; jam-Newtons.ufm
; Various takes on the Newton method,
; begun 161111 by jam

; These formulas use Newton's method or higher order methods
; to find the roots of various equations.
; The variable 'zworking' is
; used for the orbit computation, and #z
; is set to the reciprocal of the correction adjustment to
; 'zworking' after each iteration.  That is, when the orbit 
; has settled down into a root, #z approaches infinity.
; Consequently, set the bailout value to some large
;  number.  This method is employed for compatibility with
; coloring schemes that expect #z to be large on bailout.
; 
; To my knowledge, Kerry Mitchell devised the reciprocal
; bailout method.  Thanks!

jam-explogNewt4 {
;
; Uses Newton's method to find the roots
; of exp(z)-log(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zexp = complex zlog = complex zrecip = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zworking + jc1)
	zlog = log(zworking)
	zrecip = 1/zworking
elseif @eqselection == 1
	zexp = exp(zworking)
	zlog = log(zworking + jc2)
	zrecip = 1/zworking
elseif @eqselection == 2
	zexp = exp(zworking)
	zlog = log(zworking)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 3
	zexp = exp(zworking + jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/zworking
elseif @eqselection == 4
	zexp = exp(zworking)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 5
	zexp = exp(zworking + jc1)
	zlog = log(zworking)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 6
	zexp = exp(zworking + jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 7
	zexp = exp(zworking * jc1)
	zlog = log(zworking)
	zrecip = 1/zworking
elseif @eqselection == 8
	zexp = exp(zworking)
	zlog = log(zworking * jc2)
	zrecip = 1/zworking
elseif @eqselection == 9
	zexp = exp(zworking)
	zlog = log(zworking)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 10
	zexp = exp(zworking * jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/zworking
elseif @eqselection == 11
	zexp = exp(zworking)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 12
	zexp = exp(zworking * jc1)
	zlog = log(zworking)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 13
	zexp = exp(zworking * jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 14
	zexp = exp(zworking + jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/zworking
elseif @eqselection == 15
	zexp = exp(zworking)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 16
	zexp = exp(zworking + jc1)
	zlog = log(zworking)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 17
	zexp = exp(zworking * jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/zworking
elseif @eqselection == 18
	zexp = exp(zworking)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 19
	zexp = exp(zworking * jc1)
	zlog = log(zworking)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 20
	zexp = exp(zworking + jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 21
	zexp = exp(zworking + jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 22
	zexp = exp(zworking + jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 23
	zexp = exp(zworking * jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 24
	zexp = exp(zworking * jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 25
	zexp = exp(zworking * jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking + jc3)
endif ; @eqselection

funcresult = zexp - zlog + @const
derivresult = zexp - zrecip
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - log(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expcosNewt2 { ; jam 161111
;
; Uses Newton's method to find the roots
; of exp(z)cos(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zexp = complex zcos = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zworking + jc1)
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	zexp = exp(zworking)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	zexp = exp(zworking)
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	zexp = exp(zworking + jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	zexp = exp(zworking)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	zexp = exp(zworking + jc1)
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	zexp = exp(zworking + jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	zexp = exp(zworking * jc1)
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	zexp = exp(zworking)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	zexp = exp(zworking)
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	zexp = exp(zworking * jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	zexp = exp(zworking)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	zexp = exp(zworking * jc1)
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	zexp = exp(zworking * jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	zexp = exp(zworking + jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	zexp = exp(zworking)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	zexp = exp(zworking + jc1)
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	zexp = exp(zworking * jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	zexp = exp(zworking)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	zexp = exp(zworking * jc1)
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	zexp = exp(zworking + jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	zexp = exp(zworking + jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	zexp = exp(zworking + jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	zexp = exp(zworking * jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	zexp = exp(zworking * jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	zexp = exp(zworking * jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

funcresult = zexp * zcos + @const
derivresult = zexp * (zcos - zsin)
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z * cos(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-ex2tanxNewt2 { ; jam 161111
;
; Uses Newton's method to find the roots
; of exp(z^2)tan(z) + constant = 0.  Set the
; bailout value to some large number. 
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zsqr = complex ezsqr = complex ztan = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking)
elseif @eqselection == 1
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking)
elseif @eqselection == 2
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr)
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking)
elseif @eqselection == 4
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking)
elseif @eqselection == 8
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking)
elseif @eqselection == 9
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr)
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking)
elseif @eqselection == 11
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking)
elseif @eqselection == 15
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking)
elseif @eqselection == 18
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking + jc3)
endif ; @eqselection

funcresult = ezsqr * ztan + @const
derivresult = ezsqr * (2 * zworking * ztan + sqr(ztan) + 1)
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z^2 * tan(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znseczNewt { ; jam 161112
;
; Uses Newton's method to find the roots
; of z^n - sec(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex ztan = (0,0)
complex zcos = complex zsec = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zsec = 1/zcos
funcresult = zn - zsec + @const
derivresult = @power * znminus - zsec * ztan
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - sec(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znsinzNewt { ; jam 161112
;
; Uses Newton's method to find the roots
; of z^n - sin(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zcos = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
funcresult = zn - zsin + @const
derivresult = @power * znminus - zcos
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - sin(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncoszNewt { ; jam 161112
;
; Uses Newton's method to find the roots
; of z^n - cos(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zcos = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
funcresult = zn - zcos + @const
derivresult = @power * znminus + zsin
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - cos(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zntanzNewt { ; jam 161112
;
; Uses Newton's method to find the roots
; of z^n - tan(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex ztan = complex ztan2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking + jc3)
endif ; @eqselection

ztan2 = sqr(ztan)
funcresult = zn - ztan + @const
derivresult = @power * znminus - ztan2 - 1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - tan(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz3Newt {
;
; Uses Newton's method to find the roots
; of z^3 + az^2 + bz + c = 0.  Set the
; bailout value to some large number
; jam 161113

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1) + jc2
	z3 = z2 * z1
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1) + jc2
	z3 = z2 * z1
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1) * jc2
	z3 = z2 * z1
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1) * jc2
	z3 = z2 * z1
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)* jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1) * jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1) * jc2
	z3 = z2 * z1
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1) + jc2
	z3 = z2 * z1
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1) * jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1) * jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1) * jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1) * jc2
	z3 = z2 * z1 + jc3
endif ; @eqselection

funcresult = z3 + @coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 3 * z2 + + 2 * @coeff2 * z1 + @coeff1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 3 Newton"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff2
	caption = "Coefficient 2"
	default = (3,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncotzNewt { ; jam 161113
;
; Uses Newton's method to find the roots
; of z^n - cotan(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zcot = complex zcot2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking + jc3)
endif ; @eqselection

zcot2 = sqr(zcot)
funcresult = zn - zcot + @const
derivresult = @power * znminus + zcot2 + 1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - cotan(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncsczNewt { ; jam 161112
;
; Uses Newton's method to find the roots
; of z^n - csc(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex zcot = (0,0)
complex zcsc = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcsc = 1/zsin
funcresult = zn - zcsc + @const
derivresult = @power * znminus + zcsc * zcot
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - csc(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxsinzNewt { ; jam 161113
;
; Uses Newton's method to find the roots
; of z^n * sin(z)  + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zcos = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
funcresult = zn * zsin + @const
derivresult = @power * znminus * zsin + zn * zcos
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * sin(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxcoszNewt { ; jam 161113
;
; Uses Newton's method to find the roots
; of z^n * cos(z)  + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zcos = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
funcresult = zn * zcos + @const
derivresult = @power * znminus * zcos - zn * zsin
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * cos(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxtanzNewt { ; jam 161113
;
; Uses Newton's method to find the roots
; of z^n * tan(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex ztan = complex ztan2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	ztan = tan(zworking + jc3)
endif ; @eqselection

ztan2 = sqr(ztan)
funcresult = zn * ztan + @const
derivresult = @power * znminus * ztan + zn + zn * ztan2
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * tan(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxcotzNewt { ; jam 161113
;
; Uses Newton's method to find the roots
; of z^n * cotan(z)  + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zcot = complex zcot2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zn = zworking * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zn = (zworking + jc2) * znminus
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zn = (zworking * jc2) * znminus
	zcot = cotan(zworking + jc3)
endif ; @eqselection

zcot2 = sqr(zcot)
funcresult = zn * zcot + @const
derivresult = @power * znminus * zcot - zn - zn * zcot2
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * cotan(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxseczNewt { ; jam 161113
;
; Uses Newton's method to find the roots
; of z^n * sec(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex ztan = (0,0)
complex zcos = complex zsec = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zsec = 1/zcos
funcresult = zn * zsec + @const
derivresult = @power * znminus * zsec + zn * zsec * ztan
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * sec(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxcsczNewt { ; jam 161113
;
; Uses Newton's method to find the roots
; of z^n * csc(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex zcot = (0,0)
complex zcsc = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcsc = 1/zsin
funcresult = zn * zcsc + @const
derivresult = @power * znminus * zcsc - zn * zcsc * zcot
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * csc(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz4Nwt {
;
; Uses Newton's method to find the roots
; of z^4 + az^3 + bz^2 + cz + d = 0.  Set the
; bailout value to some large number
; jam 161113

