertex[ 41] = 0.4 * @nscale1 * (-0.234068, 1.92773)
		vertex[ 42] = 0.4 * @nscale1 * (-0.354605, 0.935016)
		vertex[ 43] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 44] = 0.4 * @nscale1 * (0.568065, 0.822984)
		vertex[ 45] = 0.4 * @nscale1 * (0.688601, 1.81569)
		vertex[ 46] = 0.4 * @nscale1 * (0.120537, 0.992709)
		vertex[ 47] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 48] = 0.4 * @nscale1 * (0.885456, 0.464723)
		vertex[ 49] = 0.4 * @nscale1 * (1.45352, 1.28771)
		vertex[ 50] = 0.4 * @nscale1 * (0.568065, 0.822984)
		vertex[ 51] = 0.4 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 211 ; "14-rhombstar"
		cursality = 14
		numbervertices = 56 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.4 * @nscale1 * (1.90097, 0.433884)
		vertex[ 2] = 0.4 * @nscale1 * (0.900969, 0.433884)
		vertex[ 3] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.4 * @nscale1 * (0.900969, -0.433884)
		vertex[ 5] = 0.4 * @nscale1 * (1.90097, -0.433884)
		vertex[ 6] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.4 * @nscale1 * (0.62349, -0.781831)
		vertex[ 9] = 0.4 * @nscale1 * (1.52446, -1.21572)
		vertex[ 10] = 0.4 * @nscale1 * (0.900969, -0.433884)
		vertex[ 11] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.4 * @nscale1 * (0.222521, -0.974928)
		vertex[ 13] = 0.4 * @nscale1 * (0.846011, -1.75676)
		vertex[ 14] = 0.4 * @nscale1 * (0.62349, -0.781831)
		vertex[ 15] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.4 * @nscale1 * (-0.222521, -0.974928)
		vertex[ 17] = 0.4 * @nscale1 * (0., -1.94986)
		vertex[ 18] = 0.4 * @nscale1 * (0.222521, -0.974928)
		vertex[ 19] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.4 * @nscale1 * (-0.62349, -0.781831)
		vertex[ 21] = 0.4 * @nscale1 * (-0.846011, -1.75676)
		vertex[ 22] = 0.4 * @nscale1 * (-0.222521, -0.974928)
		vertex[ 23] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.4 * @nscale1 * (-0.900969, -0.433884)
		vertex[ 25] = 0.4 * @nscale1 * (-1.52446, -1.21572)
		vertex[ 26] = 0.4 * @nscale1 * (-0.62349, -0.781831)
		vertex[ 27] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.4 * @nscale1 * (-1., 0.)
		vertex[ 29] = 0.4 * @nscale1 * (-1.90097, -0.433884)
		vertex[ 30] = 0.4 * @nscale1 * (-0.900969, -0.433884)
		vertex[ 31] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 32] = 0.4 * @nscale1 * (-0.900969, 0.433884)
		vertex[ 33] = 0.4 * @nscale1 * (-1.90097, 0.433884)
		vertex[ 34] = 0.4 * @nscale1 * (-1., 0.)
		vertex[ 35] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 36] = 0.4 * @nscale1 * (-0.62349, 0.781831)
		vertex[ 37] = 0.4 * @nscale1 * (-1.52446, 1.21572)
		vertex[ 38] = 0.4 * @nscale1 * (-0.900969, 0.433884)
		vertex[ 39] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 40] = 0.4 * @nscale1 * (-0.222521, 0.974928)
		vertex[ 41] = 0.4 * @nscale1 * (-0.846011, 1.75676)
		vertex[ 42] = 0.4 * @nscale1 * (-0.62349, 0.781831)
		vertex[ 43] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 44] = 0.4 * @nscale1 * (0.222521, 0.974928)
		vertex[ 45] = 0.4 * @nscale1 * (0., 1.94986)
		vertex[ 46] = 0.4 * @nscale1 * (-0.222521, 0.974928)
		vertex[ 47] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 48] = 0.4 * @nscale1 * (0.62349, 0.781831)
		vertex[ 49] = 0.4 * @nscale1 * (0.846011, 1.75676)
		vertex[ 50] = 0.4 * @nscale1 * (0.222521, 0.974928)
		vertex[ 51] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 52] = 0.4 * @nscale1 * (0.900969, 0.433884)
		vertex[ 53] = 0.4 * @nscale1 * (1.52446, 1.21572)
		vertex[ 54] = 0.4 * @nscale1 * (0.62349, 0.781831)
		vertex[ 55] = 0.4 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 212 ; "15-rhombstar"
		cursality = 15
		numbervertices = 60 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.4 * @nscale1 * (1.91355, 0.406737)
		vertex[ 2] = 0.4 * @nscale1 * (0.913545, 0.406737)
		vertex[ 3] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.4 * @nscale1 * (0.913545, -0.406737)
		vertex[ 5] = 0.4 * @nscale1 * (1.91355, -0.406737)
		vertex[ 6] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.4 * @nscale1 * (0.669131, -0.743145)
		vertex[ 9] = 0.4 * @nscale1 * (1.58268, -1.14988)
		vertex[ 10] = 0.4 * @nscale1 * (0.913545, -0.406737)
		vertex[ 11] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.4 * @nscale1 * (0.309017, -0.951057)
		vertex[ 13] = 0.4 * @nscale1 * (0.978148, -1.6942)
		vertex[ 14] = 0.4 * @nscale1 * (0.669131, -0.743145)
		vertex[ 15] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.4 * @nscale1 * (-0.104528, -0.994522)
		vertex[ 17] = 0.4 * @nscale1 * (0.204489, -1.94558)
		vertex[ 18] = 0.4 * @nscale1 * (0.309017, -0.951057)
		vertex[ 19] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.4 * @nscale1 * (-0.5, -0.866025)
		vertex[ 21] = 0.4 * @nscale1 * (-0.604528, -1.86055)
		vertex[ 22] = 0.4 * @nscale1 * (-0.104528, -0.994522)
		vertex[ 23] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.4 * @nscale1 * (-0.809017, -0.587785)
		vertex[ 25] = 0.4 * @nscale1 * (-1.30902, -1.45381)
		vertex[ 26] = 0.4 * @nscale1 * (-0.5, -0.866025)
		vertex[ 27] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.4 * @nscale1 * (-0.978148, -0.207912)
		vertex[ 29] = 0.4 * @nscale1 * (-1.78716, -0.795697)
		vertex[ 30] = 0.4 * @nscale1 * (-0.809017, -0.587785)
		vertex[ 31] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 32] = 0.4 * @nscale1 * (-0.978148, 0.207912)
		vertex[ 33] = 0.4 * @nscale1 * (-1.9563, 0.)
		vertex[ 34] = 0.4 * @nscale1 * (-0.978148, -0.207912)
		vertex[ 35] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 36] = 0.4 * @nscale1 * (-0.809017, 0.587785)
		vertex[ 37] = 0.4 * @nscale1 * (-1.78716, 0.795697)
		vertex[ 38] = 0.4 * @nscale1 * (-0.978148, 0.207912)
		vertex[ 39] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 40] = 0.4 * @nscale1 * (-0.5, 0.866025)
		vertex[ 41] = 0.4 * @nscale1 * (-1.30902, 1.45381)
		vertex[ 42] = 0.4 * @nscale1 * (-0.809017, 0.587785)
		vertex[ 43] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 44] = 0.4 * @nscale1 * (-0.104528, 0.994522)
		vertex[ 45] = 0.4 * @nscale1 * (-0.604528, 1.86055)
		vertex[ 46] = 0.4 * @nscale1 * (-0.5, 0.866025)
		vertex[ 47] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 48] = 0.4 * @nscale1 * (0.309017, 0.951057)
		vertex[ 49] = 0.4 * @nscale1 * (0.204489, 1.94558)
		vertex[ 50] = 0.4 * @nscale1 * (-0.104528, 0.994522)
		vertex[ 51] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 52] = 0.4 * @nscale1 * (0.669131, 0.743145)
		vertex[ 53] = 0.4 * @nscale1 * (0.978148, 1.6942)
		vertex[ 54] = 0.4 * @nscale1 * (0.309017, 0.951057)
		vertex[ 55] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 56] = 0.4 * @nscale1 * (0.913545, 0.406737)
		vertex[ 57] = 0.4 * @nscale1 * (1.58268, 1.14988)
		vertex[ 58] = 0.4 * @nscale1 * (0.669131, 0.743145)
		vertex[ 59] = 0.4 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 213 ; "16-rhombstar"
		cursality = 16
		numbervertices = 64 ; vertices only for open curves
		cincrement = 4 ; numbervertices/cursality
		; initialize arrays
		vertex[ 0] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 1] = 0.4 * @nscale1 * (1.92388, 0.382683)
		vertex[ 2] = 0.4 * @nscale1 * (0.92388, 0.382683)
		vertex[ 3] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 4] = 0.4 * @nscale1 * (0.92388, -0.382683)
		vertex[ 5] = 0.4 * @nscale1 * (1.92388, -0.382683)
		vertex[ 6] = 0.4 * @nscale1 * (1., 0.)
		vertex[ 7] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 8] = 0.4 * @nscale1 * (0.707107, -0.707107)
		vertex[ 9] = 0.4 * @nscale1 * (1.63099, -1.08979)
		vertex[ 10] = 0.4 * @nscale1 * (0.92388, -0.382683)
		vertex[ 11] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 12] = 0.4 * @nscale1 * (0.382683, -0.92388)
		vertex[ 13] = 0.4 * @nscale1 * (1.08979, -1.63099)
		vertex[ 14] = 0.4 * @nscale1 * (0.707107, -0.707107)
		vertex[ 15] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 16] = 0.4 * @nscale1 * (0., -1.)
		vertex[ 17] = 0.4 * @nscale1 * (0.382683, -1.92388)
		vertex[ 18] = 0.4 * @nscale1 * (0.382683, -0.92388)
		vertex[ 19] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 20] = 0.4 * @nscale1 * (-0.382683, -0.92388)
		vertex[ 21] = 0.4 * @nscale1 * (-0.382683, -1.92388)
		vertex[ 22] = 0.4 * @nscale1 * (0., -1.)
		vertex[ 23] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 24] = 0.4 * @nscale1 * (-0.707107, -0.707107)
		vertex[ 25] = 0.4 * @nscale1 * (-1.08979, -1.63099)
		vertex[ 26] = 0.4 * @nscale1 * (-0.382683, -0.92388)
		vertex[ 27] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 28] = 0.4 * @nscale1 * (-0.92388, -0.382683)
		vertex[ 29] = 0.4 * @nscale1 * (-1.63099, -1.08979)
		vertex[ 30] = 0.4 * @nscale1 * (-0.707107, -0.707107)
		vertex[ 31] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 32] = 0.4 * @nscale1 * (-1., 0.)
		vertex[ 33] = 0.4 * @nscale1 * (-1.92388, -0.382683)
		vertex[ 34] = 0.4 * @nscale1 * (-0.92388, -0.382683)
		vertex[ 35] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 36] = 0.4 * @nscale1 * (-0.92388, 0.382683)
		vertex[ 37] = 0.4 * @nscale1 * (-1.92388, 0.382683)
		vertex[ 38] = 0.4 * @nscale1 * (-1., 0.)
		vertex[ 39] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 40] = 0.4 * @nscale1 * (-0.707107, 0.707107)
		vertex[ 41] = 0.4 * @nscale1 * (-1.63099, 1.08979)
		vertex[ 42] = 0.4 * @nscale1 * (-0.92388, 0.382683)
		vertex[ 43] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 44] = 0.4 * @nscale1 * (-0.382683, 0.92388)
		vertex[ 45] = 0.4 * @nscale1 * (-1.08979, 1.63099)
		vertex[ 46] = 0.4 * @nscale1 * (-0.707107, 0.707107)
		vertex[ 47] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 48] = 0.4 * @nscale1 * (0., 1.)
		vertex[ 49] = 0.4 * @nscale1 * (-0.382683, 1.92388)
		vertex[ 50] = 0.4 * @nscale1 * (-0.382683, 0.92388)
		vertex[ 51] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 52] = 0.4 * @nscale1 * (0.382683, 0.92388)
		vertex[ 53] = 0.4 * @nscale1 * (0.382683, 1.92388)
		vertex[ 54] = 0.4 * @nscale1 * (0., 1.)
		vertex[ 55] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 56] = 0.4 * @nscale1 * (0.707107, 0.707107)
		vertex[ 57] = 0.4 * @nscale1 * (1.08979, 1.63099)
		vertex[ 58] = 0.4 * @nscale1 * (0.382683, 0.92388)
		vertex[ 59] = 0.4 * @nscale1 * (0., 0.)
		vertex[ 60] = 0.4 * @nscale1 * (0.92388, 0.382683)
		vertex[ 61] = 0.4 * @nscale1 * (1.63099, 1.08979)
		vertex[ 62] = 0.4 * @nscale1 * (0.707107, 0.707107)
		vertex[ 63] = 0.4 * @nscale1 * (0., 0.)
		glindex = 0
		while glindex < numbervertices
			xcoord[glindex] = real(vertex[glindex])
			ycoord[glindex] = imag(vertex[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 215 ; "dotted star"
		cursality = raynum * dotnum
		numbervertices = cursality ; single points, not line segments
		cincrement = 1 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		scratchfloat = @nscale1 / (dotnum - 1) ; spacing between dots in each ray
		scratchint = 0 ; current ray number
		while glindex < numbervertices
			glindex3 = 0
			while glindex3 < dotnum
				xcoord[glindex + glindex3] = glindex3 * scratchfloat * \
						cos(scratchint * twopi / raynum)
				ycoord[glindex + glindex3] = glindex3 * scratchfloat * \
						sin(scratchint * twopi / raynum)
				vertex[glindex + glindex3] = xcoord[glindex + \
						glindex3] + flip(ycoord[glindex + glindex3])
				glindex3 = glindex3 + 1
			endwhile ; glindex3
			scratchint = scratchint + 1 ; next ray
			glindex = glindex + dotnum
		endwhile ; glindex
	elseif traparray == 216 ; "dashed star"
		cursality = raynum * dashnum
		numbervertices = 2 * cursality ; line segments
		cincrement = 2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		scratchint = 2 * dashnum ; number of dots per ray
		scratchfloat2 = @nscale1 / (scratchint - 1) ; spacing between dots in each ray
		scratchint2 = 0 ; current ray number
		while glindex < numbervertices
			glindex3 = 0
			while glindex3 < scratchint
				xcoord[glindex + glindex3] = glindex3 * scratchfloat2 * \
						cos(scratchint2 * twopi / raynum)
				ycoord[glindex + glindex3] = glindex3 * scratchfloat2 * \
						sin(scratchint2 * twopi / raynum)
				vertex[glindex + glindex3] = xcoord[glindex + \
						glindex3] + flip(ycoord[glindex + glindex3])
				glindex3 = glindex3 + 1
			endwhile ; glindex3
			scratchint2 = scratchint2 + 1 ; next ray
			glindex = glindex + scratchint
		endwhile ; glindex
	elseif traparray == 217 ; "rhodonea"
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1
		cursality = 1
		numbervertices = granularity2 ; vertices + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		scratchfloat = hypotroA / hypotroB
		scratchfloat2 = twopi/granularity
		scratchfloat3 = scratchfloat2 * hypotroB
		while glindex < granularity2
			scratchfloat4 = sin(scratchfloat * glindex * scratchfloat3) ; radius
			xcoord[glindex] = @nscale1 * scratchfloat4 * cos(glindex * scratchfloat3)
			ycoord[glindex] = @nscale1 * scratchfloat4 * sin(glindex * scratchfloat3) 
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[granularity2] = xcoord[0]
		ycoord[granularity2] = ycoord[0]
		vertex[granularity2] = xcoord[granularity2] + flip(ycoord[granularity2])
	elseif traparray == 218 ; "cycloid"
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		cursality = 1
		numbervertices = granularity ; vertices only for open curves
		cincrement = granularity ; numbervertices/cursality
		scratchfloat = twopi * cycloidlength / granularity
		scratchfloat3 = twopi * cycloidlength /2 ; recenter the resulting cycloid on its midpoint
		; initialize arrays
		glindex = 0
		while glindex < granularity
			scratchfloat2 = scratchfloat * glindex - scratchfloat3
			xcoord[glindex] = @nscale1 * \
				(scratchfloat2 - cycloidamp * sin(scratchfloat2))
			ycoord[glindex] = @nscale1 * \
				(cycloidconst - cycloidamp * cos(scratchfloat2))
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
	elseif traparray == 219 ; "parabolic lissajous"
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1
		cursality = 1
		numbervertices = granularity2 ; n + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		scratchfloat = lissajdomain/granularity2 ; angular domain increment
		glindex = 0
		while glindex < granularity
			scratchfloat2 = @lissaamp1 * cos(@lissafreq1*glindex*scratchfloat - \
				@lissaphase1)
			scratchfloat3 = @lissaamp2 * cos(@lissafreq2*glindex*scratchfloat - \
				@lissaphase2)
			xcoord[glindex] = @nscale1 * scratchfloat2 * \
				scratchfloat3
			ycoord[glindex] = @nscale1 * 0.5 * \
				(sqr(scratchfloat3) - sqr(scratchfloat2))
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[glindex] = xcoord[0] ; close the curve
		ycoord[glindex] = ycoord[0]
		vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
		if @lissaopen ; do not connect the first and last points of the curve
			numbervertices = numbervertices - 1
			cincrement = cincrement - 1
		endif ; lissaopen
	elseif traparray == 220 ; "polar lissajous"
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1
		cursality = 1
		numbervertices = granularity2 ; n + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		scratchfloat = lissajdomain/granularity2 ; angular domain increment
		glindex = 0
		while glindex < granularity
			scratchfloat2 = @lissaamp1 * cos(@lissafreq1*glindex*scratchfloat - \
				@lissaphase1) ; r
			scratchfloat3 = @lissaamp2 * cos(@lissafreq2*glindex*scratchfloat - \
				@lissaphase2) ; theta
			xcoord[glindex] = @nscale1 * scratchfloat2 * \
				cos(scratchfloat3)
			ycoord[glindex] = @nscale1 * scratchfloat2 * \
				sin(scratchfloat3)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[glindex] = xcoord[0] ; close the curve
		ycoord[glindex] = ycoord[0]
		vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
		if @lissaopen ; do not connect the first and last points of the curve
			numbervertices = numbervertices - 1
			cincrement = cincrement - 1
		endif ; lissaopen
	elseif traparray == 221 ; "Moritz cyclic harmonic"
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1 ; for closing the curve
		cursality = 1
		numbervertices = granularity2 ; vertices + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		glindex = 0
		scratchfloat = moritzfreqD * twopi / (granularity + 1) ; angular increment
		scratchfloat2 = moritzfreqN / moritzfreqD ; cosine frequency
		while glindex < granularity
			scratchfloat3 = glindex * scratchfloat * scratchfloat2 ; current angle for Moritz curve
			scratchfloat4 = moritzconst + moritzamp * cos(scratchfloat3) ; r
			xcoord[glindex] = @nscale1 * scratchfloat4 * cos(glindex * scratchfloat)
			ycoord[glindex] = @nscale1 * scratchfloat4 * sin(glindex * scratchfloat)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[glindex] = xcoord[0]
		ycoord[glindex] = ycoord[0]
		vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
	elseif traparray == 222 ; "elliptic lissajous"
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1
		cursality = 1
		numbervertices = granularity2 ; n + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		scratchfloat = lissajdomain/granularity2 ; angular domain increment
		glindex = 0
		while glindex < granularity
			scratchfloat2 = abs(@lissaamp1 * cos(@lissafreq1*glindex*scratchfloat - \
				@lissaphase1)) ; mu
			scratchfloat3 = @lissaamp2 * (#pi * (cos(@lissafreq2*glindex*scratchfloat - \
				@lissaphase2))) + #pi ; nu
			xcoord[glindex] = @nscale1 * cosh(scratchfloat2) \
				* cos(scratchfloat3)
			ycoord[glindex] = @nscale1 * sinh(scratchfloat2) \
				* sin(scratchfloat3)
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[glindex] = xcoord[0] ; close the curve
		ycoord[glindex] = ycoord[0]
		vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
		if @lissaopen ; do not connect the first and last points of the curve
			numbervertices = numbervertices - 1
			cincrement = cincrement - 1
		endif ; lissaopen
	elseif traparray == 223 ; "bipolar lissajous"
		if @grain == "36"
			granularity = 36
		elseif @grain == "72"
			granularity = 72
		elseif @grain == "100"
			granularity = 100
		elseif @grain == "200"
			granularity = 200
		elseif @grain == "300"
			granularity = 300
		else ; @grain == "400"
			granularity = 400
		endif ; @grain
		granularity2 = granularity + 1
		cursality = 1
		numbervertices = granularity2 ; n + cursality for closed curves
		cincrement = granularity2 ; numbervertices/cursality
		; initialize arrays
		scratchfloat = lissajdomain/granularity2 ; angular domain increment
		glindex = 0
		while glindex < granularity
			scratchfloat2 = @lissaamp1 * cos(@lissafreq1*glindex*scratchfloat - \
				@lissaphase1) ; tau
			scratchfloat3 = @lissaamp2 * #pi * cos(@lissafreq2*glindex*scratchfloat - \
				@lissaphase2) ; sigma
			xcoord[glindex] = @nscale1 * sinh(scratchfloat2) \
				/ (cosh(scratchfloat2) - cos(scratchfloat3))
			ycoord[glindex] = @nscale1 * sin(scratchfloat3) \
				/ (cosh(scratchfloat2) - cos(scratchfloat3))
			vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
			glindex = glindex + 1
		endwhile ; glindex
		xcoord[glindex] = xcoord[0] ; close the curve
		ycoord[glindex] = ycoord[0]
		vertex[glindex] = xcoord[glindex] + flip(ycoord[glindex])
		if @lissaopen ; do not connect the first and last points of the curve
			numbervertices = numbervertices - 1
			cincrement = cincrement - 1
		endif ; lissaopen
	endif ; traparray
endif ; @traptype

init:
	complex juliaconst = (0,0)
	bool dontbail = TRUE
	float testvalue = float barnsleyvalue = 0.0
	complex ztemp = complex ztemp1 = complex ztemp2 = (0,0)
  complex tempc = (0,0) ; the trapped trap point
  complex traptemp = complex traptemp2 = (0,0)
  float tempangle = 0.0 ; angle of transformed, centered, etc., z
  float ftemp = float ftemp2 = float ftemp3 = float ftemp4 = 0.0 ; various uses; scratchpad variables
	float equation1 = float equation2 = 0.0 ; for heatmap option
	complex currentz = (0,0)

	if @mandy
		#z = #pixel, juliaconst = #pixel
	else ; Julia
		#z = #pixel, juliaconst = @jconstant
	endif

	complex testpt = complex minpt = complex maxpt = complex intersectpt = (0,0)
	float xtest = float ytest = 0.0
	float tparam = 0.0 ; for parametric representation of line segments
	float disttemp = float distance = float seglength = 0.0 ; temp storage, length of current line segment
	float distmin = 1e20 ; initialize minimum distance to a high value
	int lindex = int lindex2 = 0 ; loop indices
	int cindex = 0 ; cursality index
	int maxlindex = int altindex = 0
	float tempxx = float tempyy = float tempangleB = 0.0
	complex result = (0,0) ; compatibility with older code

	float rotation = @rotate * degconversion
	if ( rotation < 0 )
		rotation = rotation + twopi
	endif ; rotation

loop:
	if @heatmap
		#z = currentz ; restore proper z value
	endif ; @heatmap

	ztemp = #z ; save value for later
	ztemp1 = #z

    ; First, center #z on the trap center
    #z = #z - @center
    ; Compute rotated #z
    if rotation != 0.0
      #z = #z * exp(flip(rotation))
    endif ; rotation