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex z4 = complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2)* jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 + jc3
endif ; @eqselection

funcresult = z4 + @coeff3 * z3 + @coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 4 * z3 + 3 * @coeff3 * z2 + 2 * @coeff2 * z1 + @coeff1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 4 Newton"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (3,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znexszNewt { ; jam 161114
;
; Uses Newton's method to find the roots
; of z^n - exs(z) + constant = 0 (exsecant function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex ztan = (0,0)
complex zcos = complex zsec = complex zexs = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zsec = 1/zcos
zexs - zsec - 1
funcresult = zn - zexs + @const
derivresult = @power * znminus - zsec * ztan
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - exs(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

; black screen for all options
jam-znxexszNewt { ; jam 161114
;
; Uses Newton's method to find the roots
; of z^n * exs(z)  + constant = 0 (exsecant function).  Set the
; bailout value to some large number.
; Included for completeness though most options fail
; to provide useful results.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex ztan = (0,0)
complex zcos = complex zsec = complex zexs = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zsec = 1/zcos
zexs - zsec - 1
funcresult = zn * zexs + @const
derivresult = @power * znminus * zexs + zn * zsec * ztan
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * exs(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-ez-2asin {
;
; Uses Newton's method to find the roots
; of exp(-(z^2))- arcsin(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex z2 = complex zasin = (0,0)
complex zez2 = complex zrecip = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 1
	z2 = sqr(zworking)
	zexp = exp(-z2 + jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 2
	z2 = sqr(zworking)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 3
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 4
	z2 = sqr(zworking)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 5
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 6
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 7
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 8
	z2 = sqr(zworking)
	zexp = exp(-z2 * jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 9
	z2 = sqr(zworking)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 10
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 11
	z2 = sqr(zworking)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 12
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 13
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 14
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 15
	z2 = sqr(zworking)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 16
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 17
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 18
	z2 = sqr(zworking)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 19
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 20
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 21
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 22
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 23
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 24
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 25
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
endif ; @eqselection

zasin = asin(zworking)
funcresult = zexp - zasin + @const
derivresult = -2 * zworking * zexp - zrecip
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^(-z^2) - asin(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znexczNewt { ; jam 161116
;
; Uses Newton's method to find the roots
; of z^n - exc(z) + constant = 0 (excosecant function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex zcot = (0,0)
complex zsin = complex zcsc = complex zexc = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcsc = 1/zsin
zexc - zcsc - 1
funcresult = zn - zexc + @const
derivresult = @power * znminus + zcsc * zcot
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - exc(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

; gives black screen for all values
jam-znxexczNewt { ; jam 161116
;
; Uses Newton's method to find the roots
; of z^n * exc(z) + constant = 0 (excosecant function).  Set the
; bailout value to some large number.
; Included for completeness though most options fail
; to provide useful results.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex zcot = (0,0)
complex zsin = complex zcsc = complex zexc = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcsc = 1/zsin
zexc - zcsc - 1
funcresult = zn * zexc + @const
derivresult = @power * znminus * zexc - zn * zcsc * zcot
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * exc(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znverzNewt { ; jam 161116
;
; Uses Newton's method to find the roots
; of z^n - ver(z) + constant = 0 (versine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zsin = complex zcos = complex zver = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zver = 1 - zcos
funcresult = zn - zver + @const
derivresult = @power * znminus - zsin
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - ver(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (4,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxverzNewt { ; jam 161116
;
; Uses Newton's method to find the roots
; of z^n * ver(z) + constant = 0 (versine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zsin = complex zcos = complex zver = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zver = 1 - zcos
funcresult = zn * zver + @const
derivresult = @power * znminus * zver + zn * zsin
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * ver(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (4,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncvszNewt { ; jam 161116
;
; Uses Newton's method to find the roots
; of z^n - cvs(z)  + constant = 0 (coversine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zsin = complex zcos = complex zcvs = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcvs = 1 - zsin
funcresult = zn - zcvs + @const
derivresult = @power * znminus + zcos
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - cvs(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (4,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxcvszNewt { ; jam 161116
;
; Uses Newton's method to find the roots
; of z^n * cvs(z) + constant = 0 (coversine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zsin = complex zcos = complex zcvs = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcvs = 1 - zsin
funcresult = zn * zcvs + @const
derivresult = @power * znminus * zcvs - zn * zcos
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * cvs(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (4,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expsinNwt {
;
; Uses Newton's method to find the roots
; of exp(z)- m * sin(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zexp = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	zexp = exp(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zsin = sin(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	zexp = exp(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zsin = sin(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq * jc2)
endif ; @eqselection

zcos = cos(zfreq)
funcresult = zexp - @amplitude * zsin + @const
derivresult = zexp - @amplitude * zcos * @freq
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - m*sin(nz) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Sine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the sine function."
endparam
param freq
	caption = "Sine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the sine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expcosNwt {
;
; Uses Newton's method to find the roots
; of exp(z)- m * cos(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zexp = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	zexp = exp(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zcos = cos(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	zexp = exp(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zcos = cos(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq * jc2)
endif ; @eqselection

zsin = sin(zfreq)
funcresult = zexp - @amplitude * zcos + @const
derivresult = zexp + @amplitude * zsin * @freq
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - m*cos(nz) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Cosine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the cosine function."
endparam
param freq
	caption = "Cosine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the cosine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expz2cosNwt {
;
; Uses Newton's method to find the roots
; of exp(z^2)- m * cos(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zexp = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)
complex z2 = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq * jc2)
endif ; @eqselection

zsin = sin(zfreq)
funcresult = zexp - @amplitude * zcos + @const
derivresult = 2 * zworking * zexp + @amplitude * zsin * @freq
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^(z^2) - m*cos(nz) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Cosine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the cosine function."
endparam
param freq
	caption = "Cosine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the cosine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expz2sinNwt {
;
; Uses Newton's method to find the roots
; of exp(z^2)- m * sin(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zexp = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)
complex z2 = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq * jc2)
endif ; @eqselection

zcos = cos(zfreq)
funcresult = zexp - @amplitude * zsin + @const
derivresult = 2 * zworking * zexp - @amplitude * zcos * @freq
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^(z^2) - m*sin(nz) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Sine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the sine function."
endparam
param freq
	caption = "Sine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the sine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz5Nwt {
;
; Uses Newton's method to find the roots
; of z^5 + az^4 + bz^3 + cz^2 + dz + e = 0.  Set the
; bailout value to some large number
; jam 161117

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex z5 = complex z4 = complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 + jc3
endif ; @eqselection

funcresult = z5 + @coeff4 * z4 + @coeff3 * z3 + @coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 5 * z4 + 4 * @coeff4 * z3 + 3 * @coeff3 * z2 + 2 * @coeff2 * z1 + @coeff1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 5 Newton"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff4
	caption = "Coefficient 4"
	default = (1,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (3,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz6Nwt {
;
; Uses Newton's method to find the roots
; of z^6 + az^5 + bz^4 + cz^3 + dz^2 + ez + f = 0.  Set the
; bailout value to some large number
; jam 161117

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex z6 = complex z5 = complex z4 = complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
endif ; @eqselection

funcresult = z6 + @coeff5 * z5 + @coeff4 * z4 + @coeff3 * z3 + @coeff2 * z2 + \
	@coeff1 * z1 + @constant
derivresult = 6 * z5 + 5 * @coeff5 * z4 + 4 * @coeff4 * z3 + 3 * @coeff3 * z2 + \
	2 * @coeff2 * z1 + @coeff1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 6 Newton"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff5
	caption = "Coefficient 5"
	default = (2,0)
	hint = "This parameter if the coefficient of the quintic z term."
endparam
param coeff4
	caption = "Coefficient 4"
	default = (-3,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (1,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znvcszNewt { ; jam 161117
;
; Uses Newton's method to find the roots
; of z^n - vcs(z)  + constant = 0 (vercosine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zsin = complex zcos = complex zvcs = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zvcs = 1 + zcos
funcresult = zn - zvcs + @const
derivresult = @power * znminus + zsin
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - vcs(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (4,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxvcszNewt { ; jam 161117
;
; Uses Newton's method to find the roots
; of z^n * vcs(z) + constant = 0 (vercosine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zsin = complex zcos = complex zvcs = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zvcs = 1 + zcos
funcresult = zn * zvcs + @const
derivresult = @power * znminus * zvcs - zn * zsin
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * vcs(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (4,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz7Nwt {
;
; Uses Newton's method to find the roots
; of z^7 + az^6 + bz^5 + cz^4 + dz^3 + ez^2 + fz + g = 0.
;   Set the bailout value to some large number
; jam 161118

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex z7 = complex z6 = complex z5 = complex z4 = complex z3 = (0,0)
complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
endif ; @eqselection

funcresult = z7 + @coeff6 * z6 + @coeff5 * z5 + @coeff4 * z4 + @coeff3 * z3 + \
	@coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 7 * z6 + 6 * @coeff6 * z5 + 5 * @coeff5 * z4 + 4 * @coeff4 * z3 + \
	3 * @coeff3 * z2 + 2 * @coeff2 * z1 + @coeff1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 7 Newton"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff6
	caption = "Coefficient 6"
	default = (1,0)
	hint = "This parameter if the coefficient of the sextic z term."
endparam
param coeff5
	caption = "Coefficient 5"
	default = (2,0)
	hint = "This parameter if the coefficient of the quintic z term."
endparam
param coeff4
	caption = "Coefficient 4"
	default = (-3,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (1,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncvczNewt { ; jam 161119
;
; Uses Newton's method to find the roots
; of z^n - cvc(z) + constant = 0 (covercosine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zsin = complex zcos = complex zcvc = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcvc = 1 + zsin
funcresult = zn - zcvc + @const
derivresult = @power * znminus - zcos
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - cvc(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (3,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxcvczNewt { ; jam 161119
;
; Uses Newton's method to find the roots
; of z^n * cvc(z) + constant = 0 (covercosine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = (0,0)
complex zsin = complex zcos = complex zcvc = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcvc = 1 + zsin
funcresult = zn * zcvc + @const
derivresult = @power * znminus * zcvc + zn * zcos
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * cvc(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (3,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncrdzNewt { ; jam 161119
;
; Uses Newton's method to find the roots
; of z^n - crd(z) + constant = 0 (chord function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex zhalf = (0,0)
complex zsin = complex zcos = complex zcrd = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
endif ; @eqselection

zn = znminus * zworking
zcrd = 2 * zsin
funcresult = zn - zcrd + @const
derivresult = @power * znminus - zcos
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - crd(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (3,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znxcrdzNewt { ; jam 161119
;
; Uses Newton's method to find the roots
; of z^n * crd(z) + constant = 0 (chord function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zn = complex znminus = complex zhalf = (0,0)
complex zsin = complex zcos = complex zcrd = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2)
elseif @eqselection == 1
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 2
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 3
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 4
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 5
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 6
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 7
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2)
elseif @eqselection == 8
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 9
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 10
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 11
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 12
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 13
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 14
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 15
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 16
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 17
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 18
	znminus = (zworking)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 19
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 20
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 21
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 22
	znminus = (zworking + jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 23
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 24
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 25
	znminus = (zworking * jc1)^powerminus
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
endif ; @eqselection

zn = znminus * zworking
zcrd = 2 * zsin
funcresult = zn * zcrd + @const
derivresult = @power * znminus * zcrd + zn * zcos
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n * crd(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (3,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-eztanzNwt {
;
; Uses Newton's method to find the roots
; of exp(z)- tan(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zexp = complex ztan = complex ztan2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 1
	zexp = exp(zworking)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 2
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 3
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 4
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 5
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 6
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 7
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 8
	zexp = exp(zworking)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 9
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 10
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 11
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 12
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 13
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 14
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 15
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 16
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 17
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 18
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 19
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 20
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 21
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 22
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 23
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 24
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 25
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
endif ; @eqselection

funcresult = zexp - ztan + @const
derivresult = zexp - ztan2 - 1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - tan(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-e-ztanzNwt {
;
; Uses Newton's method to find the roots
; of exp(-z)- tan(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex zneg = -1 * zworking
complex funcresult = complex derivresult = (0,0)
complex zexp = complex ztan = complex ztan2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zneg + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 1
	zexp = exp(zneg)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 2
	zexp = exp(zneg)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 3
	zexp = exp(zneg + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 4
	zexp = exp(zneg)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 5
	zexp = exp(zneg + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 6
	zexp = exp(zneg + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 7
	zexp = exp(zneg * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 8
	zexp = exp(zneg)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 9
	zexp = exp(zneg)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 10
	zexp = exp(zneg * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 11
	zexp = exp(zneg)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 12
	zexp = exp(zneg * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 13
	zexp = exp(zneg * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 14
	zexp = exp(zneg + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 15
	zexp = exp(zneg)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 16
	zexp = exp(zneg + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 17
	zexp = exp(zneg * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 18
	zexp = exp(zneg)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 19
	zexp = exp(zneg * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 20
	zexp = exp(zneg + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 21
	zexp = exp(zneg + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 22
	zexp = exp(zneg + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 23
	zexp = exp(zneg * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 24
	zexp = exp(zneg * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 25
	zexp = exp(zneg * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
endif ; @eqselection

funcresult = zexp - ztan + @const
derivresult = -zexp - ztan2 - 1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^(-z) - tan(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-tansinNwt {
;
; Uses Newton's method to find the roots
; of tan(z)- m * sin(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex ztan = complex ztan2 = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	ztan = tan(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zsin = sin(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	ztan = tan(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zsin = sin(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq * jc2)
endif ; @eqselection

zcos = cos(zfreq)
ztan2 = sqr(ztan)
funcresult = ztan - @amplitude * zsin + @const
derivresult = 1 + ztan2 - @amplitude * zcos * @freq
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "tan(z) - m*sin(nz) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Sine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the sine function."
endparam
param freq
	caption = "Sine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the sine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-tancosNwt {
;
; Uses Newton's method to find the roots
; of tan(z)- m * cos(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex ztan = complex ztan2 = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	ztan = tan(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zcos = cos(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	ztan = tan(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zcos = cos(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq * jc2)
endif ; @eqselection

zsin = sin(zfreq)
ztan2 = sqr(ztan)
funcresult = ztan - @amplitude * zcos + @const
derivresult = 1 + ztan2 + @amplitude * zsin * @freq
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "tan(z) - m*cos(nz) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Cosine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the cosine function."
endparam
param freq
	caption = "Cosine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the cosine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz8Nwt {
;
; Uses Newton's method to find the roots
; of z^8 + az^7 + bz^6 + cz^5 + dz^4 + ez^3 + fz^2 + gz + h = 0.
;   Set the bailout value to some large number
; jam 161121