	; now, execute the trap to determine which value will be tested in the Barnsley test
	testpt = #z
	
if @traptype == 0 ; "lines & points"
	xtest = real(testpt), ytest = imag(testpt)
	; test #z against the various line segments defining the trap shape

	distmin = 1e20
	cindex = 0
	if cincrement != 1 ; test distance to each line segment
		while cindex < cursality
			lindex = cindex * cincrement, lindex2 = lindex + 1
			maxlindex = (cindex + 1) * cincrement
			while lindex2 < maxlindex
				; determine length of current line segment
				seglength = sqr(xcoord[lindex] - xcoord[lindex2]) + sqr(ycoord[lindex] - \
					ycoord[lindex2])
				; now determine the parameter t for which the current #z is closest to
				; the line containing the current line segment
				tparam = ((xtest - xcoord[lindex]) * (xcoord[lindex2] - xcoord[lindex]) + \
					(ytest - ycoord[lindex]) * (ycoord[lindex2] - ycoord[lindex]))/seglength
				if tparam < 0.0 ; the intersect lies off the line segment, beyond the first vertex
								; so return the distance to the first segment endpoint
					disttemp = sqr(xtest - xcoord[lindex]) + sqr(ytest - ycoord[lindex])
					intersectpt = vertex[lindex]
				elseif tparam > 1.0 ; the intersect lies off the segment beyond the second vertex
									; so return distance to the second segment endpoint
					disttemp = sqr(xtest - xcoord[lindex2]) + sqr(ytest - ycoord[lindex2])
					intersectpt = vertex[lindex2]
				else ; #z lies on a line that intersects the current line segment perpendicularly
						; to the closest point
					intersectpt = xcoord[lindex] + tparam * (xcoord[lindex2] - xcoord[lindex]) + \
						flip(ycoord[lindex] + tparam * (ycoord[lindex2] - ycoord[lindex]))
					disttemp = sqr(xtest - real(intersectpt)) + sqr(ytest - imag(intersectpt))
				endif ; tparam
				if disttemp < distmin
					distmin = disttemp
					minpt = intersectpt
				endif ; disttemp
				; increment the loop indices
				lindex = lindex + 1
				lindex2 = lindex2 + 1
			endwhile ; lindex2
			cindex = cindex + 1
		endwhile ; cindex
	else ; cincrement = 1 --- return distance to individual points, not line segments
		while cindex < cursality
			disttemp = sqr(xtest - xcoord[cindex]) + sqr(ytest - ycoord[cindex])
			intersectpt = vertex[cindex]
			if disttemp < distmin
				distmin = disttemp
				minpt = intersectpt
			endif ; disttemp
			; increment the loop indices
			cindex = cindex + 1
		endwhile ; cindex
	endif ; cincrement

	; save the correct trap point
	tempxx = real(minpt)
	tempyy = imag(minpt)
	result = minpt

elseif @traptype == 1 ; "polar functions"
	; In 'polar functions', the variable
	; tempxx is initially used to store the polar distance from #z,
	; not the x-coordinate

	tempangleB = atan2(#z)
	if tempangleB < 0
		tempangleB = tempangleB + twopi
	endif ; tempangleB

	disttemp = cabs(#z)
	distance = disttemp

if !polarimplicit ; distance not determined implicitly
	if traparray == 0 ; "rose"
		tempxx = sin(rosepetals * tempangleB)
	elseif traparray == 1 ; "folium"
		tempxx = (sqr(sin(foliumperturb*tempangleB)) - \
			folium) * cos(tempangleB)
	elseif traparray == 2 ; "cardioid"
		tempxx = cardioid + sin(cardioidperturb \
			* tempangleB)
	elseif traparray == 3 ; "circle"
		tempxx = 1.0
	elseif traparray == 4 ; "cissoid of Diocles"
		tempxx = sin(cissoidDioA*tempangleB) * \
			tan(cissoidDioB*tempangleB)
	elseif traparray == 5 ; "cochleoid"
		tempxx = sin(cochleoid*tempangleB)/tempangleB
	elseif traparray == 7 ; "conchoid of De Sluze"
		tempxx = conchoidA*cos(conchoidB*tempangleB) + \
			conchoidC/cos(conchoidB*tempangleB)
	elseif traparray == 8 ; "conchoid of Nicomedes"
		tempxx = conchoidA + \
			conchoidC/cos(conchoidB*tempangleB)
	elseif traparray == 9 ; "cubical parabola"
		ftemp = cubicpC/cos(cubicpB*tempangleB)
		tempxx = sqrt(ftemp*ftemp*tan(cubicpA*tempangleB))
	elseif traparray == 10 ; "ellipse"
		ftemp = abs(tan(tanfreq*tempangleB))
		tempxx = majaxis*minaxis*sqrt(1+sqr(ftemp))/ \
			(minaxis^epower + ((majaxis*ftemp)^epower))^ \
			(1/epower)
	elseif traparray == 11 ; "folium of Descartes"
	  ftemp = sin(fosinfreq*tempangleB)
	  ftemp2 = cos(focosfreq*tempangleB)
	  tempxx = sin(sinfreq2*tempangleB)/(ftemp*sqr(ftemp)+ftemp2*sqr(ftemp2))
	elseif traparray == 12 ; "hyperbolic spiral"
		ftemp = cabs(ztemp) ; r
		ftemp2 = hyperbolic/ftemp ; angle
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on spiral
		tempxx = 2.4 * cabs(ztemp - ztemp2) ; scaled distance between spiral pt and mod z
	elseif traparray == 13 ; "kampyle of Eudoxus"
		tempxx = 0.1/(cos(kampfreq*tempangleB)^kamppower)
	elseif traparray == 14 ; "kappa"
		tempxx = tan(nodalfreq*tempangleB)
	elseif traparray == 15 ; "lemniscate of Bernoulli"
		tempxx = cos(lemfreq*tempangleB)^lempower
	elseif traparray == 16 ; "limacon of Pascal"
		tempxx = limoffset + limamp*sin(limfreq*tempangleB)
	elseif traparray == 17 ; "lituus"
		tempxx = 1/(tempangleB^litpower)
	elseif traparray == 18 ; "logarithmic spiral"
		ftemp = cabs(ztemp) ; r of current modified z
		ftemp2 = (log(ftemp) - log(logspiA)) / logspiB ; angle of pt on spiral
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on spiral
		tempxx = 2.4 * cabs(ztemp - ztemp2) ; scaled distance between spiral pt and mod z			
	elseif traparray == 19 ; "parabola"
		tempxx = 0.25/(paraoffset - paraamp*cos(parafreq*tempangleB))
	elseif traparray == 20 ; "parabolic spiral"
		ftemp = cabs(ztemp) ; r of current modified z
		ftemp2 = (ftemp * paraspioffset)^paraspi ; angle of pt on spiral
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on spiral
		tempxx = 2.4 * cabs(ztemp - ztemp2) ; scaled distance between spiral pt and mod z
	elseif traparray == 21 ; "semicubical parabola"
		ftemp = tan(semicubtanfreq*tempangleB)
		tempxx = 0.25 * (ftemp^semicubpower)/cos(semicubcosfreq*tempangleB)
	elseif traparray == 22 ; "spiral of Archimedes"
		ftemp = cabs(ztemp) ; r of current modified z
		ftemp2 = ftemp * archspioffset ; angle of pt on spiral
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on spiral
		tempxx = 2.4 * cabs(ztemp - ztemp2) ; scaled distance between spiral pt and mod z
	elseif traparray == 23 ; "strophoid"
		tempxx = 0.4 * cos(strophcosfreqA * tempangleB) / \
			cos(strophcosfreqB * tempangleB)
	elseif traparray == 24 ; "Cayley's sextic"
		ftemp = cos(polarfreqA * tempangleB/3)
		tempxx = polarampA * ftemp * sqr(ftemp)
	elseif traparray == 25 ; "trisectrix limacon"
		tempxx = trilimA * (trilimB + trilimamp * cos(trilimfreq * \
			tempangleB))
	elseif traparray == 27 ; "trefoil of Habenicht"
		tempxx = trefoilconst + trefoilcosamp * \
			cos(trefoilcossym * tempangleB) + \
			trefoilsinamp * sqr(sin(trefoilsinsym * tempangleB))
	elseif traparray == 28 ; "Cayley's sextic 2"
		ftemp = disttemp ; r
		if ftemp > 1.0
			ftemp = 1
		elseif ftemp < -1.0
			ftemp = -1
		endif; ftemp
		ftemp2 = 3 * polarfreqA * acos(ftemp^onethird) ; angle
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on curve
		tempxx = cabs(ztemp - ztemp2) ; scaled distance between curve pt and mod z
	elseif traparray == 29 ; "lituus 2"
		ftemp = disttemp ; r
		ftemp2 = 1 / (ftemp^litpower) ; angle
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on curve
		tempxx = cabs(ztemp - ztemp2) ; scaled distance between curve pt and mod z
	elseif traparray == 30 ; "hippopede"
		ftemp = 1 - polarampA * sqr(sin(polarfreqA * tempangleB))
		if ftemp < 0
			ftemp2 = -1
		else
			ftemp2 = 1
		endif ; ftemp
		tempxx = ftemp2 * sqrt(abs(1 - polarampA * sqr(sin(polarfreqA * \
			tempangleB))))
	elseif traparray == 31 ; "folioid"
		ftemp = folioidamp * cos(folioidfreqN * tempangleB / folioidfreqD)
		ftemp2 = 1 - sqr(folioidamp * sin(folioidfreqN * tempangleB / folioidfreqD))
		if ftemp2 < 0
			tempxx = 1e10 ; return a really big value
		else
			ftemp2 = sqrt(ftemp2)
			ftemp3 = ftemp + ftemp2 ; r1
			ftemp4 = ftemp - ftemp2 ; r2
			tempc = cos(folioidfreqD * tempangleB) + \
				flip(sin(folioidfreqD * tempangleB))
			traptemp = ftemp3 * ftemp ; first curve possibility
			traptemp2 = ftemp4 * ftemp ; second curve possibility -- which one is closest
			if cabs(ztemp - traptemp) < cabs(ztemp - traptemp2)
				tempxx = ftemp3
			else
				tempxx = ftemp4
			endif ; cabs()
		endif ; ftemp2
	endif ; traparray

	tempxx = trapscales * tempxx
	distmin = tempxx
	result = tempxx * exp(flip(tempangleB))
	tempxx = real(result) ; this now stores the proper x-coord of the trapped point
	tempyy = imag(result) ; the y-coordinate
	minpt = result

else ; implicit polar function
	if traparray == 0 ; "rose"
		distance = disttemp - (sin(rosepetals * tempangleB))
	elseif traparray == 1 ; "folium"
		distance = disttemp - ((sqr(sin(foliumperturb*tempangleB)) - \
			folium) * cos(tempangleB))
	elseif traparray == 2 ; "cardioid"
		distance = disttemp - (cardioid + sin(cardioidperturb \
			* tempangleB))
	elseif traparray == 3 ; "circle"
		distance = disttemp - 1.0
	elseif traparray == 4 ; "cissoid of Diocles"
		distance = disttemp - (sin(cissoidDioA*tempangleB) * \
			tan(cissoidDioB*tempangleB))
	elseif traparray == 5 ; "cochleoid"
		distance = disttemp - (sin(cochleoid * tempangleB) / tempangleB)
	elseif traparray == 7 ; "conchoid of De Sluze"
		distance = disttemp - (conchoidA*cos(conchoidB*tempangleB) + \
			conchoidC/cos(conchoidB*tempangleB))
	elseif traparray == 8 ; "conchoid of Nicomedes"
		distance = disttemp - (conchoidA + \
			conchoidC/cos(conchoidB*tempangleB))
	elseif traparray == 9 ; "cubical parabola"
		ftemp = cubicpC/cos(cubicpB*tempangleB)
		distance = disttemp - (sqrt(ftemp*ftemp*tan(cubicpA*tempangleB)))
	elseif traparray == 10 ; "ellipse"
		ftemp = abs(tan(tanfreq*tempangleB))
		distance = disttemp - (majaxis*minaxis*sqrt(1+sqr(ftemp))/ \
			(minaxis^epower + ((majaxis*ftemp)^epower))^ \
			(1/epower))
	elseif traparray == 11 ; "folium of Descartes"
	  ftemp = sin(fosinfreq*tempangleB)
	  ftemp2 = cos(focosfreq*tempangleB)
	  distance = disttemp - (sin(sinfreq2*tempangleB)/(ftemp*sqr(ftemp)+ftemp2*sqr(ftemp2)))
	elseif traparray == 12 ; "hyperbolic spiral"
		ftemp = cabs(ztemp) ; r
		ftemp2 = hyperbolic/ftemp ; angle
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on spiral
		distance = disttemp - (2.4 * cabs(ztemp - ztemp2)) ; scaled distance between spiral pt and mod z
	elseif traparray == 13 ; "kampyle of Eudoxus"
		distance = disttemp - (0.1/(cos(kampfreq*tempangleB)^kamppower))
	elseif traparray == 14 ; "kappa"
		distance = disttemp - (tan(nodalfreq*tempangleB))
	elseif traparray == 15 ; "lemniscate of Bernoulli"
		distance = disttemp - (cos(lemfreq*tempangleB)^lempower)
	elseif traparray == 16 ; "limacon of Pascal"
		distance = disttemp - (limoffset + limamp*sin(limfreq*tempangleB))
	elseif traparray == 17 ; "lituus"
		distance = disttemp - (1/(tempangleB^litpower))
	elseif traparray == 18 ; "logarithmic spiral"
		ftemp = cabs(ztemp) ; r of current modified z
		ftemp2 = (log(ftemp) - log(logspiA)) / logspiB ; angle of pt on spiral
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on spiral
		distance = disttemp - (2.4 * cabs(ztemp - ztemp2)) ; scaled distance between spiral pt and mod z			
	elseif traparray == 19 ; "parabola"
		distance = disttemp - (0.25/(paraoffset - paraamp*cos(parafreq*tempangleB)))
	elseif traparray == 20 ; "parabolic spiral"
		ftemp = cabs(ztemp) ; r of current modified z
		ftemp2 = (ftemp * paraspioffset)^paraspi ; angle of pt on spiral
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on spiral
		distance = disttemp - (2.4 * cabs(ztemp - ztemp2)) ; scaled distance between spiral pt and mod z
	elseif traparray == 21 ; "semicubical parabola"
		ftemp = tan(semicubtanfreq*tempangleB)
		distance = disttemp - (0.25 * (ftemp^semicubpower)/cos(semicubcosfreq*tempangleB))
	elseif traparray == 22 ; "spiral of Archimedes"
		ftemp = cabs(ztemp) ; r of current modified z
		ftemp2 = ftemp * archspioffset ; angle of pt on spiral
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on spiral
		distance = disttemp - (2.4 * cabs(ztemp - ztemp2)) ; scaled distance between spiral pt and mod z
	elseif traparray == 23 ; "strophoid"
		distance = disttemp - (0.4 * cos(strophcosfreqA * tempangleB) / \
			cos(strophcosfreqB * tempangleB))
	elseif traparray == 24 ; "Cayley's sextic"
		ftemp = cos(polarfreqA * tempangleB/3)
		distance = disttemp - (polarampA * ftemp * sqr(ftemp))
	elseif traparray == 25 ; "trisectrix limacon"
		distance = disttemp - (trilimA * (trilimB + trilimamp * \
			cos(trilimfreq * tempangleB)))
	elseif traparray == 27 ; "trefoil of Habenicht"
		distance = disttemp - (trefoilconst + trefoilcosamp * \
			cos(trefoilcossym * tempangleB) + \
			trefoilsinamp * sqr(sin(trefoilsinsym * tempangleB)))
	elseif traparray == 28 ; "Cayley's sextic 2"
		ftemp = disttemp ; r
		if ftemp > 1.0
			ftemp = 1
		elseif ftemp < -1.0
			ftemp = -1
		endif; ftemp
		ftemp2 = 3 * polarfreqA * acos(ftemp^onethird)
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on curve
		distance = disttemp - cabs(ztemp - ztemp2) ; scaled distance between curve pt and mod z
	elseif traparray == 29 ; "lituus 2"
		ftemp = disttemp ; r
		ftemp2 = 1 / (ftemp^litpower) ; angle
		ztemp2 = ftemp * (cos(ftemp2) + flip(sin(ftemp2))) ; point on curve
		distance = disttemp - cabs(ztemp - ztemp2) ; scaled distance between curve pt and mod z
	elseif traparray == 30 ; "hippopede"
		distance = sqr(disttemp) - (1 - polarampA * sqr(sin(polarfreqA * \
			tempangleB))) ; scaled distance between curve pt and mod z
	elseif traparray == 31 ; "folioid"
		distance = sqr(disttemp) + sqr(folioidconstB) - 2 * folioidconstB * \
			disttemp * cos(folioidfreqN * tempangleB / folioidfreqD) \
			- folioidconstA
	endif ; traparray

;	if polarsmoothing
;		ftemp = abs(distance)^polarsmoothmod
;	else
;		ftemp = sqrt(abs(distance))
;	endif ; polarsmoothing[]

;	if abs(distance) == distance ; positive correction
;		distcorrection = disttemp * trapscales + ftemp
;	else ; negative correction
;		distcorrection = disttemp * trapscales - ftemp
;	endif ; abs()
;	result = distcorrection * exp(flip(tempangleB))
	result = distance * trapscales * exp(flip(tempangleB))
	tempxx = real(result)
	tempyy = imag(result)
	minpt = result
	distmin = distance
endif ; !polarimplicit[]

elseif @traptype == 2 ; "parametric functions"
	tempangleB = atan2(#z)
	if tempangleB < 0
		tempangleB = tempangleB + twopi
	endif ; tempangleB

	if traparray == 0 ; "hypocycloid"
		ftemp2 = hyponumer/hypodenom
		tempangleB = hypodenom * tempangleB
		ftemp = 1 - ftemp2
		xtest = ftemp*cos(ftemp2*tempangleB) + ftemp2*cos(ftemp*tempangleB)
		ytest = ftemp*sin(ftemp2*tempangleB) - ftemp2*sin(ftemp*tempangleB)
	elseif traparray == 1 ; "companion of cycloid"
		ftemp = cycangle * tempangleB ; stretch out angle
		xtest = companC1 * ftemp
		ytest = companC2 - cos(companfreq * ftemp)
		ztemp = xtest + flip(ytest) ; the trap pt
		ftemp2 = cabs(ztemp) ; distance from origin to trap pt
		ztemp = ftemp2 * exp(1i * tempangleB) ; move trap pt to the same direction as initial (#z) pt
		xtest = real(ztemp) ; new x-coordinate after rotation
		ytest = imag(ztemp) ; new y-coordinate
	elseif traparray == 2 ; "cycloid"
		ftemp = cycangle * tempangleB ; stretch out angle
		xtest = cycxscale * ftemp - cycampA * sin(cycsinfreq \
			* ftemp) ; x-coordinate of trap point
		ytest = cycyoffset - cycampB * cos(cyccosfreq * \
			ftemp) ; y-coordinate of trap pt
		ztemp = xtest + flip(ytest) ; the trap pt
		ftemp2 = cabs(ztemp) ; distance from origin to trap pt
		ztemp = ftemp2 * exp(1i * tempangleB) ; move trap pt to the same direction as initial (#z) pt
		xtest = 0.2 * real(ztemp) ; new x-coordinate after rotation
		ytest = 0.2 * imag(ztemp) ; new y-coordinate
	elseif traparray == 3 ; "cycloid variant"
		ftemp = cycangle * tempangleB ; stretch out angle
		xtest = cycxscale * ftemp + cycampA * sin(cycsinfreq \
			* ftemp) ; x-coordinate of trap point
		ytest = cycyoffset - cycampB * cos(cyccosfreq * \
			ftemp) ; y-coordinate of trap pt
		ztemp = xtest + flip(ytest) ; the trap pt
		ftemp2 = cabs(ztemp) ; distance from origin to trap pt
		ztemp = ftemp2 * exp(1i * tempangleB) ; move trap pt to the same direction as initial (#z) pt
		xtest = 0.2 * real(ztemp) ; new x-coordinate after rotation
		ytest = 0.2 * imag(ztemp) ; new y-coordinate
	elseif traparray == 4 ; "epicycloid"
		ftemp3 = epicycAN / epicycAD
		tempangleB = epicycAD * tempangleB
		ftemp = ftemp3 + epicycC
		ftemp2 = ftemp3 * epicycB
		xtest = 0.16666666667 * (ftemp * cos(ftemp3 * tempangleB) - \
			ftemp2 * cos(ftemp * tempangleB))
		ytest = 0.16666666667 * (ftemp * sin(ftemp3 * tempangleB) - \
			ftemp2 * sin(ftemp * tempangleB))
	elseif traparray == 5 ; "nephroid"
		xtest = nephconstB * cos(tempangleB) - cos(nephcosfreq \
			* tempangleB)
		ytest = nephconstA * sin(tempangleB) - sin(nephsinfreq \
			* tempangleB)
		xtest = 0.2 * xtest
		ytest = 0.2 * ytest
	elseif traparray == 6 ; "hyperbola"
		xtest = paraconstA / cos(parafreqA * tempangleB)
		ytest = paraconstB * tan(parafreqB * tempangleB)
	elseif traparray == 7 ; "tractrix"
		xtest = paraconstA / cosh(parafreqA * tempangleB)
		ytest = tempangleB - paraconstB * tanh(parafreqB * tempangleB)
	elseif traparray == 8 ; "wavy circle"
		ftemp = wavyradius + wavysinamp * \
			sin(wavysinfreq * tempangleB)
		xtest = ftemp * cos(tempangleB)
		ytest = ftemp * sin(tempangleB)
	elseif traparray == 9 ; "ellipse"
		xtest = paraxaxis * cos(tempangleB)
		ytest = parayaxis * sin(tempangleB)
	elseif traparray == 10 ; "serpentine" --- anguinea
		tempangleB = tempangleB - #pi ; -pi < angle < pi
		xtest = paraconstA * tan(onehalf * parafreqA * tempangleB)
		ytest = paraconstB * sin(parafreqB * tempangleB)
	elseif traparray == 11 ; "witch of Agnesi"
		tempangleB = onehalf * (tempangleB - #pi) ; -pi/2 < angle < pi/2
		xtest = paraconstA * tan(parafreqA * tempangleB)
		ytest = paraconstB * sqr(cos(parafreqB * tempangleB))
	elseif traparray == 12 ; "Abdank quadratrix"
		xtest = paraconstA * sin(parafreqA * tempangleB)
		ytest = onehalf * sqr(paraconstA) * (tempangleB + \
			sin(parafreqA * tempangleB) * cos(parafreqB * tempangleB))
	elseif traparray == 13 ; "cornoid"
		xtest = cos(2 * parafreqA * tempangleB) * cos(parafreqB * tempangleB)
		ytest = (2 + cos(2 * parafreqA * tempangleB)) * sin(parafreqB * tempangleB)
	elseif traparray == 14 ; "epicycloid 2"
		ftemp = epiradiusA / epiradiusB ; parameter "q"
		ftemp2 = ftemp + 1
		ftemp = 1/ftemp
		xtest = ftemp * epiradiusA * (ftemp2 * cos(tempangleB) - \
			cos(ftemp2 * tempangleB))
		ytest = ftemp * epiradiusA * (ftemp2 * sin(tempangleB) - \
			sin(ftemp2 * tempangleB))
	elseif traparray == 15 ; "epitrochoid"
		ftemp = epiradiusA / epiradiusB ; parameter "q"
		ftemp2 = ftemp + 1
		ftemp = 1/ftemp
		ftemp3 = epiradiusC / epiradiusB ; parameter "k"
		xtest = ftemp * epiradiusA * (ftemp2 * cos(tempangleB) - \
			ftemp3 * cos(ftemp2 * tempangleB))
		ytest = ftemp * epiradiusA * (ftemp2 * sin(tempangleB) - \
			ftemp3 * sin(ftemp2 * tempangleB))
	endif ; traparray

	result = trapscales * (xtest + flip(ytest))
	tempxx = real(result)
	tempyy = imag(result)
	minpt = result
	distmin = sqrt(sqr(tempxx = real(#z)) + sqr(tempyy - imag(#z)))

elseif @traptype == 3 ; "cartesian"
	ztemp = #z	
	tempangleB = atan2(ztemp)
	if tempangleB < 0
		tempangleB = tempangleB + twopi
	endif ; tempangleB
	ztemp = ztemp * trapscales
	xtest = real(ztemp)
	ytest = imag(ztemp)
	ftemp = sqr(xtest)
	ftemp2 = sqr(ytest)

	if traparray == 0 ; "ampersand"
		distance = (ftemp2 - ftemp) * (xtest - 1 ) * (2 * xtest - 3) \
			- 4 * sqr((ftemp + ftemp2 - 2 * xtest))
	elseif traparray == 1 ; "Alain's curve"
		distance = sqr(ftemp - ftemp2) - cartxcoeff * ftemp + \
			cartycoeff * ftemp2
	elseif traparray == 2 ; "arcs of Samothrace"
		distance = cartxcoeff * ftemp * sqr((3 * ftemp - \
			ftemp2)) - cartycoeff * ftemp2 * (ftemp + ftemp2)
	elseif traparray == 3 ; "astroid"
		distance = cartxcoeff * ftemp^onethird + cartycoeff \
			* ftemp2^onethird - cartconst
	elseif traparray == 4 ; "atriphthaloid"
		distance = sqr(ftemp) * (cartxcoeff * ftemp + cartycoeff * \
			ftemp2) - sqr(cartconst * ftemp - cartconstB)
	elseif traparray == 5 ; "bean curve 1"
		distance = sqr(cartxcoeff * ftemp + cartycoeff * ftemp2) \
			- cartconst * xtest * ftemp - cartconstB * \
			ytest * ftemp2
	elseif traparray == 6 ; "bean curve 2"
		distance = cartxcoeff * sqr(ftemp) + ftemp * ftemp2 + \
			cartycoeff * sqr(ftemp2) - xtest * (cartconst * \
			ftemp + cartconstB * ftemp2)
	elseif traparray == 7 ; "beetle curve"
		distance = (ftemp + ftemp2) * sqr(ftemp + ftemp2 - cartxcoeff * \
			xtest - cartycoeff * ytest) - cartconst * ftemp \
			* ftemp2
	elseif traparray == 8 ; "bicorn"
		distance = cartycoeff * ftemp2 * (cartconst - \
		cartxcoeff * ftemp) - sqr(ftemp + 2 * cartconstB * ytest - \
		cartconst)
	elseif traparray == 9 ; "bicuspid"
		distance = sqr(cartycoeff * ftemp2 - cartconst) - \
			(xtest + cartconst) * (cartconst - cartxcoeff \
			* xtest)^3
	elseif traparray == 10 ; "biquartic of Sacre"
		ftemp3 = sqr(ftemp) ; xtest^4
		ftemp4 = sqr(ftemp2) ; ytest^4
		distance = sqr(ftemp3) + 4 * ftemp*ftemp3*ytest + ytest*ftemp2*(ytest-1) \
			+ 3*ftemp3*ytest*(2*ytest-3) + 2*ftemp*ftemp2*(2*ytest+3)
	elseif traparray == 11 ; "cubic egg"
		distance = ftemp + ftemp2 / (1 + cartconst * xtest) - 1
	elseif traparray == 12 ; "Bolza curve"
		distance = ftemp2 - xtest * sqr(ftemp) + xtest
	elseif traparray == 13 ; "bow curve"
		distance = sqr(ftemp) - ftemp * ytest + ytest * ftemp2
	elseif traparray == 14 ; "bullet nose curve"
		distance = 1/ftemp - 1/ftemp2 - 1
	elseif traparray == 15 ; "butterfly sextic"
		distance = sqr(ftemp * xtest) + sqr(ftemp2 * ytest) - ftemp
	elseif traparray == 16 ; "butterfly 2"
		distance = (ftemp + ftemp2) * sqr(ftemp) - sqr(ftemp - ftemp2)
	elseif traparray == 17 ; "cardioid"
		distance = sqr(ftemp + ftemp2 - 2 * cartconst * xtest) - \
			sqr(cartconst) * (ftemp + ftemp2)
	elseif traparray == 18 ; "Cartesian oval"
		ftemp3 = cartconst - cartconstB
		ftemp4 = 2 * (cartconst + cartconstB)
		distance = sqr(ftemp3 * (ftemp + ftemp2 + 1) - ftemp4 * xtest) - \
			ftemp4 * (ftemp + ftemp2 + 1) - 4 * ftemp3 * xtest + 1
	elseif traparray == 19 ; "Cassini oval"
		distance = sqr(ftemp + ftemp2) + 2 * (ftemp - ftemp2) - cartconst
	elseif traparray == 20 ; "catenary"
		distance = ytest - cartconst * cosh(xtest / cartconstB)
	elseif traparray == 21 ; "Cayley's sextic"
		distance = 4 * (ftemp + ftemp2 - cartconst * xtest)^3 - 27 * \
			sqr(cartconst*(ftemp + ftemp2))
	elseif traparray == 22 ; "Ceva's trisectrix"
		distance = (ftemp + ftemp2)^3 - sqr((cartconst + 1) * ftemp - \
			(cartconst - 1) * ftemp2)
	elseif traparray == 23 ; "Chasles cubic"
		distance = ytest - cartxcoeff * xtest * ftemp - cartycoeff * ftemp * ytest - \
			cartconst * xtest * ftemp2 - cartconstB * ytest * ftemp2
	elseif traparray == 24 ; "circle"
		distance = ftemp + ftemp2 - cartconst
	elseif traparray == 25 ; "circular cubic"
		distance = xtest * (ftemp + ftemp2) + cartxcoeff * ftemp + cartycoeff * ftemp2 \
			+ cartconst * xtest + cartconstB * ytest + cartconstC
	elseif traparray == 26 ; "cissoid of Diocles"
		distance = xtest * (ftemp + ftemp2) - cartconst * ftemp2
	elseif traparray == 27 ; "clinoid"
		distance = ytest - cartconst * exp(cartxcoeff * xtest) \
			- cartconstB * exp(-cartycoeff * xtest)
	elseif traparray == 28 ; "cochleoid"
		distance = cartconst * ytest / xtest - tan(cartconstB * ytest / \
			(ftemp + ftemp2))
	elseif traparray == 29 ; "conchoid of circle"
		distance = sqr(ftemp + ftemp2 + cartconst - cartconstB) * (ftemp2 \
			+ sqr(xtest + cartconstC)) - 4 * cartconst * sqr(xtest * (xtest + \
			cartconstC) + ftemp2)
	elseif traparray == 30 ; "conchoid of Nicomedes"
		distance = sqr(xtest - cartconst) * (ftemp + ftemp2) - cartconstB * ftemp
	elseif traparray == 31 ; "conchoid of de Sluze"
		distance = cartconst * (xtest + cartconstB) * (ftemp + ftemp2) - \
			cartconstC * ftemp
	elseif traparray == 32 ; "cornoid"
		ftemp3 = sqr(ftemp)
		ftemp4 = sqr(ftemp2)
		distance = ftemp * ftemp3 + ftemp2 * ftemp4 + 3 * (ftemp3 * ftemp2 + ftemp * ftemp4 \
			+ ftemp3) - 5 * ftemp4 + 8 * ftemp2 - 4
	elseif traparray == 33 ; "cross curve"
		distance = cartxcoeff * (ftemp - cartycoeff * (ftemp / ftemp2)) - 1
	elseif traparray == 34 ; "cubic of Apollonius"
		distance = (xtest - cartconst) * (ftemp + ftemp2) + cartconstB * \
			xtest + cartconstC * ytest
	elseif traparray == 35 ; "cranoid"
		distance = sqr(ftemp + ftemp2) - 2 * ftemp2 * (xtest + ytest) + cartconst * \
			(cartconstB -1) * ftemp + (1 - cartconst) * ftemp
	elseif traparray == 36 ; "Jerabek curve"
		distance = (ftemp + ftemp2) * sqr(xtest - cartconst) - cartconstB * \
			sqr(ftemp + ftemp2 - cartconst * xtest)
	elseif traparray == 37 ; "Rosillo curve"
		distance = ftemp2 * sqr(cartconst - xtest) - sqr(cartconstB - xtest) \
			* (cartconstC - ftemp)
	elseif traparray == 38 ; "deltoid"
		distance = sqr(ftemp + ftemp2) + 8 * cartconst * xtest * (ftemp - 3 * \
			ftemp2) + 18 * sqr(cartconst) * (ftemp + ftemp2) - 27 * \
			sqr(sqr(cartconst))
	elseif traparray == 39 ; "devil's curve"
		distance = cartycoeff * sqr(ftemp2) - ftemp2 - cartxcoeff * \
			sqr(ftemp) + cartconst * ftemp
	elseif traparray == 40 ; "dipole curve"
		ftemp3 = ftemp + ftemp2
		distance = cartconst * sqr(ftemp3) * ftemp3 - cartxcoeff * ftemp
	elseif traparray == 41 ; "double egg"
		ftemp3 = ftemp + ftemp2
		distance = cartconst * sqr(ftemp3) * ftemp3 - sqr((cartconstB \
			+ 1) * ftemp - (cartconst - 1) * ftemp2)
	elseif traparray == 42 ; "double folium"
		distance = cartconst * (ftemp + ftemp2) - (cartxcoeff * xtest + \
			cartycoeff * ytest) * ftemp
	elseif traparray == 43 ; "double U curve"
		distance = ftemp2 * (cartconst - cartxcoeff * ftemp) - \
			sqr(cartconst)
	elseif traparray == 44 ; "dumbbell curve"
		ftemp3 = sqr(ftemp)
		distance = cartycoeff * ftemp2 - ftemp3 + cartxcoeff * ftemp * ftemp3
	elseif traparray == 45 ; "cubic duplicatrix"
		distance = cartycoeff * ftemp2 - cartxcoeff * ftemp * \
			(xtest + cartconst)
	elseif traparray == 46 ; "Durer's conchoid"
		distance = sqr(cartxcoeff * ftemp + xtest * ytest + xtest - \
			cartconst) - (cartconst - ftemp) * sqr(xtest - ytest + \
			cartconstB)
	elseif traparray == 47 ; "Sillke's egg of Columbus"
		distance = cartxcoeff * sqr(ftemp2) + 10 * ftemp2 * ftemp + 5 * \
			cartxcoeff * sqr(ftemp) - ytest
	elseif traparray == 48 ; "Granville's egg"
		distance = cartconstC * ftemp * ftemp2 - (xtest - cartconstB) * \
			(cartconst - xtest)
	elseif traparray == 49 ; "Kepler's egg"
		distance = sqr(cartxcoeff * ftemp + cartycoeff * ftemp2) - \
			cartconst * ftemp * xtest
	elseif traparray == 50 ; "eight curve"
		distance = sqr(ftemp) - cartconst * (cartxcoeff * ftemp - \
			cartycoeff * ftemp2)
	elseif traparray == 51 ; "ellipse"
		distance = ftemp + cartconst * ftemp2 - 1
	elseif traparray == 52 ; "superellipse"
		distance = cartxcoeff * abs(xtest)^cartexexp + \
		cartycoeff * abs(ytest)^carteyexp - 1
	elseif traparray == 53 ; "fish quartic"
		distance = cartconst * sqr(2 * ftemp + ftemp2) - 2 * xtest * sqrt(2.0) \
			* (2 * ftemp - 3 * ftemp2) + 2 * cartconstB *(ftemp2 - ftemp)
	elseif traparray == 54 ; "conic focal conchoid"
		ftemp3 = ftemp + ftemp2
		distance = sqr(ftemp3 - conchmod * coniceccent * \
			xtest) - ftemp3 * sqr(coniceccent * xtest - conchmod - 1)
	elseif traparray == 55 ; "folium 1"
		distance = sqr(ftemp + ftemp2) + cartxcoeff * xtest * ftemp - \
			(1 - cartxcoeff) * xtest * ftemp2
	elseif traparray == 56 ; "folium 2"
		distance = sqr(ftemp + ftemp2) - cartxcoeff * xtest * \
			(ftemp - ftemp2)
	elseif traparray == 57 ; "folium of Descartes"
		distance = xtest * ftemp + ytest * ftemp2 - cartconst * xtest * ytest
	elseif traparray == 58 ; "Durer's folium"
		distance = (ftemp + ftemp2) * sqr(cartconst * (ftemp + ftemp2) - \
			cartconstB) - ftemp
	elseif traparray == 59 ; "Gaussian curve"
		distance = ytest - cartconst * exp(-sqr(xtest))
	elseif traparray == 60 ; "Beutel heart"
		ftemp3 = ftemp + ftemp2 - 1
		distance = cartconst * ftemp3 * sqr(ftemp3) - cartconstB * \
			ftemp * ftemp2
	elseif traparray == 61 ; "Proclus hippopede"
		distance = cartconst * sqr(ftemp + ftemp2) - cartxcoeff * \
			ftemp - cartycoeff * ftemp2
	elseif traparray == 62 ; "Hoerl curve"
		distance = ytest - cartxcoeff * xtest^cartconst * exp( \
			cartconstB * xtest)
	elseif traparray == 63 ; "Humbert cubic"
		distance = cartxcoeff * xtest * ftemp - 3 * cartycoeff * \
			xtest * ftemp2 - cartconst
	elseif traparray == 64 ; "hyperbola"
		distance = cartxcoeff * xtest^(2 * cartconst) - \
			cartycoeff * ytest^(2 * cartconstB) - cartconstC
	elseif traparray == 65 ; "hyperbola 2"
		distance = xtest * ytest - cartconst
	elseif traparray == 66 ; "illumination curve"
		ftemp3 = ftemp + 1
		distance = ftemp2 * ftemp3 * sqr(ftemp3) - cartconst
	elseif traparray == 67 ; "kampyle of Eudoxus"
		distance = cartycoeff * ftemp2 - sqr(ftemp) + cartxcoeff * ftemp
	elseif traparray == 68 ; "kappa curve"
		distance = cartycoeff * (ftemp + ftemp2) * ftemp2 - cartxcoeff \
			* ftemp
	elseif traparray == 69 ; "Kiepert's curve"
		ftemp3 = cartconst - cartxcoeff * ftemp
		distance = cartycoeff * ftemp2 - ftemp3 * sqr(ftemp3)
	elseif traparray == 70 ; "kieroid"
		distance = ftemp2 * sqr(xtest - cartconst) + ftemp * sqr(xtest - \
			cartconstB) - cartconstC * ftemp
	elseif traparray == 71 ; "kiss curve"
		ftemp3 = cartconst - ftemp
		distance = cartycoeff * ftemp2 - ftemp3 * sqr(ftemp3)
	elseif traparray == 72 ; "Klein quartic"
		ftemp3 = sqrt(3)
		distance = sqr(ftemp + ftemp2 - 0.5 * cartconst * sqr(cartconstB)) - \
			0.25 * cartconstC * cartconstB * (ytest - cartconstB + \
			ftemp3 * xtest) * (ytest - cartconstB - ftemp3 * xtest) * \
			(2 * ytest + cartconstB)
	elseif traparray == 73 ; "Kulp quartic"
		distance = ftemp2 * (cartconst + ftemp) - cartconstB
	elseif traparray == 74 ; "limacon of Pascal"
		distance = sqr(ftemp + ftemp2 - cartconst * ytest) - ftemp - ftemp2
	elseif traparray == 75 ; "links curve"
		distance = cartconst * sqr(cartxcoeff * ftemp + cartycoeff * ftemp2) - \
			4 * cartconstB * ftemp * (cartconstC * 2 - xtest)
	elseif traparray == 76 ; "Lissajous sextic"
		distance = ftemp * sqr(4 * ftemp - 3 * cartconst) + 4 * cartconst * ftemp2 * \
			(ftemp2 - cartconst)
	elseif traparray == 77 ; "Lissajous quartic"
		distance = 2 * cartconst * sqr(2 * ftemp - sqr(cartconstB)) - cartconstB * \
			(2 * ytest - sqr(cartconstB)) * (ytest + cartconstB)
	elseif traparray == 78 ; "logistic curve"
		distance = cartycoeff * ytest - recip(cartconst + cartconstB * \
			exp(cartxcoeff * xtest))
	elseif traparray == 79 ; "Maltese cross"
		ftemp3 = ftemp + ftemp2
		distance = cartconst * ftemp3 * sqr(ftemp3) - cartconstB * ftemp * (ftemp + \
		20 * cartconstC * ftemp2) + 8 * cartconstB * ftemp2 * (ftemp2 + 2 * \
		cartconstB)
	elseif traparray  == 80 ; "semicubical parabola"
		distance = cartycoeff * ftemp2 - cartxcoeff * xtest * ftemp
	elseif traparray  == 81 ; "diverging parabola"
		distance = cartycoeff * ftemp2 - cartxcoeff * xtest * (ftemp + cartconst)
	elseif traparray == 82 ; "nephroid"
		ftemp3 = ftemp + ftemp2 - 4 * cartconst
		distance = ftemp3 * sqr(ftemp3) - 108 * cartconstB * ftemp2
	elseif traparray == 83 ; "Freeth's nephroid"
		distance = (ftemp + ftemp2) * sqr(ftemp + ftemp2 - sqr(cartconst)) - 4 * sqr(cartconst) \
		* sqr(ftemp + ftemp2 - cartconst)
	elseif traparray == 84 ; "nodal curve"
		distance = cartconst * ftemp * ftemp2 * (cartxcoeff * ftemp + cartycoeff * \
			ftemp2) - sqr(cartconstB * ftemp - cartconstC * ftemp2)
	elseif traparray == 85 ; "strophoid"
		distance = cartconst * xtest * (cartxcoeff * ftemp + cartycoeff * ftemp2) \
			+ cartconstB * (cos(cartconstB * (cartxcoeff * ftemp - cartycoeff * \
			ftemp2)) + 2 * sin(cartconstB * xtest * ytest))
	elseif traparray == 86 ; "ophiuride"
		distance = cartxcoeff * xtest * ftemp + xtest * ftemp2 - cartycoeff * ftemp2 + \
			cartconst * xtest * ytest
	elseif traparray == 87 ; "parabola"
		distance = cartycoeff * ytest - cartxcoeff * ftemp
	elseif traparray == 88 ; "parabola 2"
		distance = cartycoeff * ytest - cartxcoeff * ftemp + cartconst
	elseif traparray == 89 ; "parabolic trifolium"
		distance = ftemp * (cartxcoeff * ftemp + cartycoeff * ftemp2) - cartconst \
			* ytest * (cartxcoeff * ftemp - cartycoeff * ftemp2)
	elseif traparray == 90 ; "piriform"
		distance = cartycoeff * ftemp2 - cartxcoeff * xtest * ftemp * \
			(cartconst - xtest)
	elseif traparray == 91 ; "pearls of de Sluze"
		distance = cartycoeff * ytest^cartconst - cartxcoeff * \
			xtest^cartconstB * (1 - xtest)^cartconstC
	elseif traparray == 92 ; "pursuit curve"
		distance = cartycoeff * ytest - xtest^(cartconstB + cartconst) / \
			(cartconstB + cartconst) + xtest^(2 * cartconstC - cartconst) \
			/ (2 * cartconstC - cartconst)
	elseif traparray == 93 ; "quadratrix"
		distance = cartycoeff * ytest - cartxcoeff * xtest / (cartconst * \
			tan(cartconstB * xtest))
	elseif traparray == 94 ; "quadrifolium"
		ftemp3 = ftemp + ftemp2
		distance = cartconst * ftemp3 * sqr(ftemp3) - cartconstB * ftemp * ftemp2
	elseif traparray == 95 ; "trifolium"
		distance = cartconst * sqr(ftemp + ftemp2) - cartconstB * xtest * (ftemp - \
			cartconstC * 3 * ftemp2)
	elseif traparray == 96 ; "right strophoid"
		distance = cartycoeff * ftemp2 - cartxcoeff * ftemp * ((cartconst + \
			xtest)/(cartconstB - xtest))
	elseif traparray == 97 ; "scarabaeus"
		ftemp3 = ftemp + ftemp2
		distance = cartconst * ftemp3 * (ftemp3 + cartconstB * xtest) - \
		cartconstC * (ftemp - ftemp2)
	elseif traparray == 98 ; "scyphoid"
		distance = cartxcoeff * sqr(ftemp) - cartycoeff * sqr(ftemp2) - \
			cartconst * xtest * ftemp2
	elseif traparray == 99 ; "anguinea"
		distance = cartycoeff * ytest - cartconstB * cartconst * xtest / \
			(ftemp + sqr(cartconst))
	elseif traparray == 100 ; "damped sine"
		distance = cartycoeff * ytest - cartconst * sin(cartconstB * xtest) / \
			(cartxcoeff * xtest)
	elseif traparray == 101 ; "catastrophic sine"
		distance = cartycoeff * ytest - (cartconst * xtest + cartconstB) * \
			cartconstC * sin(cartxcoeff * xtest)
	elseif traparray == 102 ; "plane spiric"
		distance = cartconst * sqr(ftemp + ftemp2) + cartxcoeff * ftemp + cartycoeff * \
			ftemp2 + cartconstB * xtest + cartconstC
	elseif traparray == 103 ; "spiric of Perseus"
		distance = sqr(ftemp + ftemp2 - cartconst + cartconstB) - 4 * cartconstC \
			* (ftemp + cartconstB)
	elseif traparray == 104 ; "svastika"
		distance = 2 * cartconst * xtest * ytest - cartxcoeff * sqr(ftemp) + \
			cartycoeff * sqr(ftemp2)
	elseif traparray == 105 ; "syntractrix"
		ftemp3 = sqr(cartconst)
		ftemp4 = sqrt(ftemp3 - ftemp2)
		distance = cartxcoeff * xtest + ftemp4 - cartconstB * log((cartconst + \
			ftemp4) / (cartycoeff * ytest))
	elseif traparray == 106 ; "tetracuspid"
		distance = cartxcoeff * ftemp + cartycoeff * ftemp2 - cartconst + \
			27 * cartconstB * ftemp * ftemp2
	elseif traparray == 107 ; "siluroid"
		distance = cartconst * sqr(ftemp + ftemp2) - cartxcoeff * xtest * (ftemp - ftemp2)
	elseif traparray == 108 ; "trisectrix of Longchamps"
		distance = cartconst * xtest * (ftemp - 3 * ftemp2) - cartxcoeff * ftemp - \
			cartycoeff * ftemp2
	elseif traparray == 109 ; "trident"
		distance = cartycoeff * ytest - cartxcoeff * ftemp - cartconst / xtest
	elseif traparray == 110 ; "trisectrix of Delanges"
		ftemp3 = ftemp + ftemp2
		distance = cartconstB * sqr(ftemp3 - cartconst) - ftemp * ftemp3
	elseif traparray == 111 ; "trisectrix of Maclaurin"
		distance = cartxcoeff * xtest * ftemp + cartconst * xtest * ftemp2 - \
			3 * cartconstB * ftemp - cartycoeff * ftemp2
	elseif traparray == 112 ; "Trott curve"
		distance = 144 * cartconst * (sqr(ftemp) + sqr(ftemp2)) - 225 * cartconstB * \
			(ftemp + ftemp2) + 350 * cartconstC * ftemp * ftemp2 + 81 * cartxcoeff
	elseif traparray == 113 ; "Tschirnhausen's cubic"
		distance = cartycoeff * ftemp2 - cartxcoeff * ftemp * (cartconst * \
			xtest + cartconstB)
	elseif traparray == 114 ; "visiera"
		distance = cartxcoeff * xtest * (ftemp + ftemp2) - cartconst * (ftemp + 2 * \
			cartycoeff * ftemp2)
	elseif traparray == 115 ; "resonance curve"
		distance = cartycoeff * ytest - (cartconst / (cartconstB + \
			cartxcoeff * ftemp))
	elseif traparray == 116 ; "Watt's curve"
		ftemp3 = ftemp + ftemp2
		ftemp4 = sqr(ftemp3)
		distance = ftemp3 * ftemp4 - 2 * cartconst * ftemp4 + cartconstB * \
			(xtest + 4 * ftemp2) * ftemp3 - cartconstC * ftemp2
	elseif traparray == 117 ; "witch of Agnesi"
		distance = cartxcoeff * ftemp * ytest - sqr(cartconst) * \
			(cartconst - cartycoeff)
	endif ; traparray