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex z8 = complex z7 = complex z6 = complex z5 = complex z4 = (0,0)
complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
endif ; @eqselection

funcresult = z8 + @coeff7 * z7 + @coeff6 * z6 + @coeff5 * z5 + @coeff4 * z4 + \
	@coeff3 * z3 + @coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 8 * z7 + 7 * @coeff7 * z6 + 6 * @coeff6 * z5 + 5 * @coeff5 * z4 + 4 * @coeff4 * z3 + \
	3 * @coeff3 * z2 + 2 * @coeff2 * z1 + @coeff1
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 8 Newton"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff7
	caption = "Coefficient 7"
	default = (1,0)
	hint = "This parameter if the coefficient of the degree 7 z term."
endparam
param coeff6
	caption = "Coefficient 6"
	default = (1,0)
	hint = "This parameter if the coefficient of the sextic z term."
endparam
param coeff5
	caption = "Coefficient 5"
	default = (2,0)
	hint = "This parameter if the coefficient of the quintic z term."
endparam
param coeff4
	caption = "Coefficient 4"
	default = (-3,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (1,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz8Hal {
;
; Uses Householder's, Halley's, or Newton's method to find the roots
; of az^8 + bz^7 + cz^6 + dz^5 + ez^4 + fz^3 + gz^2 + hz + i = 0.
;   Set the bailout value to some large number
; jam 161211

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex const2 = 2 * @coeff2
complex const3 = 6 * @coeff3
complex const4 = 24 * @coeff4

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex z8 = complex z7 = complex z6 = complex z5 = complex z4 = (0,0)
complex z3 = complex z2 = complex z1 = (0,0) ; powers of the current z
complex funcresult = (0,0) ; result of function evaluation with current z
complex derivresult = (0,0) ; evaluation of derivative function with current z
complex deriv2result = (0,0) ; evaluation of 2nd derivative
complex deriv3result = (0,0) ; evaluation of 3rd derivative
complex deriv4result = (0,0) ; evaluation of 4th derivative
complex numerator = complex denominator = (0,0) ; for clarity in higher order methods
complex zquotient = (0,0) ; = numerator/denominator
complex f0f2 = (0,0) ; function result * 2nd derivative, saves a multiplication step
						; each iteration
complex funcresult2 = (0,0) ; square of funcresult, storing it saves steps each iter
complex derivresult2 = (0,0) ; square of derivresult
complex derivresult3 = (0,0) ; cube of derivresult
complex f0f1f2 = (0,0) ; function * derivative * 2nd derivative
complex f02f3 = (0,0) ; function squared * 3rd derivative

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
endif ; @eqselection

funcresult = @coeff8 * z8 + @coeff7 * z7 + @coeff6 * z6 + @coeff5 * z5 + @coeff4 * z4 + \
	@coeff3 * z3 + @coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 8 * @coeff8 * z7 + 7 * @coeff7 * z6 + 6 * @coeff6 * z5 + 5 * @coeff5 * z4 + 4 * @coeff4 * z3 + \
	3 * @coeff3 * z2 + const2 * z1 + @coeff1
if @method == "Newton"
	zquotient = -funcresult/derivresult
elseif @method == "Halley"
	deriv2result = 56 * @coeff8 * z6 + 42 * @coeff7 * z5 + 30 * @coeff6 * z4 + 20 * @coeff5 * z3 + \
		12 * @coeff4 * z2 + const3 * z1 + const2
	zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
elseif @method == "Order 3 Householder"
	deriv2result = 56 * @coeff8 * z6 + 42 * @coeff7 * z5 + 30 * @coeff6 * z4 + 20 * @coeff5 * z3 + \
		12 * @coeff4 * z2 + const3 * z1 + const2
	deriv3result = 336 * @coeff8 * z5 + 210 * @coeff7 * z4 + 120 * @coeff6 * z3 + 60 * @coeff5 * z2 + \
		const4 * z1 + const3
	f0f2 = funcresult * deriv2result
	zquotient = 3 * funcresult * (-2 * derivresult2 + f0f2) / (6 * derivresult3 - \
		6 * f0f2 * derivresult + sqr(funcresult) * deriv3result)
elseif @method == "Order 4 Householder"
	deriv2result = 56 * @coeff8 * z6 + 42 * @coeff7 * z5 + 30 * @coeff6 * z4 + 20 * @coeff5 * z3 + \
		12 * @coeff4 * z2 + const3 * z1 + const2
	deriv3result = 336 * @coeff8 * z5 + 210 * @coeff7 * z4 + 120 * @coeff6 * z3 + 60 * @coeff5 * z2 + \
		const4 * z1 + const3
	deriv4result = 1680 * @coeff8 * z4 + 840 * @coeff7 * z3 + 360 * @coeff6 * z2 + 120 * @coeff5 * z1 \
		+ const4
	funcresult2 = sqr(funcresult)
	derivresult2 = sqr(derivresult)
	derivresult3 = derivresult2 * derivresult
	f02f3 = funcresult2 * deriv3result
	f0f1f2 = funcresult * derivresult * deriv2result
	numerator = 4 * funcresult * (6 * derivresult3 - 6 * f0f1f2 + f02f3)
	denominator = derivresult * (-24 * derivresult3 + 36 * f0f1f2 - 8 * f02f3) + \
		funcresult2 * (-6 * sqr(deriv2result) + funcresult * deriv4result)
	zquotient = numerator/denominator
endif ; @method
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "GenDegree 8 (Comparison)"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param method
	caption = "Solving Method"
	enum = "Newton" "Halley" "Order 3 Householder" "Order 4 Householder"
	default = 1
	hint = "This parameter chooses between the various root-finding methods."
endparam
param coeff8
	caption = "Coefficient 8"
	default = (1,0)
	hint = "This parameter if the coefficient of the degree 8 z term."
endparam
param coeff7
	caption = "Coefficient 7"
	default = (1,0)
	hint = "This parameter if the coefficient of the degree 7 z term."
endparam
param coeff6
	caption = "Coefficient 6"
	default = (1,0)
	hint = "This parameter if the coefficient of the sextic z term."
endparam
param coeff5
	caption = "Coefficient 5"
	default = (2,0)
	hint = "This parameter if the coefficient of the quintic z term."
endparam
param coeff4
	caption = "Coefficient 4"
	default = (-3,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (1,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-explogHalley {
;
; Uses Halley's method to find the roots
; of exp(z)-log(z) + constant = 0.  Set the
; bailout value to some large number.
; jam 161121
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = deriv2result = (0,0)
complex zexp = complex zlog = complex zrecip = complex z2recip = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zworking + jc1)
	zlog = log(zworking)
	zrecip = 1/zworking
elseif @eqselection == 1
	zexp = exp(zworking)
	zlog = log(zworking + jc2)
	zrecip = 1/zworking
elseif @eqselection == 2
	zexp = exp(zworking)
	zlog = log(zworking)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 3
	zexp = exp(zworking + jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/zworking
elseif @eqselection == 4
	zexp = exp(zworking)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 5
	zexp = exp(zworking + jc1)
	zlog = log(zworking)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 6
	zexp = exp(zworking + jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 7
	zexp = exp(zworking * jc1)
	zlog = log(zworking)
	zrecip = 1/zworking
elseif @eqselection == 8
	zexp = exp(zworking)
	zlog = log(zworking * jc2)
	zrecip = 1/zworking
elseif @eqselection == 9
	zexp = exp(zworking)
	zlog = log(zworking)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 10
	zexp = exp(zworking * jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/zworking
elseif @eqselection == 11
	zexp = exp(zworking)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 12
	zexp = exp(zworking * jc1)
	zlog = log(zworking)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 13
	zexp = exp(zworking * jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 14
	zexp = exp(zworking + jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/zworking
elseif @eqselection == 15
	zexp = exp(zworking)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 16
	zexp = exp(zworking + jc1)
	zlog = log(zworking)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 17
	zexp = exp(zworking * jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/zworking
elseif @eqselection == 18
	zexp = exp(zworking)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 19
	zexp = exp(zworking * jc1)
	zlog = log(zworking)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 20
	zexp = exp(zworking + jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 21
	zexp = exp(zworking + jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 22
	zexp = exp(zworking + jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 23
	zexp = exp(zworking * jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking + jc3)
elseif @eqselection == 24
	zexp = exp(zworking * jc1)
	zlog = log(zworking + jc2)
	zrecip = 1/(zworking * jc3)
elseif @eqselection == 25
	zexp = exp(zworking * jc1)
	zlog = log(zworking * jc2)
	zrecip = 1/(zworking + jc3)
endif ; @eqselection

z2recip = sqr(zrecip)
funcresult = zexp - zlog + @const
derivresult = zexp - zrecip
deriv2result = zexp + z2recip
zquotient = (funcresult * derivresult) / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - log(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz4Halley {
;
; Uses Halley's method to find the roots
; of z^4 + az^3 + bz^2 + cz + d = 0.  Set the
; bailout value to some large number
; jam 161121