;	if cartsmooth[oindex] < 0.99 || cartsmooth[oindex] > 1.01
;		distance = distance^cartsmooth[oindex]
;	endif ; cartsmooth[]
	distmin = cabs(ztemp) + distance
	result = distmin * exp(flip(tempangleB))
	tempxx = real(result)
	tempyy = imag(result)
	minpt = result

endif ; @traptype

	if @trapmode == "distance"
		testvalue = distmin
	elseif @trapmode == "cabs"
		testvalue = |minpt|
	elseif @trapmode == "real"
		testvalue = abs(real(minpt))
	elseif @trapmode == "imag"
		testvalue = abs(imag(minpt))
	elseif @trapmode == "real 2"
		testvalue = real(minpt)
	elseif @trapmode == "imag 2"
		testvalue = imag(minpt)
	elseif @trapmode == "sum"
		testvalue = real(minpt) + imag(minpt)
	elseif @trapmode == "sum 2"
		testvalue = abs(real(minpt)) + abs(imag(minpt))
	elseif @trapmode == "sum 3"
		testvalue = sqr(real(minpt)) + sqr(imag(minpt))
	elseif @trapmode == "product"
		testvalue = real(minpt) * imag(minpt)
	elseif @trapmode == "product 2"
		testvalue = abs(real(minpt)) * abs(imag(minpt))
	elseif @trapmode == "product 3"
		testvalue = sqr(real(minpt) * imag(minpt))
	elseif @trapmode == "difference"
		testvalue = real(minpt) - imag(minpt)
	elseif @trapmode == "difference 2"
		testvalue = abs(real(minpt) - imag(minpt))
	elseif @trapmode == "difference 3"
		testvalue = sqr(real(minpt) - imag(minpt))
	endif ; @trapmode

	; apply an optional function
	if @testfunction != "none"
		if @testfunction == "sin" ; sine function
			testvalue = sin(testvalue)
		elseif @testfunction == "cos" ; cosine
			testvalue = cos(testvalue)
		elseif @testfunction == "tan" ; tangent
			testvalue = tan(testvalue)
		elseif @testfunction == "cot" ; cotangent
			testvalue = cotan(testvalue)
		elseif @testfunction == "sec" ; secant
			testvalue = 1/cos(testvalue)
		elseif @testfunction == "csc" ; cosecant
			testvalue = 1/sin(testvalue)
		elseif @testfunction == "ver" ; versine
			testvalue = 1 - cos(testvalue)
		elseif @testfunction == "vcs" ; vercosine
			testvalue = 1 + cos(testvalue)
		elseif @testfunction == "cvs" ; coversine
			testvalue = 1 - sin(testvalue)
		elseif @testfunction == "cvc" ; covercosine
			testvalue = 1 + sin(testvalue)
		elseif @testfunction == "exs" ; exsecant
			testvalue = 1/cos(testvalue) - 1
		elseif @testfunction == "exc" ; excosecant
			testvalue = 1/sin(testvalue) - 1
		elseif @testfunction == "crd" ; chord
			testvalue = 2 * sin(testvalue/2)
		elseif @testfunction == "asin" ; arcsine
			testvalue =  asin(testvalue - trunc(testvalue)) 
		elseif @testfunction == "acos" ; arccosine
			testvalue = acos(testvalue - trunc(testvalue))
		elseif @testfunction == "atan" ; arctangent
			testvalue = atan(testvalue)
		elseif @testfunction == "acot" ; arccotangent
			testvalue = halfpi - atan(testvalue)
		elseif @testfunction == "asec" ; arcsecant
			testvalue = acos(1/testvalue - trunc(1/testvalue))
		elseif @testfunction == "acsc" ; arccosecant
			testvalue = asin(1/testvalue - trunc(1/testvalue))
		elseif @testfunction == "aver" ; arcversine
			testvalue = acos(1 - testvalue - trunc(1-testvalue))
		elseif @testfunction == "avcs" ; arcvercosine
			testvalue = acos(1 + testvalue - trunc(1+testvalue))
		elseif @testfunction == "acvs" ; arccoversine
			testvalue = asin(1 - testvalue - trunc(1-testvalue))
		elseif @testfunction == "acvc" ; arccovercosine
			testvalue = asin(1 + testvalue - trunc(1+testvalue))
		elseif @testfunction == "aexs" ; arcexsecant
			testvalue = acos( (1/(testvalue+1)) - trunc( (1/(testvalue+1)) ) )
		elseif @testfunction == "aexc" ; arcexcosecant
			testvalue = asin( (1/(testvalue+1)) - trunc( (1/(testvalue+1)) ) )
		elseif @testfunction == "acrd" ; arcchord
			testvalue = 2 * asin( testvalue/2 - trunc(testvalue/2) )
		elseif @testfunction == "exp" ; exponential
			testvalue = exp(testvalue)
		elseif @testfunction == "exp(-n)" ; negative exponential
			testvalue = exp(-testvalue)
		elseif @testfunction == "exp(1/n)" ; recip exponential
			testvalue = exp(1/testvalue)
		elseif @testfunction == "exp(-1/n)" ; neg recip exponential
			testvalue = exp(-1/testvalue)
		elseif @testfunction == "exp(n^2)" ; z^2 exponential
			testvalue = exp(sqr(testvalue))
		elseif @testfunction == "exp(-n^2)" ; -z^2 exponential
			testvalue = exp(-sqr(testvalue))
		elseif @testfunction == "exp(1/n^2)" ; recip z^2 exponential
			testvalue = exp(1/sqr(testvalue))
		elseif @testfunction == "exp(-1/n^2)" ; -recip z^2 exponential
			testvalue = exp(-1/sqr(testvalue))
		elseif @testfunction == "sinh" ; hyperbolic sine
			testvalue = sinh(testvalue)
		elseif @testfunction == "asinh" ; inverse hyperbolic sine
			testvalue = asinh(testvalue)
		elseif @testfunction == "cosh" ; hyperbolic cosine
			testvalue = cosh(testvalue)
		elseif @testfunction == "acosh" ; inverse hyperbolic cosine
			testvalue = acosh(testvalue)
		elseif @testfunction == "tanh" ; hyperbolic tangent
			testvalue = tanh(testvalue)
		elseif @testfunction == "atanh" ; inverse hyperbolic tangent
			testvalue = atanh(testvalue)
		elseif @testfunction == "cotanh" ; hyperbolic cotangent
			testvalue = cotanh(testvalue)
		elseif @testfunction == "sqr" ; square
			testvalue = sqr(testvalue)
		elseif @testfunction == "sqrt" ; square root
			testvalue = sqrt(testvalue)
		elseif @testfunction == "power" ; power
			testvalue = testvalue^@testpower
		elseif @testfunction == "log" ; logarithm
			testvalue = log(testvalue)
		elseif @testfunction == "log(-n)" ;
			testvalue = log(-testvalue)
		elseif @testfunction == "log(1/n)" ;
			testvalue = log(1/testvalue)
		elseif @testfunction == "log(-1/n)" ;
			testvalue = log(-1/testvalue)
		elseif @testfunction == "1/n" ; reciprocal
			testvalue = 1/testvalue
		elseif @testfunction == "absolute value" ; absolute value
			testvalue = abs(testvalue)
		elseif @testfunction == "ceiling" ; ceiling
			testvalue = ceil(testvalue)
		elseif @testfunction == "floor" ; floor
			testvalue = floor(testvalue)
		elseif @testfunction == "truncation" ; truncation
			testvalue = trunc(testvalue)
		elseif @testfunction == "rounding" ; rounding
			testvalue = round(testvalue)
		elseif @testfunction == "asin 2" ; arcsine
			testvalue = asin(testvalue)
		elseif @testfunction == "acos 2" ; arccosine
			testvalue = acos(testvalue)
		elseif @testfunction == "atan 2" ; arctangent
			testvalue = atan2(testvalue)
		elseif @testfunction == "acot 2" ; arccotangent
			testvalue = halfpi - atan2(testvalue)
		elseif @testfunction == "asec 2" ; arcsecant
			testvalue = acos(1/testvalue)
		elseif @testfunction == "acsc 2" ; arccosecant
			testvalue = asin(1/testvalue)
		elseif @testfunction == "aver 2" ; arcversine
			testvalue = acos(1 - testvalue)
		elseif @testfunction == "avcs 2" ; arcvercosine
			testvalue = acos(1 + testvalue)
		elseif @testfunction == "acvs 2" ; arccoversine
			testvalue = asin(1 - testvalue)
		elseif @testfunction == "acvc 2" ; arccovercosine
			testvalue = asin(1 + testvalue)
		elseif @testfunction == "aexs 2" ; arcexsecant
			testvalue = acos( (1/(testvalue+1)))
		elseif @testfunction == "aexc 2" ; arcexcosecant
			testvalue = asin( (1/(testvalue+1)))
		elseif @testfunction == "acrd 2" ; arcchord
			testvalue = 2 * asin( testvalue/2 )
		elseif @testfunction == "log(n^2)" ; 
			testvalue = log(sqr(testvalue))
		elseif @testfunction == "log(-n^2)" ; 
			testvalue = log(-sqr(testvalue))
		elseif @testfunction == "log(1/n^2)" ; 
			testvalue = log(1/sqr(testvalue))
		elseif @testfunction == "log(-1/n^2)" ; 
			testvalue = log(-1/sqr(testvalue))
		elseif @testfunction == "log log" ; 
			testvalue = log( log(testvalue) )
		elseif @testfunction == "exp(exp)" ; 
			testvalue = exp( exp(testvalue) )
		elseif @testfunction == "n^n" ; 
			testvalue = testvalue^testvalue
		elseif @testfunction == "n^n^n" ; 
			testvalue = testvalue^(testvalue^testvalue)
		elseif @testfunction == "constant^n" ; 
			testvalue = @testbase^testvalue
		elseif @testfunction == "constant^n^n" ; 
			testvalue = @testbase^(testvalue^testvalue)
		endif ; @testfunction
	endif ; @testfunction

	testvalue = testvalue + @testadjustment

	if @fixbug
		#z = ztemp
	endif ; @fixbug

	if @barnsleymode == "cabs"
		barnsleyvalue = |#z|
	elseif @barnsleymode == "real"
		barnsleyvalue = abs(real(#z))
	elseif @barnsleymode == "imag"
		barnsleyvalue = abs(imag(#z))
	elseif @barnsleymode == "real 2"
		barnsleyvalue = real(#z)
	elseif @barnsleymode == "imag 2"
		barnsleyvalue = imag(#z)
	elseif @barnsleymode == "sum"
		barnsleyvalue = real(#z) + imag(#z)
	elseif @barnsleymode == "sum 2"
		barnsleyvalue = abs(real(#z)) + abs(imag(#z))
	elseif @barnsleymode == "sum 3"
		barnsleyvalue = sqr(real(#z)) + sqr(imag(#z))
	elseif @barnsleymode == "product"
		barnsleyvalue = real(#z) * imag(#z)
	elseif @barnsleymode == "product 2"
		barnsleyvalue = abs(real(#z)) * abs(imag(#z))
	elseif @barnsleymode == "product 3"
		barnsleyvalue = sqr(real(#z) * imag(#z))
	elseif @barnsleymode == "difference"
		barnsleyvalue = real(#z) - imag(#z)
	elseif @barnsleymode == "difference 2"
		barnsleyvalue = abs(real(#z) - imag(#z))
	elseif @barnsleymode == "difference 3"
		barnsleyvalue = sqr(real(#z) - imag(#z))
	elseif @barnsleymode == "test constant"
		barnsleyvalue = @barntestconst
	endif ; @barnsleymode

	if @barnsleytype == "1"
		if barnsleyvalue <= testvalue
			#z = (#z - flip(1)+ @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (#z + flip(1) + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif ; barnsleyvalue
	elseif @barnsleytype == "2"
		if barnsleyvalue <= testvalue
			#z = (#z - 1 + @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (#z + 1 + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "3"
		if barnsleyvalue <= testvalue
			#z = #z * juliaconst - 1 + @barnconst1
			equation1 = equation1 + 1
		else
			#z = #z * juliaconst + 1 + @barnconst2
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "4"
		if barnsleyvalue <= testvalue
			#z = #z * juliaconst - (0,1) + @barnconst1
			equation1 = equation1 + 1
		else
			#z = #z * juliaconst + (0,1) + @barnconst2
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "5"
		if barnsleyvalue <= testvalue
			#z = (sqr(#z) - (0,1) + @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (sqr(#z) + (0,1) + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "6"
		if barnsleyvalue <= testvalue
			#z = (sqr(#z) - 1 + @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (sqr(#z) + 1 + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "7"
		if barnsleyvalue <= testvalue
			#z = sqr(#z) * juliaconst - (0,1) + @barnconst1
			equation1 = equation1 + 1
		else
			#z = sqr(#z) * juliaconst + (0,1) + @barnconst2
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "8"
		if barnsleyvalue <= testvalue
			#z = sqr(#z) * juliaconst - 1 + @barnconst1
			equation1 = equation1 + 1
		else
			#z = sqr(#z) * juliaconst + 1 + @barnconst2
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "9"
		if barnsleyvalue <= testvalue
			#z = (sqr(#z) + #z  + @barnconst1) * juliaconst - 1
			equation1 = equation1 + 1
		else
			#z = (sqr(#z) - #z  + @barnconst2) * juliaconst + 1
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "10"
		if barnsleyvalue <= testvalue
			#z = (sqr(#z) + 2 * #z  + @barnconst1) * juliaconst
			equation1 = equation1 + 1
		else
			#z = (sqr(#z) - 2 * #z  + @barnconst2) * juliaconst
			equation2 = equation2 + 1
		endif
	elseif @barnsleytype == "11"
		if barnsleyvalue <= testvalue
			#z = ( (#z - 1) * log(#z) + @barnconst1) * juliaconst
		else
			#z = ( (#z + 1) * log(#z) + @barnconst2) * juliaconst
		endif ; zangle
	elseif @barnsleytype == "12"
		if barnsleyvalue <= testvalue
			#z = ( (#z - (0,1)) * log(#z) + @barnconst1) * juliaconst
		else
			#z = ( (#z + (0,1)) * log(#z) + @barnconst2) * juliaconst
		endif ; zangle
	elseif @barnsleytype == "13"
		if barnsleyvalue <= testvalue
			#z = ( #z * log(#z-1) + @barnconst1) * juliaconst
		else
			#z = ( #z * log(#z+1) + @barnconst2) * juliaconst
		endif ; zangle
	elseif @barnsleytype == "14"
		if barnsleyvalue <= testvalue
			#z = ( #z * log(#z-(0,1)) + @barnconst1) * juliaconst
		else
			#z = ( #z * log(#z+(0,1)) + @barnconst2) * juliaconst
		endif ; zangle
	endif ; @barnsleytype
	
	if @bailtest == "mod"
		dontbail = (|#z| <= @bailout)
	elseif @bailtest == "real"
		dontbail = (sqr(real(#z)) <= @bailout)
	elseif @bailtest == "imag"
		dontbail = (sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "and"
		dontbail = (sqr(real(#z)) <= @bailout && sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "or"
		dontbail = (sqr(real(#z)) <= @bailout || sqr(imag(#z)) <= @bailout)
	elseif @bailtest == "eor"
		if sqr(real(#z)) <= @bailout
			dontbail = (sqr(imag(#z)) > @bailout)
		else
			dontbail = (sqr(imag(#z)) <= @bailout)
		endif ; sqr()
	elseif @bailtest == "manh"
		dontbail = (sqr(abs(real(#z)) + abs(imag(#z))) <= @bailout)
	elseif @bailtest == "manr"
		dontbail = (sqr(real(#z) + imag(#z)) <= @bailout)
	elseif @bailtest == "real 2"
		dontbail = (abs(real(#z)) <= @bailout)
	elseif @bailtest == "imag 2"
		dontbail = (abs(imag(#z)) <= @bailout)
	elseif @bailtest == "sum"
		dontbail = (abs(real(#z) + imag(#z)) <= @bailout)
	elseif @bailtest == "sum 2"
		dontbail = (abs(real(#z)) + abs(imag(#z)) <= @bailout)
	elseif @bailtest == "product"
		dontbail = (abs(real(#z) * imag(#z)) <= @bailout)
	elseif @bailtest == "difference"
		dontbail = (abs(real(#z)) - abs(imag(#z)) <= @bailout)
	elseif @bailtest == "difference 2"
		dontbail = (abs(real(#z) - imag(#z)) <= @bailout)
	elseif @bailtest == "difference 3"
		dontbail = (abs(imag(#z)) - abs(real(#z)) <= @bailout)
	elseif @bailtest == "quotient"
		dontbail = (abs(real(#z)) / abs(imag(#z)) <= @bailout)
	elseif @bailtest == "quotient 2"
		dontbail = (abs(imag(#z)) / abs(real(#z)) <= @bailout)
	endif ; @bailtest

	if @heatmap ; encode the eq1/eq2 ration in #z
		currentz = #z
		#z = equation1 + flip(equation2)
	endif ; @heatmap

bailout:
	dontbail

default:
	title = "Barnsley - Orbit Traps"
	center = (0,0)
	maxiter = 500
	method = multipass
	periodicity = 0
	magn = 0.75

param trapmode
	caption = "Trap Mode"
	enum = "distance" "cabs" "real" "imag" "real 2" "imag 2" "sum" "sum 2" "sum 3" \
		"product" "product 2" "product 3" "difference" "difference 2" "difference 3"
	default = 0
	hint = "This setting determines how the trapped point is used in the Barnsley \
		comparison.  With the default settings, 'Trap Mode' = 'distance' and \
		parameter 'Barnsley Mode' = 'test constant', then if the distance between #z \
		and the trap point <= the value of 'test constant', Barnsley equation 1 is \
		executed; otherwise, equation 2 is executed."
endparam
param traptype
	caption = "Trap Type"
	enum = "lines & points" "polar functions" "parametric functions" "cartesian"
	default = 0
	hint = "This setting determines the method used for the 'Trap Shape'."
endparam
param trapshape
	caption = "Trap Shape"
	enum = "line" "triangle" "isosceles" "3-asterisk" "3-star" "3-star 2" \
		"polytriangle" "trigram" "nested triangles" "nested triangle 2" \
		"twisted triangles" "twisted triangle 2" "3-rhombstar" \
		"square" "square 2" "rhombus" "kite" "dart" "rectangle" "4-asterisk" \
		"4-star" "flat 4-star" "4-star 2" "bowtie" "windowpane" "tetragram" "tetragram 2" \
		"nested squares" "nested square 2" "twisted squares" \
		"twisted square 2" "windmill" "windmill 2" \
		"pentagon" "pentagon 2" "pentagram" "pentagram 2" "pentagram 3" \
		"pentagram 4" "pentagram 5" "5-asterisk" "5-star" "5-star 2" "5-star 3" "nested pentagons" \
		"nested pentagon 2" "twisted pentagons" "twisted pentagon 2" "5-rhombstar" \
		"hexagon" "hexagon 2" "hexagram" "hexagram 2" "hexagram 3" \
		"hexagram 4" "hexagram 5" "hexagram 6" "hexagram 7" "honeycomb" \
		"6-asterisk" "6-star" "6-star 2" "6-star 3" "nested hexagons" "nested hexagon 2" \
		"twisted hexagons" "twisted hexagon 2" "6-rhombstar" \
		"zigzag-3" "zigzag-4" "zigzag-5" "zigzag-6" "zigzag-7" \
		"sawtooth-1" "sawtooth-2" "sawtooth-3" "sawtooth-4" \
		"square-1" "square-2" "square-3" "square-4" "peano curve" "roots of unity" \
		"hand" "lissajous 1" "lissajous 2" "lissajous 3" "superellipse" "hypotrochoid" "epitrochoid" \
		"collinear spots" "triangular array" "square array" "pentagonal array" "hexagonal array" \
		"triangular spiral" "square spiral" "pentagonal spiral" "hexagonal spiral" "octagonal spiral" \
		"nested circles" "osculant circles" "dotted star" "dashed star" \
		"heptagon" "heptagon 2" "heptagram" "heptagram 2" "heptagram 3" "heptagram 4" \
		"heptagram 5" "heptagram 6" "heptagram 7" "7-asterisk" "7-star" "7-star 2" "7-star 3" \
		"nested heptagons" "nested heptagon 2" "twisted heptagons" "twisted heptagon 2" "7-rhombstar" \
		"octagon" "octagon 2" "octagram" "octagram 2" "octagram 3" \
		"octagram 4" "octagram 5" "octagram 6" "octagram 7" "octagram 8" \
		"octagram 9" "octagram 10" "8-asterisk" "8-star" "8-star 2" "8-rhombstar" \
		"nonagon" "nonagram" "nonagram 2" "nonagram 3" "nonagram 4" "nonagram 5" \
		"nonagram 6" "nonagram 7" "9-asterisk" "9-star" "9-star 2" "9-star 3" "9-rhombstar" \
		"decagon" "decagram" "decagram 2" "decagram 3" "decagram 4" "decagram 5" "10-asterisk" "10-star" \
		"10-star 2" "10-star 3" "10-rhombstar" "more polygons" "more spirolaterals" "more curves"
	default = 0
	hint = "This parameter determines what geometrical figure to use \
		as a trap."
	visible = @traptype == "lines & points"
endparam
param morepolygons1
	caption = "Polygon Shape"
	enum = "11-gon" "11-gram 1" "11-gram 2" "11-gram 3" "11-gram 4" "11-star" \
		"11-star 2" "11-rhombstar" "11-asterisk" \
		"12-gon" "12-gram 1" "12-gram 2" "12-gram 3" "12-gram 4" "12-gram 5" "12-star" \
		"12-star 2" "12-rhombstar" "12-asterisk" \
		"13-gon" "13-star" "13-rhombstar" "13-asterisk" "14-gon" "14-star" "14-rhombstar" "14-asterisk" \
		"15-gon" "15-star" "15-rhombstar" "15-asterisk" \
		"16-gon" "16-star" "16-rhombstar" "16-asterisk"
	default = 0
	hint = "If 'Trap Shape' is set to 'more polygons', this parameter determines which \
		polygon shape to use as a trap."
	visible = @trapshape == "more polygons"  && (@traptype == "lines & points")
endparam
param morespirolaterals1
	caption = "Spirolateral Shape"
	enum = "1,1,1,2,3;1/2" "1,6,6,6;1/4,1/4,-5/6" "1,1,2,1,3;1/2" "1,1,2,2,4;1/2" "1,1,4,5,4;1/2" "1,2,2,2,5;1/2" \
		"1,2,5,3,5;1/2" "2,2,1,4,3;1/2" "2,2,4,4,3;1/2" "2,3,5,3,2;1/2" \
		"1,6,6,2;3/4,-1/4,-1/6" "1,2,1,3;-4/5" "1,2,1,3;-4/5,-4/5,0" "1,2,1,3;-4/5,-1/5,-4/5" "1,3;1/5,3/5,-1/5" \
		"1,2,3,3,2,1;5/6,1/6,1/6" "1,1,3,1;-5/6,-1/6,3/7" "1,1,3,1;-1/6,1/6,-3/7" "1,1,3,1;5/6,1/6,4/7" \
		"1,3,1,4,2;-1/2,1/6"
	default = 0
	hint = "If 'Trap Shape' is set to 'more spirolaterals', this parameter determines which \
		shape to use as a trap.  Some of these settings will require reducing the trap size parameter."
	visible = @trapshape == "more spirolaterals"  && (@traptype == "lines & points")
endparam
param morecurves1
	caption = "Curve Shape"
	enum = "cycloid" "bipolar lissajous" "elliptic lissajous" "parabolic lissajous" "polar lissajous" \
		"Moritz cyclic harmonic" "rhodonea"
	default = 0
	hint = "If 'Trap Shape' is set to 'more curves', this parameter determines which \
		curve to use as a trap."
	visible = @trapshape == "more curves" && @traptype == "lines & points"
endparam
param polarshape1
	caption = "Trap Shape"
	enum = "cardioid" "circle" "Cayley's sextic" "Cayley's sextic 2" "cissoid of Diocles" "cochleoid" \
		"conchoid of De Sluze" "conchoid of Nicomedes" "cubical parabola" \
		"ellipse" "folioid" "folium" "folium of Descartes" "hippopede" "hyperbolic spiral" \
		"kampyle of Eudoxus" "kappa" "lemniscate of Bernoulli" \
		"limacon of Pascal" "lituus" "lituus 2" "logarithmic spiral""parabola" \
		"parabolic spiral" "rose" "semicubical parabola" "spiral of Archimedes" \
		"strophoid" "trefoil of Habenicht" "trisectrix limacon"
	default = 0
	hint = "If 'Trap Type' is set to 'polar functions', then this setting determines \
		the function to use."
	visible = @traptype == "polar functions"
endparam
param polarmode1
	caption = "Function 1 Mode"
	enum = "normal" "implicit"
	default = 0
	hint = "If 'Trap Type' is set to 'polar functions', this setting determines \
		how the function is used.  This option primarily affects the way the coloring \
		is applied."
	visible = @traptype == "polar functions"
endparam
param parashape1
	caption = "Trap Shape"
	enum = "hypocycloid" "Abdank quadratrix" "companion of cycloid" "cornoid" "cycloid" \
		"cycloid variant" "ellipse" "epicycloid" "epicycloid 2" "epitrochoid" \
		"hyperbola" "nephroid" \
		"serpentine" "tractrix" "wavy circle" "witch of Agnesi"
		default = 0
	hint = "If 'Trap Type' is set to 'parametric functions', then this setting \
		determines the function to use."
	visible = @traptype == "parametric functions"
endparam
param xyshape1
	caption = "Trap Shape"
	enum = "ampersand" "Alain's curve" "anguinea" "arcs of Samothrace" "astroid" \
		"atriphthaloid" "bean curve 1" "bean curve 2" "beetle curve" "Beutel heart" \
		"bicorn" "bicuspid" "biquartic of Sacre" "Bolza curve" "bow curve" \
		"bullet nose curve" "butterfly sextic" "butterfly 2" "cardioid" "Cartesian oval" \
		"Cassini oval" "catastrophic sine" "catenary" "Cayley's sextic" "Ceva's trisectrix" \
		"Chasles cubic"  "circle" \
		"circular cubic" "cissoid of Diocles" "clinoid" "cochleoid" "conchoid of circle" \
		"conchoid of Nicomedes" "conchoid of de Sluze" "conic focal conchoid" \
		"cornoid" "cranoid"  "cross curve" \
		"cubic duplicatrix" "cubic egg" "cubic of Apollonius" "damped sine" "deltoid" "devil's curve" \
		"dipole curve" "diverging parabola" "double egg" \
		"double folium" "double U curve" "dumbbell curve" "Durer's conchoid" "Durer's folium" \
		"eight curve" "ellipse" "fish quartic" "folium 1" "folium 2" "folium of Descartes" \
		"Freeth's nephroid" \
		"Gaussian curve" "Granville's egg" "Hoerl curve" "Humbert cubic" "hyperbola" "hyperbola 2" \
		"illumination curve" "Jerabek curve" "kampyle of Eudoxus" "kappa curve" "Kepler's egg" \
		"Kiepert's curve" "kieroid" "kiss curve" "Klein quartic" "Kulp quartic" "limacon of Pascal" \
		"links curve" "Lissajous quartic" "Lissajous sextic" "logistic curve" "Maltese cross" \
		"nephroid" "nodal curve" "ophiuride" "parabola" "parabola 2" "parabolic trifolium" \
		"pearls of de Sluze" "piriform" "plane spiric" "Proclus hippopede" "pursuit curve" \
		"quadrafolium" "quadratrix" "resonance curve" \
		"right strophoid" "Rosillo curve" "scarabaeus" "scyphoid" "semicubical parabola" \
		"Sillke's egg of Columbus" "siluroid" "spiric of Perseus" "strophoid" \
		"superellipse" "svastika" "syntractrix" "tetracuspid" "trident" "trifolium" "trisectrix of Delanges" \
		"trisectrix of Longchamps" "trisectrix of Maclaurin" "Trott curve" "Tschirnhausen's cubic" \
		"visiera" "Watt's curve" "witch of Agnesi"
	default = 0
	hint = "If 'Trap 1 Type' is set to 'cartesian', then this setting determines \
		the function to use."
	visible = @traptype == "cartesian"
endparam
param fixtrapbug
	caption = "Fix Trap Bug?"
	default = TRUE
	hint = "If enabled, an error in an early version of this formula that affected the rendering of \
		some of the trap shapes will be corrected.  Disable to recover the original version."
	visible = ((@trapshape == "square array") || (@trapshape == "roots of unity") || (@trapshape == \
		"superellipse") || (@trapshape == "hypotrochoid") || (@trapshape == "epitrochoid") || \
		(@trapshape == "collinear spots") || (@trapshape == "triangular array") || (@trapshape == \
		"pentagonal array") || (@trapshape == "hexagonal array") || (@trapshape == "triangular spiral") \
		|| (@trapshape == "square spiral") || (@trapshape == "pentagonal spiral") || (@trapshape == \
		"hexagonal spiral") || (@trapshape == "octagonal spiral") || (@trapshape == "nested circles") || \
		(@trapshape == "osculant circles")) && @traptype == "lines & points"
endparam
param nscale1
	caption = "Trap Scale"
	default = 1.5
	hint = "This parameter fixes the overall size of the trap shape."
endparam
param rotate
	caption = "Rotation Angle"
	default = 0.0
	min = -179.98
	max = 359.98
	hint = "Number of degrees (0-359) that the trap should be rotated from its default position"
endparam
param center
	caption = "Center"
	default = (0,0)
	hint = "Enter coordinates of trap center"
endparam
param isocheight
	caption = "Isosceles Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'isosceles', then this setting \
		determines the height of the isosceles triangle."
	visible = @trapshape == "isosceles"  && (@traptype == "lines & points")
endparam
param isocwidth
	caption = "Isosceles Width"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'isosceles', then this setting \
		determines the width of the isosceles triangle base."
	visible = @trapshape == "isosceles"   && (@traptype == "lines & points")
endparam
param fixisosceles
	caption = "Fix Isosceles Bug?"
	default = FALSE
	hint = "If enabled and 'Trap Shape' is set to 'isosceles', then this \
		setting corrects a bug in the scaling of the isosceles triangle."
	visible = @trapshape == "isosceles"  && (@traptype == "lines & points")
endparam
param leafAlength
	caption = "Leaf 1 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '3-asterisk', '4-asterisk', etc., \
		then this setting adjusts the length of the 1st leaflet."
	visible = ((@trapshape == "3-asterisk") || (@trapshape == "4-asterisk") || \
		(@trapshape == "5-asterisk") || (@trapshape == "6-asterisk") || (@trapshape == "7-asterisk") || \
		(@trapshape == "8-asterisk")|| (@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafBlength
	caption = "Leaf 2 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '3-asterisk', '4-asterisk', etc., \
		then this setting adjusts the length of the 2nd leaflet."
	visible = ((@trapshape == "3-asterisk") || (@trapshape == "4-asterisk") || \
		(@trapshape == "5-asterisk") || (@trapshape == "6-asterisk") || (@trapshape == "7-asterisk") || \
		(@trapshape == "8-asterisk")|| (@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafClength
	caption = "Leaf 3 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '3-asterisk', '4-asterisk', etc., \
		then this setting adjusts the length of the 3rd leaflet."
	visible = ((@trapshape == "3-asterisk") || (@trapshape == "4-asterisk") || \
		(@trapshape == "5-asterisk") || (@trapshape == "6-asterisk") || (@trapshape == "7-asterisk") || \
		(@trapshape == "8-asterisk")|| (@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafDlength
	caption = "Leaf 4 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '4-asterisk', '5-asterisk', etc., \
		then this setting adjusts the length of the 4th leaflet."
	visible = ((@trapshape == "4-asterisk") || \
		(@trapshape == "5-asterisk") || (@trapshape == "6-asterisk") || (@trapshape == "7-asterisk") || \
		(@trapshape == "8-asterisk")|| (@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafElength
	caption = "Leaf 5 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '5-asterisk', '6-asterisk', etc., \
		then this setting adjusts the length of the 5th leaflet."
	visible = ((@trapshape == "5-asterisk") || (@trapshape == "6-asterisk") || (@trapshape == "7-asterisk") || \
		(@trapshape == "8-asterisk")|| (@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafFlength
	caption = "Leaf 6 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '6-asterisk', '7-asterisk', etc., \
		then this setting adjusts the length of the 6th leaflet."
	visible = ((@trapshape == "6-asterisk") || (@trapshape == "7-asterisk") || \
		(@trapshape == "8-asterisk")|| (@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafGlength
	caption = "Leaf 7 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '7-asterisk', etc., \
		then this setting adjusts the length of the 7th leaflet."
	visible = ((@trapshape == "7-asterisk") || \
		(@trapshape == "8-asterisk")|| (@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafHlength
	caption = "Leaf 8 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '8-asterisk', etc., \
		then this setting adjusts the length of the 8th leaflet."
	visible = ((@trapshape == "8-asterisk")|| (@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafIlength
	caption = "Leaf 9 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '9-asterisk', etc., \
		then this setting adjusts the length of the 9th leaflet."
	visible = ((@trapshape == "9-asterisk") || (@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafJlength
	caption = "Leaf 10 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to '10-asterisk', etc., \
		then this setting adjusts the length of the 10th leaflet."
	visible = ((@trapshape == "10-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafKlength
	caption = "Leaf 11 Length"
	default = 1.0
	hint = "If the trap shape is set to '11-asterisk', etc., \
		then this setting adjusts the length of the 11th leaflet."
	visible = ((@trapshape == "more polygons" && @morepolygons1 == "11-asterisk") || \
		(@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param leafLlength
	caption = "Leaf 12 Length"
	default = 1.0
	hint = "If the trap shape is set to '12-asterisk', \
		then this setting adjusts the length of the 12th leaflet."
	visible = ((@trapshape == "more polygons" && @morepolygons1 == "12-asterisk"))  && (@traptype == "lines & points")
endparam
param starspikiness
	caption = "Star Spikiness"
	default = 0.75
	hint = "If parameter 'Trap Shape' is set to '3-star', '4-star', etc., \
		then this setting determines the length of the star points."
	visible = ((@trapshape == "3-star") || (@trapshape == "4-star") || \
		(@trapshape == "5-star") || (@trapshape == "6-star") || (@trapshape == "7-star") || (@trapshape == "8-star") \
		|| (@trapshape == "9-star") || (@trapshape == "10-star") || (@trapshape == "more polygons" && @morepolygons1 == "11-star") \
		|| (@trapshape == "more polygons" && @morepolygons1 == "12-star"))  && (@traptype == "lines & points")
endparam
param innerscale
	caption = "Inner Scale"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to one of the 'nested' options, \
		then this setting adjusts the size of the inner polygon."
	visible = ((@trapshape == "nested triangles") || (@trapshape == "nested \
		triangle 2") || (@trapshape == "nested squares") || (@trapshape == \
		"nested square 2") || (@trapshape == "nested pentagons") || \
		(@trapshape == "nested pentagon 2") || (@trapshape == "nested \
		hexagons") || (@trapshape == "nested heptagons") || (@trapshape == "nested heptagon 2") || \
		(@trapshape == "nested hexagon 2"))  && (@traptype == "lines & points")
endparam
param rhombheight
	caption = "Rhombus Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'rhombus', then this setting \
		determines its relative height."
	visible =(@trapshape == "rhombus")  && (@traptype == "lines & points")
endparam
param rhombwidth
	caption = "Rhombus Width"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'rhombus', then this setting \
		determines its relative height."
	visible = (@trapshape == "rhombus")  && (@traptype == "lines & points")
endparam
param kiteheight
	caption = "Kite Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'kite', then this setting \
		determines its relative height."
	visible = (@trapshape == "kite")  && (@traptype == "lines & points")
endparam
param kitewidth
	caption = "Kite Width"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'kite', then this setting \
		determines its relative height."
	visible = (@trapshape == "kite")  && (@traptype == "lines & points")
endparam
param dartheight
	caption = "Dart Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'dart', then this setting \
		determines its relative height."
	visible = (@trapshape == "dart")  && (@traptype == "lines & points")
endparam
param dartwidth
	caption = "Dart Width"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'dart', then this setting \
		determines its relative height."
	visible = (@trapshape == "dart")  && (@traptype == "lines & points")
endparam
param rectlength
	caption = "Rectangle Length"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'rectangle', then this setting \
		determines its relative length."
	visible = @trapshape == "rectangle"  && (@traptype == "lines & points")
endparam
param rectwidth
	caption = "Rectangle Width"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'rectangle', then this setting \
		determines its relative width."
	visible = @trapshape == "rectangle"  && (@traptype == "lines & points")
endparam
param flat4height
	caption = "Flat Star Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'flat 4-star', then this setting \
		determines its relative height."
	visible = (@trapshape == "flat 4-star")  && (@traptype == "lines & points")
endparam
param flat4width
	caption = "Flat Star Width"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'flat 4-star', then this setting \
		determines its relative height."
	visible = (@trapshape == "flat 4-star")  && (@traptype == "lines & points")
endparam
param finger1length
	caption = "Finger 1 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'hand', \
		then this setting adjusts the length of the 1st finger."
	visible = (@trapshape == "hand")  && (@traptype == "lines & points")
endparam
param finger2length
	caption = "Finger 2 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'hand', \
		then this setting adjusts the length of the 2nd finger."
	visible = (@trapshape == "hand" )  && (@traptype == "lines & points")
endparam
param finger3length
	caption = "Finger 3 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'hand', \
		then this setting adjusts the length of the 3rd finger."
	visible = (@trapshape == "hand")  && (@traptype == "lines & points")
endparam
param finger4length
	caption = "Finger 4 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'hand', \
		then this setting adjusts the length of the 4th finger."
	visible = (@trapshape == "hand")  && (@traptype == "lines & points")
endparam
param finger5length
	caption = "Finger 5 Length"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'hand', \
		then this setting adjusts the length of the 5th finger."
	visible = (@trapshape == "hand")  && (@traptype == "lines & points")
endparam
param sawheight
	caption = "Sawtooth Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to a 'sawtooth' option, \
		then this setting adjusts the relative height of the wave."
	visible = ((@trapshape == "sawtooth-1") || (@trapshape == "sawtooth-2") \
		|| (@trapshape == "sawtooth-3") || (@trapshape == "sawtooth-4"))  && (@traptype == "lines & points")
endparam
param windheight
	caption = "Windblade Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'Windmill', then this setting \
		adjusts the height of one of the windmill blades."
	visible = ((@trapshape == "windmill") || (@trapshape == "windmill 2"))  && (@traptype == "lines & points")
endparam
param windwidth
	caption = "Windblade Width"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'Windmill', then this setting \
		adjusts the width of one of the windmill blades."
	visible = ((@trapshape == "windmill") || (@trapshape == "windmill 2"))  && (@traptype == "lines & points")
endparam
param sqrheight
	caption = "Squarewave Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'square-1' etc, then this setting \
		adjusts the height of the square wave."
	visible = ((@trapshape == "square-1") || (@trapshape == "square-2") || (@trapshape == "square-3") \
			|| (@trapshape == "square-4"))  && (@traptype == "lines & points")
endparam
param sqrwidth
	caption = "Squarewave Width"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'square-1' etc, then this setting \
		adjusts the width of the square wave."
	visible = ((@trapshape == "square-1") || (@trapshape == "square-2") || \
			(@trapshape == "square-3") || (@trapshape == "square-4"))  && (@traptype == "lines & points")
endparam
param unityroot1
	caption = "How Many Roots?"
	default = 5
	min = 1
	max = 16
	hint = "If parameter 'Trap Shape' is set to 'roots of unity', \
		then this setting determines which set of roots to use (1-16)."
	visible = @trapshape == "roots of unity"  && (@traptype == "lines & points")
endparam
param singleroot1
	caption = "Single Root?"
	default = FALSE
	hint = "If parameter 'Trap Shape' is set to 'roots of unity', \
		enabling this setting allows the use of just one of the roots \
		 as the trap, instead of using the entire set of roots."
	visible = @trapshape == "roots of unity"  && (@traptype == "lines & points")
endparam
param whichroot1
	caption = "Which Root?"
	default = 1
	min = 1
	max = 16
	hint = "If parameter 'Trap Shape' is set to 'roots of unity' and \
		 'Single Root' is enabled, then this setting determines which root to use \
		 (1-up to the max set by param 'How Many Roots')."
	visible = (@trapshape == "roots of unity" && @singleroot1)  && (@traptype == "lines & points")
endparam
param collinearspot1
	caption = "How Many Spots?"
	default = 4
	min = 1
	max = 16
	hint = "If parameter 'Trap Shape' is set to 'collinear spots', \
		then this setting determines the number of points to use (1-16)."
	visible = @trapshape == "collinear spots"  && (@traptype == "lines & points")
endparam
param squarespot1
	caption = "Array Size?"
	default = 4
	min = 2
	max = 6
	hint = "If parameter 'Trap Shape' is set to 'square array', \
		then this setting determines the array size (2-6)."
	visible = @trapshape == "square array"  && (@traptype == "lines & points")
endparam
param triarray1
	caption = "Array Order?"
	default = 2
	min = 2
	max = 4
	hint = "If parameter 'Trap Shape' is set to 'triangular array', pentagonal array' etc. \
		then this setting determines the array size (2-4)."
	visible = (@trapshape == "triangular array" || @trapshape == "pentagonal array" || \
			@trapshape == "hexagonal array")  && (@traptype == "lines & points")
endparam
param raynumber
	caption = "Number of Rays?"
	default = 3
	min = 3
	max = 16
	hint = "If parameter 'Trap Shape' is set to 'dotted star' or 'dashed star' \
		then this setting determines the number of star 'points' (3-16)."
	visible = (@traptype == "lines & points"  && ((@trapshape == "dashed star" \
		|| @trapshape == "dotted star")))
endparam
param dotnumber
	caption = "Number of Dots?"
	default = 3
	min = 2
	max = 5
	hint = "If parameter 'Trap Shape' is set to 'dotted star' \
		then this setting determines the number of dots in each star ray (2-5)."
	visible = @traptype == "lines & points" && @trapshape == "dotted star"
endparam
param dashnumber
	caption = "Number of Dashes?"
	default = 2
	min = 2
	max = 4
	hint = "If parameter 'Trap Shape' is set to 'dashed star' \
		then this setting determines the number of dashes in each star ray (2-4)."
	visible = @traptype == "lines & points" && @trapshape == "dashed star"
endparam
param spiralorder1
	caption = "Spiral Order?"
	default = 2
	min = 1
	max = 4
	hint = "If parameter 'Trap Shape' is set to 'triangular spiral', 'square spiral', etc. \
		then this setting determines the number of spiral windings (1-4)."
	visible = (@trapshape == "triangular spiral" || @trapshape == "square spiral" || \
		@trapshape == "pentagonal spiral" || @trapshape == "hexagonal spiral" || \
				@trapshape == "octagonal spiral")  && (@traptype == "lines & points")
endparam
param ellipseexponent1
	caption = "SE1 Exponent"
	default = 2.5
	hint = "If parameter 'Trap Shape' is set to 'superellipse', then this parameter \
		determines the exponent used for the trap."
	visible = (@trapshape == "superellipse")  && (@traptype == "lines & points")
endparam
param ellipseheight1
	caption = "SE1 Height"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'superellipse', then this setting \
		adjusts the height of the trap."
	visible = (@trapshape == "superellipse")  && (@traptype == "lines & points")
endparam
param ellipsewidth1