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex const2 = 2.0 * @coeff2

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex z4 = complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2)* jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2)
	z3 = z2 * z1 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) + jc2
	z3 = z2 * z1 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z4 = sqr(z2) * jc2
	z3 = z2 * z1 + jc3
endif ; @eqselection

funcresult = z4 + @coeff3 * z3 + @coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 4 * z3 + 3 * @coeff3 * z2 + const2 * z1 + @coeff1
deriv2result = 12 * z2 + 6 * @coeff3 * z1 + const2
zquotient = (funcresult * derivresult) / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 4 Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (3,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znsinzHalley { ; jam 161121
;
; Uses Halley's method to find the roots
; of z^n - sin(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powercoeff = @power * powerminus

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex znminus2 = (0,0)
complex zcos = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

znminus = znminus2 * zworking
zn = znminus * zworking
funcresult = zn - zsin + @const
derivresult = @power * znminus - zcos
deriv2result = powercoeff * znminus2 + zsin
zquotient = (funcresult * derivresult) / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - sin(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (4,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-eztanzHalley {
;
; Uses Halley's method to find the roots
; of exp(z)- tan(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zexp = complex ztan = complex ztan2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 1
	zexp = exp(zworking)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 2
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 3
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 4
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 5
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 6
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 7
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 8
	zexp = exp(zworking)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 9
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 10
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 11
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 12
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 13
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 14
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 15
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 16
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 17
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 18
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 19
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 20
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 21
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 22
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 23
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 24
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 25
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
endif ; @eqselection

funcresult = zexp - ztan + @const
derivresult = zexp - ztan2 - 1
deriv2result = zexp - 2 * ztan * (ztan2 + 1)
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - tan(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-e-ztanzHalley {
;
; Uses Halley's method to find the roots
; of exp(-z)- tan(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex zneg = -1 * zworking
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zexp = complex ztan = complex ztan2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zneg + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 1
	zexp = exp(zneg)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 2
	zexp = exp(zneg)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 3
	zexp = exp(zneg + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 4
	zexp = exp(zneg)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 5
	zexp = exp(zneg + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 6
	zexp = exp(zneg + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 7
	zexp = exp(zneg * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 8
	zexp = exp(zneg)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 9
	zexp = exp(zneg)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 10
	zexp = exp(zneg * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 11
	zexp = exp(zneg)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 12
	zexp = exp(zneg * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 13
	zexp = exp(zneg * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 14
	zexp = exp(zneg + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 15
	zexp = exp(zneg)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 16
	zexp = exp(zneg + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 17
	zexp = exp(zneg * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 18
	zexp = exp(zneg)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 19
	zexp = exp(zneg * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 20
	zexp = exp(zneg + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 21
	zexp = exp(zneg + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 22
	zexp = exp(zneg + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 23
	zexp = exp(zneg * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 24
	zexp = exp(zneg * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 25
	zexp = exp(zneg * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
endif ; @eqselection

funcresult = zexp - ztan + @const
derivresult = -zexp - ztan2 - 1
deriv2result = zexp - 2.0 * ztan * (ztan2 + 1)
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^(-z) - tan(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-ez-2asinHalley {
;
; Uses Halley's method to find the roots
; of exp(-(z^2))- arcsin(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex z2 = complex zasin = (0,0)
complex zez2 = complex zrecip = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 1
	z2 = sqr(zworking)
	zexp = exp(-z2 + jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 2
	z2 = sqr(zworking)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 3
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 4
	z2 = sqr(zworking)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 5
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 6
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 7
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 8
	z2 = sqr(zworking)
	zexp = exp(-z2 * jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 9
	z2 = sqr(zworking)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 10
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 11
	z2 = sqr(zworking)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 12
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 13
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 14
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 15
	z2 = sqr(zworking)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 16
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 17
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/sqrt(1-z2)
elseif @eqselection == 18
	z2 = sqr(zworking)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 19
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 20
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 21
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 22
	z2 = sqr(zworking + jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 23
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
elseif @eqselection == 24
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 + jc2)
	zrecip = 1/(sqrt(1-z2) * jc3)
elseif @eqselection == 25
	z2 = sqr(zworking * jc1)
	zexp = exp(-z2 * jc2)
	zrecip = 1/(sqrt(1-z2) + jc3)
endif ; @eqselection

zasin = asin(zworking)
funcresult = zexp - zasin + @const
derivresult = -2 * zworking * zexp - zrecip
deriv2result = -2 * zexp + 4 * z2 * zexp - zworking * (1-z2)^(-1.5)
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^(-z^2) - asin(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expsinHalley {
;
; Uses Halley's method to find the roots
; of exp(z)- m * sin(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zexp = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	zexp = exp(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zsin = sin(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	zexp = exp(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zsin = sin(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zsin = sin(zfreq * jc2)
endif ; @eqselection

zcos = cos(zfreq)
funcresult = zexp - @amplitude * zsin + @const
derivresult = zexp - @amplitude * zcos * @freq
deriv2result = zexp + @amplitude * sqr(@freq) * zsin
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - m*sin(nz) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Sine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the sine function."
endparam
param freq
	caption = "Sine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the sine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-exp-cosHalley {
;
; Uses Halley's method to find the roots
; of exp(z)- m * cos(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zexp = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	zexp = exp(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zcos = cos(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	zexp = exp(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zcos = cos(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	zexp = exp(zworking * jc1)
	zcos = cos(zfreq * jc2)
endif ; @eqselection

zsin = sin(zfreq)
funcresult = zexp - @amplitude * zcos + @const
derivresult = zexp + @amplitude * zsin * @freq
deriv2result = zexp + @amplitude * sqr(@freq) * zcos
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - m*cos(nz) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Cosine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the cosine function."
endparam
param freq
	caption = "Cosine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the cosine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expz2cosHalley {
;
; Uses Halley's method to find the roots
; of exp(z^2)- m * cos(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zexp = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)
complex z2 = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zcos = cos(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zcos = cos(zfreq * jc2)
endif ; @eqselection

zsin = sin(zfreq)
z2 = sqr(zworking)
funcresult = zexp - @amplitude * zcos + @const
derivresult = 2 * zworking * zexp + @amplitude * zsin * @freq
deriv2result = 2 * zexp + 4 * z2 * zexp + @amplitude * sqr(@freq) * zcos
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^(z^2)-m*cos(nz) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Cosine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the cosine function."
endparam
param freq
	caption = "Cosine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the cosine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expz2sinHalley {
;
; Uses Halley's method to find the roots
; of exp(z^2)- m * sin(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zexp = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)
complex z2 = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking))
	zsin = sin(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	zexp = exp(sqr(zworking) * jc1)
	zsin = sin(zfreq * jc2)
endif ; @eqselection