	caption = "SE1 Width"
	default = 0.6
	hint = "If parameter 'Trap Shape' is set to 'superellipse', then this setting \
		adjusts the width of the trap."
	visible = (@trapshape == "superellipse")  && (@traptype == "lines & points")
endparam
param hypotrochA1
	caption = "Hypotro1 RadA"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'hypotrochoid' or 'epitrochoid', then this parameter \
		is the radius of the fixed circle."
	visible = ((@trapshape == "hypotrochoid") || (@trapshape == "epitrochoid"))  && (@traptype == "lines & points")
endparam
param hypotrochB1
	caption = "Hypotro1 RadB"
	default = 0.25
	hint = "If parameter 'Trap Shape' is set to 'hypotrochoid' or 'epitrochoid', then this parameter \
		is the radius of the rolling circle.  Try RadA/RadB a rational number."
	visible = ((@trapshape == "hypotrochoid") || (@trapshape == "epitrochoid"))  && (@traptype == "lines & points")
endparam
param hypotrochH1
	caption = "Hypotro1 DistH"
	default = 1.25
	hint = "If parameter 'Trap Shape' is set to 'hypotrochoid' or 'epitrochoid', then this parameter \
		is the distance of the point from the rolling circle center."
	visible = ((@trapshape == "hypotrochoid") || (@trapshape == "epitrochoid"))  && (@traptype == "lines & points")
endparam
param cycloidamp1
	caption = "Cycloid 1 Amplitude"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cycloid', then this parameter \
		fixes the amplitude."
	visible = (@traptype == "lines & points" && \
		((@trapshape == "more curves" && @morecurves1 == "cycloid")))  && (@traptype == "lines & points")
endparam
param cycloidconst1
	caption = "Cycloid 1 Constant"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cycloid', then this parameter \
		distorts the shape."
	visible = (@traptype == "lines & points" && \
		((@trapshape == "more curves" && @morecurves1 == "cycloid")))  && (@traptype == "lines & points")
endparam
param cycloidlength1
	caption = "Cycloid 1 Length"
	default = 2.0
	min = 0.5
	max = 6
	hint = "If parameter 'Trap Shape' is set to 'cycloid', then this parameter \
		sets the number of cycles plotted, in units of 2 pi."
	visible = (@traptype == "lines & points" && \
		((@trapshape == "more curves" && @morecurves1 == "cycloid")))  && (@traptype == "lines & points")
endparam
param grain
	caption = "Curve Granularity"
	enum = "36" "72" "100" "200" "300" "400"
	default = 1
	hint = "Increasing this number results in smoother curves, but slower execution."
	visible = ((@traptype == "lines & points" && ( \
		@trapshape == "hypotrochoid" || @trapshape == "epitrochoid" || \
		@trapshape == "superellipse" || @trapshape == "lissajous 3" || \
		(@trapshape == "more curves" && \
		(@morecurves1 == "rhodonea" || @morecurves1 == "cycloid" || \
		@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 ==  "Moritz cyclic harmonic" || @morecurves1 == "elliptic lissajous" || \
		@morecurves1 == "bipolar lissajous")))))
endparam
param lissaamp1
	caption = "Lissa1 Amplitude"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'lissajous 3', then this parameter \
		is the amplitude of the first cosine function."
	visible = (@trapshape == "lissajous 3")|| \
		(@trapshape == "more curves" && \
		(@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 == "elliptic lissajous" || @morecurves1 == "bipolar lissajous"))  && (@traptype == "lines & points")
endparam
param lissafreq1
	caption = "Lissa1 Frequency"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'lissajous 3', then this parameter \
		is the frequency of the first cosine function."
	visible = (@trapshape == "lissajous 3")|| \
		(@trapshape == "more curves" && \
		(@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 == "elliptic lissajous" || @morecurves1 == "bipolar lissajous"))  && (@traptype == "lines & points")
endparam
param lissaphase1
	caption = "Lissa1 Phase"
	default = 0.0
	hint = "If parameter 'Trap Shape' is set to 'lissajous 3', then this parameter \
		is the phase of the first cosine function."
	visible = (@trapshape == "lissajous 3")|| \
		(@trapshape == "more curves" && \
		(@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 == "elliptic lissajous" || @morecurves1 == "bipolar lissajous"))  && (@traptype == "lines & points")
endparam
param lissaamp2
	caption = "Lissa2 Amplitude"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'lissajous 3', then this parameter \
		is the amplitude of the first cosine function."
	visible = (@trapshape == "lissajous 3")|| \
		(@trapshape == "more curves" && \
		(@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 == "elliptic lissajous" || @morecurves1 == "bipolar lissajous"))  && (@traptype == "lines & points")
endparam
param lissafreq2
	caption = "Lissa2 Frequency"
	default = 4.0
	hint = "If parameter 'Trap Shape' is set to 'lissajous 3', then this parameter \
		is the frequency of the first cosine function."
	visible = (@trapshape == "lissajous 3")|| \
		(@trapshape == "more curves" && \
		(@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 == "elliptic lissajous" || @morecurves1 == "bipolar lissajous"))  && (@traptype == "lines & points")
endparam
param lissaphase2
	caption = "Lissa2 Phase"
	default = 0.52359877559829887307710723054658 ; pi/6
	hint = "If parameter 'Trap Shape' is set to 'lissajous 3', then this parameter \
		is the phase of the first cosine function."
	visible = (@trapshape == "lissajous 3")|| \
		(@trapshape == "more curves" && \
		(@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 == "elliptic lissajous" || @morecurves1 == "bipolar lissajous"))  && (@traptype == "lines & points")
endparam
param lissadomain
	caption = "Lissa Domain"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'lissajous 3', then this parameter \
		is the domain of the cosine functions, in multiples of pi."
	visible = (@trapshape == "lissajous 3")|| \
		(@trapshape == "more curves" && \
		(@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 == "elliptic lissajous" || @morecurves1 == "bipolar lissajous"))  && (@traptype == "lines & points")
endparam
param lissaopen
	caption = "Open Lissajous?"
	default = FALSE
	hint = "If parameter 'Trap Shape' is set to 'lissajous 3', then enabling this parameter \
		leaves the ends of the lissajous curve unconnected."
	visible = (@trapshape == "lissajous 3")|| \
		(@trapshape == "more curves" && \
		(@morecurves1 == "parabolic lissajous" || @morecurves1 == "polar lissajous" || \
		@morecurves1 == "elliptic lissajous" || @morecurves1 == "bipolar lissajous"))  && (@traptype == "lines & points")
endparam
param moritzamp1
	caption = "Moritz 1 Amplitude"
	default = 0.75
	hint = "If parameter 'Trap Shape' is set to 'Moritz cyclic harmonic', \
		then this parameter is the amplitude of the cosine function."
	visible = (@traptype == "lines & points" && (@trapshape == "more curves" \
		&& @morecurves1 == "Moritz cyclic harmonic"))  && (@traptype == "lines & points")
endparam
param moritzfreqN1
	caption = "Moritz 1 Numerator"
	default = 3.0
	hint = "If parameter 'Trap Shape' is set to 'Moritz cyclic harmonic', \
		then this parameter is the numerator of the frequency of the cosine function."
	visible = (@traptype == "lines & points" && (@trapshape == "more curves" \
		&& @morecurves1 == "Moritz cyclic harmonic"))  && (@traptype == "lines & points")
endparam
param moritzfreqD1
	caption = "Moritz 1 Denominator"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'Moritz cyclic harmonic', \
		then this parameter is the denominator of the frequency of the cosine function."
	visible = (@traptype == "lines & points" && (@trapshape == "more curves" \
		&& @morecurves1 == "Moritz cyclic harmonic"))  && (@traptype == "lines & points")
endparam
param moritzconst1
	caption = "Moritz 1 Constant"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'Moritz cyclic harmonic', \
		then this parameter functions as an additional shape modulator."
	visible = (@traptype == "lines & points" && (@trapshape == "more curves" \
		&& @morecurves1 == "Moritz cyclic harmonic"))  && (@traptype == "lines & points")
endparam
param circlenum1
	caption = "Circle #"
	default = 2
	min = 2
	max = 4
	hint = "If 'Trap Shape' is set to 'nested circles' or 'osculant circles', then this setting fixes the number of circles (2-4)."
	visible = ((@trapshape == "nested circles") || (@trapshape == "osculant circles"))  && (@traptype == "lines & points")
endparam
param rose1
	caption = "Rose Petals"
	default = 3
	min = 2
	hint = "If parameter 'Trap Shape' is set to 'rose', then this setting \
		determines the number of petals."
	visible = @traptype == "polar functions" && @polarshape1 == "rose" 
endparam
param folium1
	caption = "Folium Shaper"
	default = 0.5
	hint = "If parameter 'Trap Shape' is set to 'folium', then this setting \
		determines the particular shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "folium") 
endparam
param foliumperturb1
	caption = "Folium Perturb"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'folium', then this setting \
		determines the particular shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "folium")
endparam
param cardioid1
	caption = "Cardioid Shaper"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cardioid', then this setting \
		determines the particular shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "cardioid") 
endparam
param cardioidperturb1
	caption = "Cardioid Perturb"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cardioid', then this setting \
		determines the particular shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "cardioid") 
endparam
param cissoidDioA1
	caption = "Cissoid Sine Freq"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cissoid of Diocles', then this setting \
		determines the particular shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "cissoid of Diocles") 
endparam
param cissoidDioB1
	caption = "Cissoid Tangent Freq"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cissoid of Diocles', then this setting \
		determines the particular shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "cissoid of Diocles") 
endparam
param cochleoid1
	caption = "Cochleoid Sine Freq"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cochleoid', then this setting \
		determines the particular shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "cochleoid") 
endparam
param conchoidA1
	caption = "Conchoid Constant"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'conchoid of Nicomedes' or 'conchoid of De Sluze', \
		then this setting determines the particular shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "conchoid of Nicomedes" || \
		@polarshape1 == "conchoid of De Sluze") 
endparam
param conchoidB1
	caption = "Conchoid Cos Freq"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'conchoid of Nicomedes' or 'conchoid of De Sluze', \
		then this setting determines the cosine function."
	visible = (@traptype == "polar functions") && (@polarshape1 == "conchoid of Nicomedes" || \
		@polarshape1 == "conchoid of De Sluze") 
endparam
param conchoidC1
	caption = "Conchoid Numerator"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'conchoid of Nicomedes' or 'conchoid of De Sluze', \
		then this setting is the numerator of the cosine term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "conchoid of Nicomedes" || \
		@polarshape1 == "conchoid of De Sluze") 
endparam
param cubicpA1
	caption = "Cubic Tan Freq"
	default = 0.1
	hint = "If parameter 'Trap Shape' is set to 'cubical parabola', \
		then this setting is the frequency of the tangent term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "cubical parabola") 
endparam
param cubicpB1
	caption = "Cubic Cos Freq"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cubical parabola', \
		then this setting is the frequency of the cosine term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "cubical parabola") 
endparam
param cubicpC1
	caption = "Cubic Numerator"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'cubical parabola', \
		then this constant is the numerator of the cosine term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "cubical parabola") 
endparam
param majaxis1
	caption = "Major Axis"
	default = 1.5
	hint = "If parameter 'Trap Shape' is set to 'ellipse', \
		then this setting is the length of the major axis."
	visible = (@traptype == "polar functions") && (@polarshape1 == "ellipse") 
endparam
param minaxis1
	caption = "Minor Axis"
	default = 0.9
	hint = "If parameter 'Trap Shape' is set to 'ellipse', \
		then this setting is the length of the minor axis."
	visible = (@traptype == "polar functions") && (@polarshape1 == "ellipse") 
endparam
param epower1
	caption = "Ellipse Exponent"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'ellipse', \
		then this setting is the exponent.  Ellipse = 2, superellipse > 2, \
		subellipse 1< exp <2, astroid < 1."
	visible = (@traptype == "polar functions") && (@polarshape1 == "ellipse") 
endparam
param tanfreq1
	caption = "Tangent Freq"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'ellipse', \
		then this setting is the frequency of the tangent term. \
		Try integers for star-like shapes."
	visible = (@traptype == "polar functions") && (@polarshape1 == "ellipse") 
endparam
param fosinfreq1
	caption = "Sine 1 Freq 1"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'folium of Descartes', \
		then this setting is the frequency of the sine term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "folium of Descartes") 
endparam
param focosfreq1
	caption = "Cos 1 Freq"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'folium of Descartes', \
		then this setting is the frequency of the cosine term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "folium of Descartes") 
endparam
param sinfreq21
	caption = "Sine 1 Freq 2"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'folium of Descartes', \
		then this setting modulates the frequency of the numerator sine term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "folium of Descartes") 
endparam
param hyperbolic1
	caption = "Hyperbolic Spiral Adjustment"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'hyperbolic spiral', then this parameter modifies \
		the curve shape."
	visible = (@traptype == "polar functions") && (@polarshape1 == "hyperbolic spiral") 
endparam
param kampfreq1
	caption = "Kampyle Frequency"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'kampyle of Eudoxus', \
		then this setting modulates the cosine term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "kampyle of Eudoxus") 
endparam
param kamppower1
	caption = "Kampyle Power"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'kampyle of Eudoxus', \
		then this setting is the exponent of the cosine term."
	visible = (@traptype == "polar functions") && (@polarshape1 == "kampyle of Eudoxus") 
endparam
param nodalfreq1
	caption = "Tangent Frequency"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'kappa', \
		then this setting modulates the frequency of the nodal curve. \
		1.0 corresponds to the kappa curve."
	visible = (@traptype == "polar functions") && (@polarshape1 == "kappa") 
endparam
param lemfreq1
	caption = "Cosine Frequency"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'lemniscate of Bernoulli', \
		then this setting modulates the cosine term.  2.0 corresponds to the lemniscate."
	visible = (@traptype == "polar functions") && (@polarshape1 == "lemniscate of Bernoulli") 
endparam
param lempower1
	caption = "Lemniscate Power"
	default = 0.5
	hint = "If parameter 'Trap Shape' is set to 'lemniscate of Bernoulli', \
		then this setting is the exponent of the cosine term.  0.5 corresponds to the lemniscate."
	visible = (@traptype == "polar functions") && (@polarshape1 == "lemniscate of Bernoulli") 
endparam
param limfreq1
	caption = "Sine Frequency"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'limacon of Pascal', \
		then this setting modulates the sine term.  1.0 corresponds to the limacon."
	visible = (@traptype == "polar functions") && (@polarshape1 == "limacon of Pascal") 
endparam
param limamp1
	caption = "Sine Amplitude"
	default = 0.6666666666666667
	hint = "If parameter 'Trap Shape' is set to 'limacon of Pascal', \
		then this setting is the amplitude of the sine term.  2/3 corresponds to the limacon."
	visible = (@traptype == "polar functions") && (@polarshape1 == "limacon of Pascal") 
endparam
param limoffset1
	caption = "Limacon Offset"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'limacon of Pascal', \
		then this setting is the offset of the sine term.  1.0 corresponds to the limacon."
	visible = (@traptype == "polar functions") && (@polarshape1 == "limacon of Pascal") 
endparam
param litpower1
	caption = "Lituus Power"
	default = 0.5
	hint = "If parameter 'Trap Shape' is set to 'lituus', \
		then this setting is the exponent that is used.  0.5 corresponds to the lituus."
	visible = (@traptype == "polar functions") && (@polarshape1 == "lituus" || @polarshape1 == "lituus 2") 
endparam
param logspiA1
	caption = "Log Spiral Adjustment"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'logarithmic spiral', \
		then this setting adjusts the winding."
	visible = (@traptype == "polar functions") && (@polarshape1 == "logarithmic spiral") 
endparam
param logspiB1
	caption = "Log Spiral Winding"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'logarithmic spiral', \
		then this setting adjusts the tightness of the winding.  Smaller numbers \
		result in a tighter spiral."
	visible = (@traptype == "polar functions") && (@polarshape1 == "logarithmic spiral") 
endparam
param parafreq1
	caption = "Cos Frequency"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'parabola', \
		then this setting modulates the cosine term.  1.0 corresponds to the parabola."
	visible = (@traptype == "polar functions") && (@polarshape1 == "parabola") 
endparam
param paraamp1
	caption = "Cos Amplitude"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'parabola', \
		then this setting is the amplitude of the cosine term.  1.0 corresponds to the parabola. \
		0.0 = circle, 0-1 = ellipse, 2 = hyperbola."
	visible = (@traptype == "polar functions") && (@polarshape1 == "parabola") 
endparam
param paraoffset1
	caption = "Parabola Offset"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'parabola', \
		then this setting is the offset of the cosine term.  1.0 corresponds to the parabola."
	visible = (@traptype == "polar functions") && (@polarshape1 == "parabola") 
endparam
param paraspi1
	caption = "Parabolic Spiral Power"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'parabolic spiral', \
		then this setting is the exponent.  2.0 corresponds to the parabolic spiral."
	visible = (@traptype == "polar functions") && (@polarshape1 == "parabolic spiral")  
endparam
param paraspioffset1
	caption = "Parabolic Spiral Coefficient"
	default = 8.0
	hint = "If parameter 'Trap Shape' is set to 'parabolic spiral', \
		then this setting afjusts the spiral tightness."
	visible = (@traptype == "polar functions") && (@polarshape1 == "parabolic spiral") 
endparam
param semicubtanfreq1
	caption = "Semicubic Tan Frequency"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'semicubical parabola', \
		then this setting is the frequency of  the tangent term.  1.0 corresponds to the \
		semicubic parabola."
	visible = (@traptype == "polar functions") && (@polarshape1 == "semicubical parabola") 
endparam
param semicubcosfreq1
	caption = "Semicubic Cos Frequency"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'semicubical parabola', \
		then this setting is the frequency of  the cosine term.  1.0 corresponds to the \
		semicubic parabola."
	visible = (@traptype == "polar functions") && (@polarshape1 == "semicubical parabola") 
endparam
param semicubpower1
	caption = "Semicubic Power"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'semicubical parabola', \
		then this setting is the exponent of  the tangent term.  2.0 corresponds to the \
		semicubic parabola."
	visible = (@traptype == "polar functions") && (@polarshape1 == "semicubical parabola")
endparam
param archspioffset1
	caption = "Archimedes Spiral Adjustment"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'spiral of Archimedes', \
		then this setting affects the tightness of the winding."
	visible = (@traptype == "polar functions") && (@polarshape1 == "spiral of Archimedes") 
endparam
param strophcosfreqA1
	caption = "Strophoid 1st Cos Frequency"
	default = 2.0
	hint = "If parameter 'Trap Shape' is set to 'strophoid', \
		then this setting is the frequency of the 1st (numerator) cosine term.  \
		2.0 corresponds to the strophoid."
	visible = (@traptype == "polar functions") && (@polarshape1 == "strophoid") 
endparam
param strophcosfreqB1
	caption = "Strophoid 2nd Cos Frequency"
	default = 1.0
	hint = "If parameter 'Trap Shape' is set to 'strophoid', \
		then this setting is the frequency of the 2nd (denominator) cosine term.  \
		1.0 corresponds to the strophoid."
	visible = (@traptype == "polar functions") && (@polarshape1 == "strophoid") 
endparam
param polarfreqA1
	caption = "Polar Frequency A"
	default = 1.0
	hint = "If 'Trap Type' is set to 'polar functions', some of the curves use this \
		parameter as the frequency."
	visible =  @traptype == "polar functions" && \
		(@polarshape1 == "Cayley's sextic" || @polarshape1 == "Cayley's sextic 2" || \
			@polarshape1 == "hippopede")
endparam
param polarampA1
	caption = "Polar Amplitude A"
	default = 1.0
	hint = "If 'Trap Type' is set to 'polar functions', some of the curves use this \
		parameter as the amplitude."
	visible =  @traptype == "polar functions" && \
		(@polarshape1 == "Cayley's sextic" || \
			@polarshape1 == "hippopede")
endparam
param trefoilcosamp1
	caption = "Trefoil Cos Amplitude"
	default = 1.0
	hint = "If 'Trap Type' is set to 'trefoil of Habenicht', this \
		parameter sets the amplitude of the cosine term."
	visible =  @traptype == "polar functions" && \
		(@polarshape1 == "trefoil of Habenicht")
endparam
param trefoilsinamp1
	caption = "Trefoil Sine Amplitude"
	default = 1.0
	hint = "If 'Trap Type' is set to 'trefoil of Habenicht', this \
		parameter sets the amplitude of the cosine term."
	visible =  @traptype == "polar functions" && \
		(@polarshape1 == "trefoil of Habenicht")
endparam
param trefoilcossymmetry1
	caption = "Trefoil Cos Symmetry"
	default = 3.0
	hint = "If 'Trap Type' is set to 'trefoil of Habenicht', this \
		parameter sets the symmetry of the cosine term."
	visible =  @traptype == "polar functions" && \
		(@polarshape1 == "trefoil of Habenicht")
endparam
param trefoilsinsymmetry1
	caption = "Trefoil Sine Symmetry"
	default = 3.0
	hint = "If 'Trap Type' is set to 'trefoil of Habenicht', this \
		parameter sets the symmetry of the sine term."
	visible =  @traptype == "polar functions" && \
		(@polarshape1 == "trefoil of Habenicht")
endparam
param trefoilconstant1
	caption = "Trefoil Constant"
	default = 1.0
	hint = "If 'Trap Type' is set to 'trefoil of Habenicht', this \
		parameter affects the scale of the curve."
	visible =  @traptype == "polar functions" && \
		(@polarshape1 == "trefoil of Habenicht")
endparam
param trilimA1
	caption = "Trisectrix Multiplier"
	default = 2.0
	hint = "If 'Trap Type' is set to 'trisectrix limacon', this factor scales the entire equation."
	visible =  @traptype == "polar functions" && @polarshape1 == "trisectrix limacon"
endparam
param trilimB1
	caption = "Trisectrix Constant"
	default = 1.0
	hint = "If 'Trap Type' is set to 'trisectrix limacon', this value is added to the cosine term."
	visible =  @traptype == "polar functions" && @polarshape1 == "trisectrix limacon"
endparam
param trilimamp1
	caption = "Trisectrix Amplitude"
	default = 2.0
	hint = "If 'Trap Type' is set to 'trisectrix limacon', this value is the cosine amplitude."
	visible =  @traptype == "polar functions" && @polarshape1 == "trisectrix limacon"
endparam
param trilimfreq1
	caption = "Trisectrix Frequency"
	default = 1.0
	hint = "If 'Trap Type' is set to 'trisectrix limacon', this value is the cosine frequency."
	visible =  @traptype == "polar functions" && @polarshape1 == "trisectrix limacon"
endparam
param folioidamp1
	caption = "Folioid Amplitude"
	default = 2.2
	hint = "If 'Trap Type' is set to 'polar functions' and 'Trap Shape' \
		is 'folioid', then this parameter fixes the amplitude of the cosine term."
	visible =  (@traptype == "polar functions" && @polarshape1 == "folioid" \
		&& @polarmode1 == "normal")
endparam
param folioidfreqN1
	caption = "Folioid Numerator"
	default = 3.0
	hint = "If 'Trap Type' is set to 'polar functions' and 'Trap Shape' \
		is 'folioid', then this parameter fixes the numerator of the frequency of the cosine term."
	visible =  (@traptype == "polar functions" && @polarshape1 == "folioid")
endparam
param folioidfreqD1
	caption = "Folioid Denominator"
	default = 1.0
	hint = "If 'Trap Type' is set to 'polar functions' and 'Trap Shape' \
		is 'folioid', then this parameter fixes the denominator of the frequency of the cosine term."
	visible =  (@traptype == "polar functions" && @polarshape1 == "folioid")
endparam
param folioidconstA1
	caption = "Folioid Const A"
	default = 1.5
	hint = "If 'Trap Type' is set to 'polar functions' and 'Trap Shape' \
		is 'folioid', then this parameter is the first of two shaping terms."
	visible =  (@traptype == "polar functions" && @polarshape1 == "folioid" \
		&& @polarmode1 == "implicit")
endparam
param folioidconstB1
	caption = "Folioid Const B"
	default = 1.5
	hint = "If 'Trap Type' is set to 'polar functions' and 'Trap Shape' \
		is 'folioid', then this parameter is the second of two shaping terms."
	visible =  (@traptype == "polar functions" && @polarshape1 == "folioid" \
		&& @polarmode1 == "implicit")
endparam
param hyponumerator1
	caption = "Hypocycloid Numerator"
	default = 1
	hint = "If 'Trap Shape' is set to 'hypocycloid', then this setting \
		determines the numerator of the shaping parameter.  In conjunction with \