zcos = cos(zfreq)
z2 = sqr(zworking)
funcresult = zexp - @amplitude * zsin + @const
derivresult = 2 * zworking * zexp - @amplitude * zcos * @freq
deriv2result = 2 * zexp + 4 * z2 * zexp - @amplitude * sqr(@freq) * zsin
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^(z^2)-m*sin(nz) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Sine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the sine function."
endparam
param freq
	caption = "Sine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the sine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-expcosHalley { ; jam 161126
;
; Uses Halley's method to find the roots
; of exp(z)cos(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zexp = complex zcos = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zworking + jc1)
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	zexp = exp(zworking)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	zexp = exp(zworking)
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	zexp = exp(zworking + jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	zexp = exp(zworking)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	zexp = exp(zworking + jc1)
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	zexp = exp(zworking + jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	zexp = exp(zworking * jc1)
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	zexp = exp(zworking)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	zexp = exp(zworking)
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	zexp = exp(zworking * jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	zexp = exp(zworking)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	zexp = exp(zworking * jc1)
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	zexp = exp(zworking * jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	zexp = exp(zworking + jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	zexp = exp(zworking)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	zexp = exp(zworking + jc1)
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	zexp = exp(zworking * jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	zexp = exp(zworking)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	zexp = exp(zworking * jc1)
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	zexp = exp(zworking + jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	zexp = exp(zworking + jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	zexp = exp(zworking + jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	zexp = exp(zworking * jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	zexp = exp(zworking * jc1)
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	zexp = exp(zworking * jc1)
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

funcresult = zexp * zcos + @const
derivresult = zexp * (zcos - zsin)
deriv2result = -2 * zexp * zsin
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z * cos(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-ez2tanzHalley { ; jam 161126
;
; Uses Halley's method to find the roots
; of exp(z^2)tan(z) + constant = 0.  Set the
; bailout value to some large number. 
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zsqr = complex ezsqr = complex ztan = (0,0)
complex ztan2 = complex zworking2 = complex zplus1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking)
elseif @eqselection == 1
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking)
elseif @eqselection == 2
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr)
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking)
elseif @eqselection == 4
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking)
elseif @eqselection == 8
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking)
elseif @eqselection == 9
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr)
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking)
elseif @eqselection == 11
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking)
elseif @eqselection == 15
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking)
elseif @eqselection == 18
	zsqr = sqr(zworking)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr)
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	zsqr = sqr(zworking + jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	zsqr = sqr(zworking * jc1)
	ezsqr = exp(zsqr * jc2)
	ztan = tan(zworking + jc3)
endif ; @eqselection

ztan2 = sqr(ztan)
zworking2 = 2 * zworking
zplus1 = ztan2 + 1
funcresult = ezsqr * ztan + @const
derivresult = ezsqr * (zworking2 * ztan + zplus1)
deriv2result = ezsqr * (4 * zsqr * ztan + zworking2 * ztan2 + zworking2 + 2 * ztan + zworking2 * \
	zplus1 + 2 * ztan * zplus1)
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z^2 * tan(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz5Halley {
;
; Uses Halley's method to find the roots
; of z^5 + az^4 + bz^3 + cz^2 + dz + e = 0.  Set the
; bailout value to some large number
; jam 161126

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex twocoeff2 = 2 * @coeff2

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex z5 = complex z4 = complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2 + jc3
endif ; @eqselection

funcresult = z5 + @coeff4 * z4 + @coeff3 * z3 + @coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 5 * z4 + 4 * @coeff4 * z3 + 3 * @coeff3 * z2 + twocoeff2 * z1 + @coeff1
deriv2result = 20 * z3 + 12 * @coeff4 * z2 + 6 * @coeff3 * z1 + twocoeff2
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 5 Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff4
	caption = "Coefficient 4"
	default = (1,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (3,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz6Halley {
;
; Uses Halley's method to find the roots
; of z^6 + az^5 + bz^4 + cz^3 + dz^2 + ez + f = 0.  Set the
; bailout value to some large number
; jam 161117

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex twocoeff2 = 2 * @coeff2

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex z6 = complex z5 = complex z4 = complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2 + jc3
endif ; @eqselection

funcresult = z6 + @coeff5 * z5 + @coeff4 * z4 + @coeff3 * z3 + @coeff2 * z2 + \
	@coeff1 * z1 + @constant
derivresult = 6 * z5 + 5 * @coeff5 * z4 + 4 * @coeff4 * z3 + 3 * @coeff3 * z2 + \
	twocoeff2 * z1 + @coeff1
deriv2result = 30 * z4 + 20 * @coeff5 * z3 + 12 * @coeff4 * z2 + 6 * @coeff3 * z1 + \
	twocoeff2
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 6 Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff5
	caption = "Coefficient 5"
	default = (2,0)
	hint = "This parameter if the coefficient of the quintic z term."
endparam
param coeff4
	caption = "Coefficient 4"
	default = (-3,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (1,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz7Halley {
;
; Uses Halley's method to find the roots
; of z^7 + az^6 + bz^5 + cz^4 + dz^3 + ez^2 + fz + g = 0.
;   Set the bailout value to some large number
; jam 161206

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex twocoeff2 = 2 * @coeff2

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex z7 = complex z6 = complex z5 = complex z4 = complex z3 = (0,0)
complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3 + jc3
endif ; @eqselection

funcresult = z7 + @coeff6 * z6 + @coeff5 * z5 + @coeff4 * z4 + @coeff3 * z3 + \
	@coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 7 * z6 + 6 * @coeff6 * z5 + 5 * @coeff5 * z4 + 4 * @coeff4 * z3 + \
	3 * @coeff3 * z2 + twocoeff2 * z1 + @coeff1
deriv2result = 42 * z5 + 30 * @coeff6 * z4 + 20 * @coeff5 * z3 + 12 * @coeff4 * z2 \
	+ 6 * @coeff3 * z1 + twocoeff2
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 7 Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff6
	caption = "Coefficient 6"
	default = (1,0)
	hint = "This parameter if the coefficient of the sextic z term."
endparam
param coeff5
	caption = "Coefficient 5"
	default = (2,0)
	hint = "This parameter if the coefficient of the quintic z term."
endparam
param coeff4
	caption = "Coefficient 4"
	default = (-3,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (1,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-genz8Halley2 {
;
; Uses Halley's method to find the roots
; of z^8 + az^7 + bz^6 + cz^5 + dz^4 + ez^3 + fz^2 + gz + h = 0.
;   Set the bailout value to some large number
; jam 161206

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex twocoeff2 = 2 * @coeff2

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; 'Explore Mode' is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex z8 = complex z7 = complex z6 = complex z5 = complex z4 = (0,0)
complex z3 = complex z2 = complex z1 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 1
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 2
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 3
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 4
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 5
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 6
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 7
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 8
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 9
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 10
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 11
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)* jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 12
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 13
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 14
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 15
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 16
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 17
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4)
elseif @eqselection == 18
	z1 = zworking
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 19
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2)
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 20
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 21
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 22
	z1 = zworking + jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 23
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
elseif @eqselection == 24
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) + jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) * jc3
elseif @eqselection == 25
	z1 = zworking * jc1
	z2 = sqr(z1)
	z3 = z2 * z1
	z4 = sqr(z2) * jc2
	z5 = z3 * z2
	z6 = z4 * z2
	z7 = z4 * z3
	z8 = sqr(z4) + jc3
endif ; @eqselection