		parameter 'Hypocycloid 1 Denominator', try simple fractions."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "hypocycloid"
endparam
param hypodenom1
	caption = "Hypocycloid Denominator"
	default = 3
	hint = "If 'Trap Shape' is set to 'hypocycloid', then this setting \
		determines the denominator of the shaping parameter.  In conjunction with \
		parameter 'Hypocycloid 1 Numerator', try simple fractions."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "hypocycloid"
endparam
param companC11
	caption = "Companion X-scale"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'companion of cycloid', then this setting \
		sets the scale of the x-coordinate."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "companion of cycloid"
endparam
param companC21
	caption = "Companion Y-offset"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'companion of cycloid', then this setting \
		sets the offset of the y-coordinate."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "companion of cycloid"
endparam
param companfreq1
	caption = "Companion Frequency"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'companion of cycloid', then this setting \
		is the frequency of the y-coordinate cosine."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "companion of cycloid"
endparam
param cycampA1
	caption = "Cycloid Sine Amplitude"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'cycloid', then this setting \
		is the amplitude of the x-coordinate sine function.  Ordinary cycloid:  a = 1, \
		prolate cycloid: a > 1, curtate cycloid: a < 1."
	visible =  @traptype == "parametric functions" && \
		((@parashape1 == "cycloid") || (@parashape1 == "cycloid variant"))
endparam
param cycampB1
	caption = "Cycloid Cos Amplitude"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'cycloid', then this setting \
		is the amplitude of the y-coordinate cosine function."
	visible =  @traptype == "parametric functions" && \
		((@parashape1 == "cycloid") || (@parashape1 == "cycloid variant"))
endparam
param cycxscale1
	caption = "Cycloid X-scale"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'cycloid', then this setting \
		is the coefficient of the x-coordinate angular term."
	visible =  @traptype == "parametric functions" && \
		((@parashape1 == "cycloid") || (@parashape1 == "cycloid variant"))
endparam
param cycyoffset1
	caption = "Cycloid Y-offset"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'cycloid', then this setting \
		is the constant term of the y-coordinate."
	visible =  @traptype == "parametric functions" && \
		((@parashape1 == "cycloid") || (@parashape1 == "cycloid variant"))
endparam
param cycsinfreq1
	caption = "Cycloid Sine Freq"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'cycloid', then this setting \
		is the frequency of the x-coordinate sine function."
	visible =  @traptype == "parametric functions" && \
		((@parashape1 == "cycloid") || (@parashape1 == "cycloid variant"))
endparam
param cyccosfreq1
	caption = "Cycloid Cos Freq"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'cycloid', then this setting \
		is the frequency of the y-coordinate cosine function."
	visible =  @traptype == "parametric functions" && \
		((@parashape1 == "cycloid") || (@parashape1 == "cycloid variant"))
endparam
param cycangle1
	caption = "Angle Coefficient"
	default = 4.0
	hint = "For some of the curves, this setting \
		stretches the angle to provide more waviness."
	visible =  @traptype == "parametric functions" && \
		((@parashape1 == "cycloid") || (@parashape1 == "cycloid variant"))
endparam
param epicycAN1
	caption = "Epicycloid A Numerator"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'epicycloid', then this setting \
		affects the amplitudes and frequencies of the trig functions."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "epicycloid"
endparam
param epicycAD1
	caption = "Epicycloid A Denominator"
	default = 4.0
	hint = "If 'Trap Shape' is set to 'epicycloid', then this setting \
		affects the amplitudes and frequencies of the trig functions."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "epicycloid"
endparam
param epicycB1
	caption = "Epicycloid B"
	default = 5.0
	hint = "If 'Trap Shape' is set to 'epicycloid', then this setting \
		affects the amplitudes of two of the trig functions."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "epicycloid"
endparam
param epicycC1
	caption = "Epicycloid C"
	default = 1.0
	hint = "If 'Trap Shape' is set to 'epicycloid', then this setting \
		adjusts the amplitudes and frequencies of the trig functions."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "epicycloid"
endparam
param nephsinfreq1
	caption = "Nephroid Sine Frequency"
	default = 3.0
	hint = "If 'Trap Shape' is set to 'nephroid', then this setting \
		adjusts the frequency of the sine function."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "nephroid"
endparam
param nephcosfreq1
	caption = "Nephroid Cos Frequency"
	default = 3.0
	hint = "If 'Trap Shape' is set to 'nephroid', then this setting \
		adjusts the frequency of the cosine function."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "nephroid"
endparam
param nephconstA1
	caption = "Nephroid Constant 1"
	default = 3.0
	hint = "If 'Trap Shape' is set to 'nephroid', then this setting \
		adjusts the amplitude of the sine function."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "nephroid"
endparam
param nephconstB1
	caption = "Nephroid Constant 2"
	default = 3.0
	hint = "If 'Trap Shape' is set to 'nephroid', then this setting \
		adjusts the amplitude of the cosine function."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "nephroid"
endparam
param parafreqA1
	caption = "Parametric Frequency 1"
	default = 1.0
	hint = "For some of the parametric functions, this term adjusts the frequency \
		of one of the trig functions."
	visible =  @traptype == "parametric functions" && \
		(@parashape1 == "hyperbola" || @parashape1 == "tractrix" || \
		@parashape1 == "serpentine" || @parashape1 ==  "witch of Agnesi" || \
		@parashape1 == "Abdank quadratrix" || @parashape1 == "cornoid")
endparam
param parafreqB1
	caption = "Parametric Frequency 2"
	default = 1.0
	hint = "For some of the parametric functions, this term adjusts the frequency \
		of one of the trig functions."
	visible =  @traptype == "parametric functions" && \
		(@parashape1 == "hyperbola" || @parashape1 == "tractrix" || \
		@parashape1 == "serpentine" || @parashape1 ==  "witch of Agnesi" || \
		@parashape1 == "Abdank quadratrix" || @parashape1 == "cornoid")
endparam
param paraconstA1
	caption = "Parametric Constant 1"
	default = 1.0
	hint = "For some of the parametric functions, this term modulates the shape \
		or amplitude of one of the trig functions."
	visible =  @traptype == "parametric functions" && \
		(@parashape1 == "hyperbola" || @parashape1 == "tractrix" || \
		@parashape1 == "serpentine" || @parashape1 ==  "witch of Agnesi" || \
		@parashape1 == "Abdank quadratrix")
endparam
param paraconstB1
	caption = "Parametric Constant 2"
	default = 1.0
	hint = "For some of the parametric functions, this term modulates the shape \
		or amplitude of one of the trig functions."
	visible =  @traptype == "parametric functions" && \
		(@parashape1 == "hyperbola" || @parashape1 == "tractrix" || \
		@parashape1 == "serpentine" || @parashape1 ==  "witch of Agnesi")
endparam
param wavysinfreq1
	caption = "Wave Frequency 1"
	default = 20.0
	hint = "If 'Trap Type' is 'parametric functions' and 'Trap Shape' is set to \
		'wavy circle', this term adjusts the frequency of the waviness."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "wavy circle"
endparam
param wavysinamp1
	caption = "Wave Amplitude 1"
	default = 0.1
	hint = "If 'Trap Type' is 'parametric functions' and 'Trap Shape' is set to \
		'wavy circle', this term adjusts the size of the waves."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "wavy circle"
endparam
param wavyradius1
	caption = "Circle Radius 1"
	default = 1.0
	hint = "If 'Trap Type' is 'parametric functions' and 'Trap Shape' is set to \
		'wavy circle', this term adjusts the size of the circle."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "wavy circle"
endparam
param paraxaxis1
	caption = "Ellipse X-axis"
	default = 1.0
	hint = "The parameter sets the semimajor axis of the ellipse."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "ellipse"
endparam
param parayaxis1
	caption = "Ellipse Y-axis"
	default = 0.5
	hint = "The parameter sets the semiminor axis of the ellipse."
	visible =  @traptype == "parametric functions" && \
		@parashape1 == "ellipse"
endparam
param epiradiusA1
	caption = "Base Circle Radius"
	default = 1.0
	hint = "The parameter sets the radius of the base circle defining the epicycloid \
		or epitrochoid."
	visible =  @traptype == "parametric functions" && \
		(@parashape1 == "epicycloid 2" || @parashape1 == "epitrochoid")
endparam
param epiradiusB1
	caption = "Rolling Circle Radius"
	default = 0.33333333333333333333
	hint = "The parameter sets the radius of the rolling circle defining the epicycloid \
		or epitrochoid."
	visible =  @traptype == "parametric functions" && \
		(@parashape1 == "epicycloid 2" || @parashape1 == "epitrochoid")
endparam
param epiradiusC1
	caption = "Rolling Point Distance"
	default = 0.66666666666666666667
	hint = "The parameter sets the distance of the moving point from the center of \
		the rolling circle defining the epitrochoid."
	visible =  @traptype == "parametric functions" && \
		(@parashape1 == "epitrochoid")
endparam
param cartxcoeff1
	caption = "X-coefficient"
	default = 1.0
	hint = "If 'Trap Type' is 'cartesian', then this shaping parameter \
		modifies the x-variable."
	visible =  @traptype == "cartesian" && \
		(@xyshape1 == "Alain's curve" || @xyshape1 == "arcs of Samothrace" || \
		@xyshape1 == "astroid" || @xyshape1 == "atriphthaloid" || \
		@xyshape1 == "bean curve 1" || @xyshape1 == "bean curve 2" || @xyshape1 \
		== "beetle curve" || @xyshape1 == "bicorn" || @xyshape1 == "bicuspid" || @xyshape1 == "Chasles cubic" \
		|| @xyshape1 == "circular cubic" || @xyshape1 == "clinoid" || @xyshape1 == "cross curve" \
		|| @xyshape1 == "devil's curve" || @xyshape1 == "dipole curve" || @xyshape1 == "double folium" \
		|| @xyshape1 == "double U curve" || @xyshape1 == "dumbbell curve" || @xyshape1 == "Durer's conchoid"\
		|| @xyshape1 == "cubic duplicatrix" || @xyshape1 == "Sillke's egg of Columbus" \
		|| @xyshape1 == "Kepler's egg" || @xyshape1 == "eight curve" || @xyshape1 == "hyperbola" || \
		@xyshape1 == "superellipse" || @xyshape1 == "folium 1" || @xyshape1 == "folium 2" \
		|| @xyshape1 == "Proclus hippopede" || @xyshape1 == "Hoerl curve" || @xyshape1 == "Humbert cubic" \
		|| @xyshape1 == "kampyle of Eudoxus" || @xyshape1 == "kappa curve" || @xyshape1 == "Kiepert's curve" \
		|| @xyshape1 == "links curve" || @xyshape1 == "logistic curve" || @xyshape1 == "semicubical parabola" \
		|| @xyshape1 == "diverging parabola" || @xyshape1 == "nodal curve" || @xyshape1 == "strophoid" \
		|| @xyshape1 == "ophiuride" || @xyshape1 == "parabola" || @xyshape1 == "parabola 2" \
		|| @xyshape1 == "parabolic trifolium" || @xyshape1 == "piriform" || @xyshape1 == "pearls of de Sluze" \
		|| @xyshape1 == "quadratrix" || @xyshape1 == "right strophoid" || @xyshape1 == "scyphoid" \
		|| @xyshape1 == "damped sine" || @xyshape1 == "catastrophic sine" || @xyshape1 == "plane spiric" \
		|| @xyshape1 == "svastika" || @xyshape1 == "syntractrix" || @xyshape1 == "tetracuspid" || \
		@xyshape1 == "siluroid" \
		|| @xyshape1 == "trisectrix of Longchamps" || @xyshape1 == "trident" || @xyshape1 == "trisectrix of Maclaurin" \
		|| @xyshape1 == "Trott curve"  \
		|| @xyshape1 == "Tschirnhausen's cubic" || @xyshape1 == "visiera" || @xyshape1 == "resonance curve" \
		|| @xyshape1 == "witch of Agnesi")
endparam
param cartycoeff1
	caption = "Y-coefficient"
	default = 1.0
	hint = "If 'Trap Type' is 'cartesian', then this shaping parameter \
		modifies the y-variable."
	visible =  @traptype == "cartesian" && \
		(@xyshape1 == "Alain's curve" || @xyshape1 == "arcs of Samothrace" || \
		@xyshape1 == "astroid" || @xyshape1 == "atriphthaloid" || \
		@xyshape1 == "bean curve 1" || @xyshape1 == "bean curve 2" || @xyshape1 \
		== "beetle curve" || @xyshape1 == "bicorn" || @xyshape1 == "bicuspid" || @xyshape1 == "Chasles cubic" \
		|| @xyshape1 == "circular cubic" || @xyshape1 == "clinoid" || @xyshape1 == "cross curve" \
		|| @xyshape1 == "devil's curve" || @xyshape1 == "double folium" || @xyshape1 == "dumbbell curve" \
		|| @xyshape1 == "cubic duplicatrix" || @xyshape1 == "Sillke's egg of Columbus" \
		|| @xyshape1 == "Kepler's egg" || @xyshape1 == "eight curve" || \
		@xyshape1 == "superellipse" || @xyshape1 == "Humbert cubic" || @xyshape1 == "hyperbola" \
		|| @xyshape1 == "Proclus hippopede" || @xyshape1 == "kappa curve" \
		|| @xyshape1 == "kampyle of Eudoxus" || @xyshape1 == "Kiepert's curve" || @xyshape1 == "kiss curve" \
		|| @xyshape1 == "links curve" || @xyshape1 == "logistic curve" || @xyshape1 == "semicubical parabola" \
		|| @xyshape1 == "diverging parabola" || @xyshape1 == "nodal curve" || @xyshape1 == "strophoid" \
		|| @xyshape1 == "ophiuride" || @xyshape1 == "parabola" || @xyshape1 == "parabola 2" \
		|| @xyshape1 == "parabolic trifolium" || @xyshape1 == "piriform" || @xyshape1 == "pearls of de Sluze" \
		|| @xyshape1 == "quadratrix" || @xyshape1 == "pursuit curve" || @xyshape1 == "right strophoid" \
		|| @xyshape1 == "scyphoid" || @xyshape1 == "anguinea" || @xyshape1 == "damped sine" \
		|| @xyshape1 == "catastrophic sine" || @xyshape1 == "plane spiric" || @xyshape1 == "svastika" \
		|| @xyshape1 == "syntractrix" || @xyshape1 == "tetracuspid" || @xyshape1 == \
		"trisectrix of Longchamps" || @xyshape1 == "trident" || @xyshape1 == "trisectrix of Maclaurin" \
		|| @xyshape1 == "Tschirnhausen's cubic" || @xyshape1 == "visiera" || @xyshape1 == "resonance curve" \
		|| @xyshape1 == "witch of Agnesi")
endparam
param cartconstant1
	caption = "Constant Term"
	default = 1.0
	hint = "If 'Trap Type' is 'cartesian', then this shaping parameter \
		modifies some of the curve equations."
	visible =  @traptype == "cartesian" && \
		(@xyshape1 == "astroid" || @xyshape1 == "atriphthaloid" || \
		@xyshape1 == "bean curve 1" || @xyshape1 == "bean curve 2" || @xyshape1 \
		== "beetle curve" || @xyshape1 == "bicorn" || @xyshape1 == "bicuspid" \
		|| @xyshape1 == "cubic egg" || @xyshape1 == "cardioid" || @xyshape1 == "Cartesian oval" \
		|| @xyshape1 == "Cassini oval"|| @xyshape1 == "catenary"|| @xyshape1 == \
		"Cayley's sextic"|| @xyshape1 == "Ceva's trisectrix" || @xyshape1 == "Chasles cubic" \
		 || @xyshape1 == "circle" || @xyshape1 == "cissoid of Diocles" \
		|| @xyshape1 == "circular cubic" || @xyshape1 == "clinoid" || @xyshape1 == "cochleoid" \
		|| @xyshape1 == "conchoid of circle" || @xyshape1 == "conchoid of Nicomedes" \
		|| @xyshape1 == "conchoid of de Sluze" || @xyshape1 == "cubic of Apollonius" \
		|| @xyshape1 == "cranoid" || @xyshape1 == "Jerabek curve" || \
		@xyshape1 == "Rosillo curve" || @xyshape1 == "deltoid" || @xyshape1 == "Humbert cubic" \
		|| @xyshape1 == "devil's curve" || @xyshape1 == "dipole curve" || @xyshape1 == "double egg" \
		|| @xyshape1 == "double folium" || @xyshape1 == "double U curve" || @xyshape1 == "cubic duplicatrix" \
		|| @xyshape1 == "Durer's conchoid" || @xyshape1 == "Granville's egg" || @xyshape1 == "hyperbola 2" \
		|| @xyshape1 == "Kepler's egg" || @xyshape1 == "eight curve" || @xyshape1 == \
		"ellipse" || @xyshape1 == "fish quartic" || @xyshape1 == "folium of Descartes" || \
		@xyshape1 == "Durer's folium" || @xyshape1 == "Gaussian curve" || @xyshape1 == "Beutel heart" \
		|| @xyshape1 == "Proclus hippopede" || @xyshape1 == "Hoerl curve" || @xyshape1 == "hyperbola" \
		|| @xyshape1 == "illumination curve" || @xyshape1 == "Kiepert's curve" || @xyshape1 == "kieroid" \
		|| @xyshape1 == "kiss curve" || @xyshape1 == "Klein quartic" || @xyshape1 == "Kulp quartic" \
		|| @xyshape1 == "limacon of Pascal" || @xyshape1 == "links curve" || @xyshape1 == "logistic curve" \
		|| @xyshape1 == "Lissajous sextic" || @xyshape1 == "Lissajous quartic" || @xyshape1 == "Maltese cross" \
		|| @xyshape1 == "diverging parabola" || @xyshape1 == "nephroid" || @xyshape1 == "Freeth's nephroid" \
		 || @xyshape1 == "nodal curve" || @xyshape1 == "strophoid" \
		|| @xyshape1 == "ophiuride" || @xyshape1 == "parabola 2" \
		|| @xyshape1 == "parabolic trifolium" || @xyshape1 == "piriform" || @xyshape1 == "pearls of de Sluze" \
		|| @xyshape1 == "quadratrix" || @xyshape1 == "pursuit curve" || @xyshape1 == "quadrafolium" \
		|| @xyshape1 == "trifolium" || @xyshape1 == "right strophoid" || @xyshape1 == "scarabaeus" \
		|| @xyshape1 == "scyphoid" || @xyshape1 == "anguinea" || @xyshape1 == "damped sine" \
		|| @xyshape1 == "catastrophic sine" || @xyshape1 == "plane spiric" || @xyshape1 == "spiric of Perseus" \
		|| @xyshape1 == "svastika" || @xyshape1 == "syntractrix" || @xyshape1 == "tetracuspid" || \
		@xyshape1 == "siluroid" \
		|| @xyshape1 == "trisectrix of Longchamps" || @xyshape1 == "trident" || @xyshape1 == "trisectrix of Maclaurin" \
		|| @xyshape1 == "Trott curve"  \
		|| @xyshape1 == "Tschirnhausen's cubic" || @xyshape1 == "visiera" || @xyshape1 == "resonance curve" \
		|| @xyshape1 == "witch of Agnesi" || @xyshape1 == "trisectrix of Delanges" || @xyshape1 == "Watt's curve")
endparam
param cartconstantB1
	caption = "Constant B Term"
	default = 1.0
	hint = "If 'Trap Type' is 'cartesian', then this 2nd shaping parameter \
		modifies some of the curve equations."
	visible =  @traptype == "cartesian" && \
		(@xyshape1 == "atriphthaloid" || @xyshape1 == "bean curve 1" \
		 || @xyshape1 == "bean curve 2" || @xyshape1 == "bicorn" || @xyshape1 == \
		 "Cartesian oval" || @xyshape1 == "catenary" || @xyshape1 == "Chasles cubic" \
		|| @xyshape1 == "circular cubic" || @xyshape1 == "clinoid" || @xyshape1 == "cochleoid" \
		|| @xyshape1 == "conchoid of circle" || @xyshape1 == "conchoid of Nicomedes" \
		|| @xyshape1 == "conchoid of de Sluze" || @xyshape1 == "cubic of Apollonius" \
		|| @xyshape1 == "cranoid" || @xyshape1 == "Jerabek curve" || @xyshape1 == "Rosillo curve" \
		|| @xyshape1 == "double egg" || @xyshape1 == "Durer's conchoid" \
		|| @xyshape1 == "Granville's egg" || @xyshape1 == "fish quartic" || @xyshape1 == "Hoerl curve" \
		|| @xyshape1 == "Durer's folium" || @xyshape1 == "Beutel heart" || @xyshape1 == "hyperbola" \
		|| @xyshape1 == "kieroid" || @xyshape1 == "Klein quartic" || @xyshape1 == "Kulp quartic" || \
		@xyshape1 == "links curve" || @xyshape1 == "logistic curve" || @xyshape1 == "Maltese cross" \
		|| @xyshape1 == "Lissajous quartic" || @xyshape1 == "nephroid" \
		|| @xyshape1 == "nodal curve" || @xyshape1 == "strophoid" \
		|| @xyshape1 == "pearls of de Sluze" \
		|| @xyshape1 == "quadratrix" || @xyshape1 == "pursuit curve" || @xyshape1 == "quadrafolium" \
		|| @xyshape1 == "trifolium" || @xyshape1 == "right strophoid" || @xyshape1 == "scarabaeus" \
		|| @xyshape1 == "anguinea" || @xyshape1 == "damped sine" \
		|| @xyshape1 == "catastrophic sine" || @xyshape1 == "plane spiric" || @xyshape1 == "spiric of Perseus" \
		|| @xyshape1 == "syntractrix" || @xyshape1 == "tetracuspid" || @xyshape1 == "trisectrix of Maclaurin" \
		|| @xyshape1 == "Trott curve"  \
		|| @xyshape1 == "Tschirnhausen's cubic" || @xyshape1 == "resonance curve" \
		|| @xyshape1 == "trisectrix of Delanges" || @xyshape1 == "Watt's curve")
endparam
param cartconstantC1
	caption = "Constant C Term"
	default = 1.0
	hint = "If 'Trap Type' is 'cartesian', then this 3rd shaping parameter \
		modifies some of the curve equations."
	visible =  @traptype == "cartesian" && \
		(@xyshape1 == "circular cubic" \
		|| @xyshape1 == "conchoid of circle" || @xyshape1 == "conchoid of de Sluze" \
		|| @xyshape1 == "cubic of Apollonius" || @xyshape1 == "Rosillo curve" \
		|| @xyshape1 == "Granville's egg" || @xyshape1 == "kieroid" || @xyshape1 == "Klein quartic" \
		|| @xyshape1 == "links curve" || @xyshape1 == "Maltese cross" \
		|| @xyshape1 == "Lissajous quartic" || @xyshape1 == "nephroid" \
		|| @xyshape1 == "nodal curve" || @xyshape1 == "pearls of de Sluze" \
		|| @xyshape1 == "pursuit curve" || @xyshape1 == "trifolium" || @xyshape1 == "scarabaeus" \
		|| @xyshape1 == "catastrophic sine" || @xyshape1 == "plane spiric" || @xyshape1 == "spiric of Perseus" \
		|| @xyshape1 == "Trott curve" || @xyshape1 == "Watt's curve")
endparam
param cartexexp1
	caption = "Ellipse X-exponent"
	default = 2.5
	hint = "If 'Trap Shape' is set to 'superellipse', this parameter determines the \
		exponent used for the x-coordinate."
	visible = @traptype == "cartesian" && @xyshape1 == \
		"superellipse"
endparam
param carteyexp1
	caption = "Ellipse Y-exponent"
	default = 2.5
	hint = "If 'Trap Shape' is set to 'superellipse', this parameter determines the \
		exponent used for the y-coordinate."
	visible = @traptype == "cartesian" && @xyshape1 == \
		"superellipse"
endparam
param coniceccent1
	caption = "Conic Eccentricity"
	default = 1.5
	hint = "If 'Trap Shape' is set to 'conic focal conchoid', this parameter determines the \
		eccentricity of the conic curve. circle, e = 0; ellipse, 0<e<1; parabola, e=1; \
		hyperbola, e>1."
	visible = @traptype == "cartesian" && @xyshape1 == \
		"conic focal conchoid"
endparam
param conchmod1
	caption = "Conchoid Modulus"
	default = 1.5
	hint = "If 'Trap Shape' is set to 'conic focal conchoid', this parameter determines the \
		modulus of the conchoid."
	visible = @traptype == "cartesian" && @xyshape1 == \
		"conic focal conchoid"
endparam
param testfunction
	caption = "Z Function"
	enum = "none" "sin" "cos" "tan" "cot" "sec" "csc" "ver" "vcs" "cvs" "cvc" \
		"exs" "exc" "crd" "asin" "acos" "atan" "acot" "asec" "acsc" "aver" \
		"avcs" "acvs" "acvc" "aexs" "aexc" "acrd" "exp" "exp(-n)" "exp(1/n)" \
		"exp(-1/n)" "exp(n^2)" "exp(-n^2)" "exp(1/n^2)" "exp(-1/n^2)" "sinh" \
		"asinh" "cosh" "acosh" "tanh" "atanh" "cotanh" "sqr" "sqrt" "power" \
		"log" "log(-n)" "log(1/n)" "log(-1/n)" "1/n" "absolute value" \
		"ceiling" "floor" "truncation" "rounding" "asin 2" "acos 2" "atan 2" "aexs 2" \
		"acot 2" "asec 2" "acsc 2" "aver 2" "avcs 2" "acvs 2" "acvc 2" "aexc 2" "acrd 2" \
		"log(n^2)" "log(-n^2)" "log(1/n^2)" "log(-1/n^2)" "log log" \
		"exp(exp)" "n^n" "n^n^n" "constant^n" "constant^n^n"
	default = 0
	hint = "This setting enables an optional function to be applied before \
		the Barnsley comparison."
endparam
param functionmode
	caption = "Function Mode"
	enum = "cabs" "real" "imag" "real 2" "imag 2" "sum" "sum 2" "sum 3" \
		"product" "product 2" "product 3" "difference" "difference 2" \
		"difference 3"
	default = 0
	hint = "This setting makes no contribution to this formula, but was \
		inadvertently introduced into early versions, so it is retained \
		for compatibility, but now hidden.."
	visible = FALSE
endparam
param testpower
	caption = "Function Exponent"
	default = 3.0
	hint = "If the 'Test Function' is set to 'power', then this is the \
		exponent that is used."
	visible = (@testfunction == "power")
endparam
param testbase
	caption = "Function Base"
	default = 4.0
	hint = "If the 'Test Function' is set to 'constant^n' or 'constant^n^n', \
		then this is the constant that is used."
	visible = ((@testfunction == "constant^n")  || (@testfunction == "constant^n^n"))
endparam
param testadjustment
	caption = "Z Adjustment"
	default = 0.0
	hint = "This value is added to the #z before the Barnsley test."
endparam
param barnsleymode
	caption = "Barnsley Mode"
	enum = "cabs" "real" "imag" "real 2" "imag 2" "sum" "sum 2" "sum 3" \
		"product" "product 2" "product 3" "difference" "difference 2" \
		"difference 3" "test constant"
	default = 14
	hint = "This setting determines what is compared to the trapped point \
			or its test function.  If 'test constant' is selected, then the \
			orbit trap 'Trap Mode' value is compared directly to the 'Barnsley \
			Test Constant' value rather than to #z itself."
endparam
param barntestconst
	caption = "Barnsley Test Constant"
	default = 0.3
	hint = "If parameter 'Barnsley Mode' is set to 'test constant', \
			then this is the constant used to test the trapped point \
			'Trap Mode'."
	visible = @barnsleymode == "test constant"
endparam
param barnsleytype
	caption = "Barnsley Type"
	enum = "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14"
	hint = "This setting determines which set of equations is used."
endparam
param barnconst1
	caption = "1st Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 1st Barnsley equation."
endparam
param barnconst2
	caption = "2nd Barnsley Constant"
	default = (0,0)
	hint = "This parameter modifies the 2nd Barnsley equation."
endparam
param bailtest
	caption = "Bailout Test"
	enum = "mod" "real" "imag" "and" "or" "eor" "manh" "manr" "real 2" "imag 2" \
		"sum" "sum 2" "product" "difference" "difference 2" "difference 3" \
		"quotient" "quotient 2"
	default = 0
endparam
param bailout 
	caption = "Bailout Value"
	default = 4.0
	min = 0.001
endparam
param heatmap
	caption = "Heat Map?"
	default = FALSE
	hint = "If enabled, #z encodes the ratio of the number of times that Barnsley equation \
		#1 is used to that of Barnsley equation #2, i.e., real(#z) = number \
		of uses of equation 1, and imag(#z) = number of uses of equation 2. \
		This value can be used with the 'Heat Map' coloring in jam2.ucl \
		to determine how often each Barnsley equation is chosen."
endparam
param jconstant 
	caption = "Seed/Perturbation"
	default = (0,0)
endparam
param fixbug
	caption = "Fix Barnsley Bug?"
	default = TRUE
	hint = "Enabling this setting fixes an error in the barnsley routine."
endparam
param mandy
	caption = "Mandelbrot flag"
	default = TRUE
	hint = "Works in combination with the Julia flag for switching"
	visible = FALSE
endparam
param julia
	caption = "Julia flag"
	default = FALSE
	hint = "Works in combination with the Mandelbrot flag for switching"
	visible = FALSE
endparam