funcresult = z8 + @coeff7 * z7 + @coeff6 * z6 + @coeff5 * z5 + @coeff4 * z4 + \
	@coeff3 * z3 + @coeff2 * z2 + @coeff1 * z1 + @constant
derivresult = 8 * z7 + 7 * @coeff7 * z6 + 6 * @coeff6 * z5 + 5 * @coeff5 * z4 + 4 * @coeff4 * z3 + \
	3 * @coeff3 * z2 + twocoeff2 * z1 + @coeff1
deriv2result = 56 * z6 + 42 * @coeff7 * z5 + 30 * @coeff6 * z4 + 20 * @coeff5 * z3 + \
	12 * @coeff4 * z2 + 6 * @coeff3 * z + twocoeff2
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "General Degree 8 Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param coeff7
	caption = "Coefficient 7"
	default = (1,0)
	hint = "This parameter if the coefficient of the degree 7 z term."
endparam
param coeff6
	caption = "Coefficient 6"
	default = (1,0)
	hint = "This parameter if the coefficient of the sextic z term."
endparam
param coeff5
	caption = "Coefficient 5"
	default = (2,0)
	hint = "This parameter if the coefficient of the quintic z term."
endparam
param coeff4
	caption = "Coefficient 4"
	default = (-3,0)
	hint = "This parameter if the coefficient of the quartic z term."
endparam
param coeff3
	caption = "Coefficient 3"
	default = (3,0)
	hint = "This parameter if the coefficient of the cubic z term."
endparam
param coeff2
	caption = "Coefficient 2"
	default = (1,0)
	hint = "This parameter if the coefficient of the quadratic z term."
endparam
param coeff1
	caption = "Coefficient 1"
	default = (-2,0)
	hint = "This parameter if the coefficient of the linear z term."
endparam
param constant
	caption = "Constant Term"
	default = (-1,0)
	hint = "This parameter is the constant term in the quadratic equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-tancosHalley {
;
; Uses Halley's method to find the roots
; of tan(z)- m * cos(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex freq2 = sqr(@freq)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex ztan = complex ztan2 = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	ztan = tan(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zcos = cos(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	ztan = tan(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zcos = cos(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zcos = cos(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zcos = cos(zfreq * jc2)
endif ; @eqselection

zsin = sin(zfreq)
ztan2 = sqr(ztan)
funcresult = ztan - @amplitude * zcos + @const
derivresult = 1 + ztan2 + @amplitude * zsin * @freq
deriv2result = 2 * ztan * (1 + ztan2) + @amplitude * freq2 * zcos
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "tan(z) - m*cos(nz) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Cosine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the cosine function."
endparam
param freq
	caption = "Cosine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the cosine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-tansinHalley {
;
; Uses Halley's method to find the roots
; of tan(z)- m * sin(nz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex freq2 = sqr(@freq)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex ztan = complex ztan2 = complex zsin = complex zcos = (0,0)
complex zfreq = complex zamp = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 1
	zfreq = @freq*zworking
	ztan = tan(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 2
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zsin = sin(zfreq)
elseif @eqselection == 3
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 4
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 5
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 6
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 7
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 8
	zfreq = @freq*zworking
	ztan = tan(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 9
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zsin = sin(zfreq)
elseif @eqselection == 10
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 11
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 12
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 13
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 14
	zfreq = @freq*zworking
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 15
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 16
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq)
elseif @eqselection == 17
	zfreq = @freq*zworking
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 18
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 19
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq)
elseif @eqselection == 20
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 21
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 22
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking + jc1)
	zsin = sin(zfreq * jc2)
elseif @eqselection == 23
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 24
	zfreq = @freq*zworking * jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq + jc2)
elseif @eqselection == 25
	zfreq = @freq*zworking + jc3
	ztan = tan(zworking * jc1)
	zsin = sin(zfreq * jc2)
endif ; @eqselection

zcos = cos(zfreq)
ztan2 = sqr(ztan)
funcresult = ztan - @amplitude * zsin + @const
derivresult = 1 + ztan2 - @amplitude * zcos * @freq
deriv2result = 2 * ztan * (1 + ztan2) + @amplitude * freq2 * zsin
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "tan(z) - m*sin(nz) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param amplitude
	caption = "Sine Amplitude"
	default = (4,0)
	hint = "This parameter sets the amplitude,'m' of the sine function."
endparam
param freq
	caption = "Sine Frequency"
	default = (4,0)
	hint = "This parameter sets the frequency,'n' of the sine function."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncoszHalley { ; jam 161206
;
; Uses Halley's method to find the roots
; of z^n - cos(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powerpowerminus = powerminus * @power

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex znminus2 = (0,0)
complex zcos = complex zsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

znminus = znminus2 * zworking
zn = znminus * zworking
funcresult = zn - zcos + @const
derivresult = @power * znminus + zsin
deriv2result = powerpowerminus * znminus2 + zcos
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - cos(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncotzHalley { ; jam 161206
;
; Uses Halley's method to find the roots
; of z^n - cotan(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powerpowerminus = powerminus * @power

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex znminus2 = (0,0)
complex zcot = complex zcot2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	znminus = zworking * znminus2
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	znminus = zworking * znminus2
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	znminus = zworking * znminus2
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	znminus = zworking * znminus2
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	znminus = zworking * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	znminus = zworking * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	znminus = zworking * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	znminus = zworking * znminus2
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	znminus = (zworking + jc2) * znminus2
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	znminus = (zworking * jc2) * znminus2
	zcot = cotan(zworking + jc3)
endif ; @eqselection

zn = znminus * zworking
zcot2 = sqr(zcot)
funcresult = zn - zcot + @const
derivresult = @power * znminus + zcot2 + 1
deriv2result = powerpowerminus * znminus2 - 2 * zcot * (1 + zcot2)
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - cotan(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncrdzHalley { ; jam 161207
;
; Uses Halley's method to find the roots
; of z^n - crd(z) + constant = 0 (chord function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powerpowerminus = powerminus * @power

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex zhalf = complex znminus2 = (0,0)
complex zsin = complex zcos = complex zcrd = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2)
	zcos = cos(zworking/2)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2)
	zcos = cos(zworking/2)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2 + jc2)
	zcos = cos(zworking/2 * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking/2 * jc2)
	zcos = cos(zworking/2 + jc3)
endif ; @eqselection

znminus = znminus2 * zworking
zn = znminus * zworking
zcrd = 2 * zsin
funcresult = zn - zcrd + @const
derivresult = @power * znminus - zcos
deriv2result = powerpowerminus * znminus2 + 0.5 * zsin
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - crd(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (3,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncsczHalley { ; jam 161207
;
; Uses Halley's method to find the roots
; of z^n - csc(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powerpowerminus = powerminus * @power

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex zcot = complex zcot2 = (0,0)
complex zcsc = complex zsin = complex znminus2 = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
endif ; @eqselection

znminus = znminus2 * zworking
zn = znminus * zworking
zcsc = 1/zsin
zcot2 = sqr(zcot)
funcresult = zn - zcsc + @const
derivresult = @power * znminus + zcsc * zcot
deriv2result = powerpowerminus * znminus2 - 2 * (zcsc * zcot2) - zcsc
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - csc(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-eztanzHouse3 {
;
; Uses 3rd-order Householder's method to find the roots
; of exp(z)- tan(z) + constant = 0.  Set the
; bailout value to some large number.
; jam 161207

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zexp = complex ztan = complex ztan2 = (0,0)
complex deriv3result = complex ztan2p1 = (0,0)
complex zquotient = complex f0f2 = (0,0)
complex derivresult2 = complex derivresult3 = (0,0)

loop:
if @eqselection == 0
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 1
	zexp = exp(zworking)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 2
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 3
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 4
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 5
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 6
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 7
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan)
elseif @eqselection == 8
	zexp = exp(zworking)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 9
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 10
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 11
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 12
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 13
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 14
	zexp = exp(zworking + jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 15
	zexp = exp(zworking)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 16
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 17
	zexp = exp(zworking * jc1)
	ztan = tan(zworking)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 18
	zexp = exp(zworking)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 19
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan)
elseif @eqselection == 20
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 21
	zexp = exp(zworking + jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 22
	zexp = exp(zworking + jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
elseif @eqselection == 23
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 24
	zexp = exp(zworking * jc1)
	ztan = tan(zworking * jc3)
	ztan2 = sqr(ztan + jc2)
elseif @eqselection == 25
	zexp = exp(zworking * jc1)
	ztan = tan(zworking + jc3)
	ztan2 = sqr(ztan * jc2)
endif ; @eqselection

ztan2p1 = ztan2 + 1
funcresult = zexp - ztan + @const
derivresult = zexp - ztan2p1
deriv2result = zexp - 2 * ztan * ztan2p1
deriv3result = zexp - 2 * sqr(ztan2p1) - 4 * ztan2 * ztan2p1
f0f2 = funcresult * deriv2result
derivresult2 = sqr(derivresult)
derivresult3 = derivresult2 * derivresult
zquotient = 3 * funcresult * (-2 * derivresult2 + f0f2) / (6 * derivresult3 - \
	6 * f0f2 * derivresult + sqr(funcresult) * deriv3result)
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "e^z - tan(z) + c House3"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncvczHalley { ; jam 161207
;
; Uses Halley's method to find the roots
; of z^n - cvc(z) + constant = 0 (covercosine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powerpowerminus = powerminus * @power