switch:
	type = "jam-OrbitTrapBarnsley"
	trapmode = trapmode
	traptype = traptype
	trapshape = trapshape
	morepolygons1 = morepolygons1
	morespirolaterals1 = morespirolaterals1
	morecurves1 = morecurves1
	polarshape1 = polarshape1
	polarmode1 = polarmode1
	parashape1 = parashape1
	xyshape1 = xyshape1
	fixtrapbug = fixtrapbug
	nscale1 = nscale1
	rotate = rotate
	center = center
	isocheight = isocheight
	isocwidth = isocwidth
	fixisosceles = fixisosceles
	leafAlength = leafAlength
	leafBlength = leafBlength
	leafClength = leafClength
	leafDlength = leafDlength
	leafElength = leafElength
	leafFlength = leafFlength
	leafGlength = leafGlength
	leafHlength = leafHlength
	leafIlength = leafIlength
	leafJlength = leafJlength
	leafKlength = leafKlength
	leafLlength = leafLlength
	starspikiness = starspikiness
	innerscale = innerscale
	rhombheight = rhombheight
	rhombwidth = rhombwidth
	kiteheight = kiteheight
	kitewidth = kitewidth
	dartheight = dartheight
	dartwidth = dartwidth
	rectlength = rectlength
	rectwidth = rectwidth
	flat4height = flat4height
	flat4width = flat4width
	finger1length = finger1length
	finger2length = finger2length
	finger3length = finger3length
	finger4length = finger4length
	finger5length = finger5length
	sawheight = sawheight
	windheight = windheight
	windwidth = windwidth
	sqrheight = sqrheight
	sqrwidth = sqrwidth
	unityroot1 = unityroot1
	singleroot1 = singleroot1
	whichroot1 = whichroot1
	collinearspot1 = collinearspot1
	squarespot1 = squarespot1
	triarray1 = triarray1
	raynumber = raynumber
	dotnumber = dotnumber
	dashnumber = dashnumber
	spiralorder1 = spiralorder1
	ellipseexponent1 = ellipseexponent1
	ellipseheight1 = ellipseheight1
	ellipsewidth1 = ellipsewidth1
	hypotrochA1 = hypotrochA1
	hypotrochB1 = hypotrochB1
	hypotrochH1 = hypotrochH1
	cycloidamp1 = cycloidamp1
	cycloidconst1 = cycloidconst1
	cycloidlength1 = cycloidlength1
	grain = grain
	lissaamp1 = lissaamp1
	lissafreq1 = lissafreq1
	lissaphase1 = lissaphase1
	lissaamp2 = lissaamp2
	lissafreq2 = lissafreq2
	lissaphase2 = lissaphase2
	lissadomain = lissadomain
	lissaopen = lissaopen
	moritzamp1 = moritzamp1
	moritzfreqN1 = moritzfreqN1
	moritzfreqD1 = moritzfreqD1
	moritzconst1 = moritzconst1
	circlenum1 = circlenum1
	rose1 = rose1
	folium1 = folium1
	foliumperturb1 = foliumperturb1
	cardioid1 = cardioid1
	cardioidperturb1 = cardioidperturb1
	cissoidDioA1 = cissoidDioA1
	cissoidDioB1 = cissoidDioB1
	cochleoid1 = cochleoid1
	conchoidA1 = conchoidA1
	conchoidB1 = conchoidB1
	conchoidC1 = conchoidC1
	cubicpA1 = cubicpA1
	cubicpB1 = cubicpB1
	cubicpC1 = cubicpC1
	majaxis1 = majaxis1
	minaxis1 = minaxis1
	epower1 = epower1
	tanfreq1 = tanfreq1
	fosinfreq1 = fosinfreq1
	focosfreq1 = focosfreq1
	sinfreq21 = sinfreq21
	hyperbolic1 = hyperbolic1
	kampfreq1 = kampfreq1
	kamppower1 = kamppower1
	nodalfreq1 = nodalfreq1
	lemfreq1 = lemfreq1
	lempower1 = lempower1
	limfreq1 = limfreq1
	limamp1 = limamp1
	limoffset1 = limoffset1
	litpower1 = litpower1
	logspiA1 = logspiA1
	logspiB1 = logspiB1
	parafreq1 = parafreq1
	paraamp1 = paraamp1
	paraoffset1 = paraoffset1
	paraspi1 = paraspi1
	paraspioffset1 = paraspioffset1
	semicubtanfreq1 = semicubtanfreq1
	semicubcosfreq1 = semicubcosfreq1
	semicubpower1 = semicubpower1
	archspioffset1 = archspioffset1
	strophcosfreqA1 = strophcosfreqA1
	strophcosfreqB1 = strophcosfreqB1
	polarfreqA1 = polarfreqA1
	polarampA1 = polarampA1
	trefoilcosamp1 = trefoilcosamp1
	trefoilsinamp1 = trefoilsinamp1
	trefoilcossymmetry1 = trefoilcossymmetry1
	trefoilsinsymmetry1 = trefoilsinsymmetry1
	trefoilconstant1 = trefoilconstant1
	trilimA1 = trilimA1
	trilimB1 = trilimB1
	trilimamp1 = trilimamp1
	trilimfreq1 = trilimfreq1
	folioidamp1 = folioidamp1
	folioidfreqN1 = folioidfreqN1
	folioidfreqD1 = folioidfreqD1
	folioidconstA1 = folioidconstA1
	folioidconstB1 = folioidconstB1
	hyponumerator1 = hyponumerator1
	hypodenom1 = hypodenom1
	companC11 = companC11
	companC21 = companC21
	companfreq1 = companfreq1
	cycampV1 = cycampA1
	cycampB1 = cycampB1
	cycxscale1 = cycxscale1
	cycyoffset1 = cycyoffset1
	cycsinfreq1 = cycsinfreq1
	cyccosfreq1 = cyccosfreq1
	cycangle1 = cycangle1
	epicycAN1 = epicycAN1
	epicycAD1 = epicycAD1
	epicycB1 = epicycB1
	epicycC1 = epicycC1
	nephsinfreq1 = nephsinfreq1
	nephcosfreq1 = nephcosfreq1
	nephconstA1 = nephconstA1
	nephconstB1 = nephconstB1
	parafreqA1 = parafreqA1
	parafreqB1 = parafreqB1
	paraconstA1 = paraconstA1
	paraconstB1 = paraconstB1
	wavysinfreq1 = wavysinfreq1
	wavysinamp1 = wavysinamp1
	wavyradius1 = wavyradius1
	paraxaxis1 = paraxaxis1
	parayaxis1 = parayaxis1
	epiradiusA1 = epiradiusA1
	epiradiusB1 = epiradiusB1
	epiradiusC1 = epiradiusC1
	cartxcoeff1 = cartxcoeff1
	cartycoeff1 = cartycoeff1
	cartconstant1 = cartconstant1
	cartconstantB1 = cartconstantB1
	cartconstantC1 = cartconstantC1
	cartexexp1 = cartexexp1
	carteyexp1 = carteyexp1
	coniceccent1 = coniceccent1
	conchmod1 = conchmod1
	testfunction = testfunction
	functionmode = functionmode
	testpower = testpower
	testbase = testbase
	testadjustment = testadjustment
	barnsleymode = barnsleymode
	barntestconst = barntestconst
	barnsleytype = barnsleytype
	barnconst1 = barnconst1
	barnconst2 = barnconst2
	bailtest = bailtest
	bailout = bailout
;	heatmap = heatmap ; don't want heat map showing in the Julia version
	jconstant = #pixel
	fixbug = fixbug
	mandy = julia
	julia = mandy
}