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex znminus2 = (0,0)
complex zsin = complex zcos = complex zcvc = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

znminus = znminus2 * zworking
zn = znminus * zworking
zcvc = 1 + zsin
funcresult = zn - zcvc + @const
derivresult = @power * znminus - zcos
deriv2result = powerpowerminus * znminus2 + zsin
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - cvc(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (3,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-zncvszHalley { ; jam 161207
;
; Uses Halley's method to find the roots
; of z^n - cvs(z) + constant = 0 (coversine function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powerpowerminus = powerminus * @power

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex znminus2 = (0,0)
complex zsin = complex zcos = complex zcvs = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcos = cos(zworking + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcos = cos(zworking * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcos = cos(zworking + jc3)
endif ; @eqselection

znminus = znminus2 * zworking
zn = znminus * zworking
zcvs = 1 - zsin
funcresult = zn - zcvs + @const
derivresult = @power * znminus + zcos
deriv2result = powerpowerminus * znminus2 - zsin
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - cvs(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (4,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znexczHalley { ; jam 161207
;
; Uses Halley's method to find the roots
; of z^n - exc(z) + constant = 0 (excosecant function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powerpowerminus = powerminus * @power

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex znminus2 = complex zcot = (0,0)
complex zsin = complex zcsc = complex zexc = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking + jc2)
	zcot = cotan(zworking * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	zsin = sin(zworking * jc2)
	zcot = cotan(zworking + jc3)
endif ; @eqselection

znminus = znminus2 * zworking
zn = znminus * zworking
zcsc = 1/zsin
zexc - zcsc - 1
funcresult = zn - zexc + @const
derivresult = @power * znminus + zcsc * zcot
deriv2result = powerpowerminus * znminus2 - zcsc * (2 * sqr(zcot) + 1)
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - exc(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-znexszHalley { ; jam 161207
;
; Uses Halley's method to find the roots
; of z^n - exs(z) + constant = 0 (exsecant function).  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)
complex powerminus = @power - (1,0)
complex powerminus2 = powerminus - (1,0)
complex powerpowerminus = powerminus * @power

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = complex deriv2result = (0,0)
complex zn = complex znminus = complex znminus2 = complex ztan = (0,0)
complex zcos = complex zsec = complex zexs = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 1
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 2
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 3
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 4
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 5
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 6
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 7
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	ztan = tan(zworking)
elseif @eqselection == 8
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 9
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 10
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 11
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 12
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 13
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 14
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking)
elseif @eqselection == 15
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 16
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking)
	ztan = tan(zworking * jc3)
elseif @eqselection == 17
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking)
elseif @eqselection == 18
	znminus2 = (zworking)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 19
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking)
	ztan = tan(zworking + jc3)
elseif @eqselection == 20
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 21
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 22
	znminus2 = (zworking + jc1)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 23
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking + jc3)
elseif @eqselection == 24
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking + jc2)
	ztan = tan(zworking * jc3)
elseif @eqselection == 25
	znminus2 = (zworking * jc1)^powerminus2
	zcos = cos(zworking * jc2)
	ztan = tan(zworking + jc3)
endif ; @eqselection

znminus = znminus2 * zworking
zn = znminus * zworking
zsec = 1/zcos
zexs - zsec - 1
funcresult = zn - zexs + @const
derivresult = @power * znminus - zsec * ztan
deriv2result = powerpowerminus * znminus2 - zsec * (2 * sqr(ztan) + 1)
zquotient = funcresult * derivresult / (0.5 * funcresult * deriv2result - sqr(derivresult))
zworking = zworking + zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "z^n - exs(z) + c Halley"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param power
	caption = "Exponent"
	default = (2,0)
	hint = "This is the power to which #z will be raised."
endparam
param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-coszverzNwt { ; jam 161219
;
; Uses Newton's method to find the roots
; of cos(z) - ver(z) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zcos = complex zsin = complex zver = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	zcos = cos(zworking)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 2
	zcos = cos(zworking)
	zver = 1 - cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 3
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 4
	zcos = cos(zworking)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 5
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 6
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 7
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking)
	zsin = sin(zworking)
elseif @eqselection == 8
	zcos = cos(zworking)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 9
	zcos = cos(zworking)
	zver = 1 - cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 10
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 11
	zcos = cos(zworking)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 12
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 13
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 14
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking)
elseif @eqselection == 15
	zcos = cos(zworking)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 16
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking)
	zsin = sin(zworking * jc3)
elseif @eqselection == 17
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking)
elseif @eqselection == 18
	zcos = cos(zworking)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 19
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking)
	zsin = sin(zworking + jc3)
elseif @eqselection == 20
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 21
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 22
	zcos = cos(zworking + jc1)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 23
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking + jc3)
elseif @eqselection == 24
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking + jc2)
	zsin = sin(zworking * jc3)
elseif @eqselection == 25
	zcos = cos(zworking * jc1)
	zver = 1 - cos(zworking * jc2)
	zsin = sin(zworking + jc3)
endif ; @eqselection

funcresult = zcos - zver + @const
derivresult = -2 * zsin
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "cos(z) - ver(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}

jam-sinexpcosNwt { ; jam 170524
;
; Uses Newton's method to find the roots
; of sin(e^-z) * sin(e^z) - cos(mz) + constant = 0.  Set the
; bailout value to some large number.
;

global:
complex jc1 = complex jc2 = complex jc3 = (0,0)

; fix the jc's for those that are multiplicative rather than additive
if !@explore
	if @eqselection == 7
		jc1 = (1,0)
	elseif @eqselection == 8
		jc2 = (1,0)
	elseif @eqselection == 9
		jc3 = (1,0)
	elseif @eqselection == 10
		jc1 = (1,0), jc2 = (1,0)
	elseif @eqselection == 11
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 12
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 13
		jc1 = (1,0), jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 14
		jc2 = (1,0)
	elseif @eqselection == 15
		jc3 = (1,0)
	elseif @eqselection == 16
		jc3 = (1,0)
	elseif @eqselection == 17
		jc1 = (1,0)
	elseif @eqselection == 18
		jc2 = (1,0)
	elseif @eqselection == 19
		jc1 = (1,0)
	elseif @eqselection == 20
		jc2 = (1,0), jc3 = (1,0)
	elseif @eqselection == 21
		jc3 = (1,0)
	elseif @eqselection == 22
		jc2 = (1,0)
	elseif @eqselection == 23
		jc1 = (1,0)
	elseif @eqselection == 24
		jc1 = (1,0), jc3 = (1,0)
	elseif @eqselection == 25
		jc1 = (1,0), jc2 = (1,0)
	endif ; @eqselection
else ; Explore Mode is enabled
	jc1 = @jconstant1
	jc2 = @jconstant2
	jc3 = @jconstant3
endif ; @explore

init:
complex zworking = #pixel
complex funcresult = complex derivresult = (0,0)
complex zcos = complex zsin = complex zexp = complex zmexp = (0,0)
complex zmsin = (0,0)
complex zquotient = (0,0)

loop:
if @eqselection == 0
	zcos = cos(zworking + jc1)
	zexp = exp(zworking)
	zsin = sin(zworking)
elseif @eqselection == 1
	zcos = cos(zworking)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp)
elseif @eqselection == 2
	zcos = cos(zworking)
	zexp = exp(zworking)
	zsin = sin(zexp + jc3)
elseif @eqselection == 3
	zcos = cos(zworking + jc1)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp)
elseif @eqselection == 4
	zcos = cos(zworking)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp + jc3)
elseif @eqselection == 5
	zcos = cos(zworking + jc1)
	zexp = exp(zworking)
	zsin = sin(zexp + jc3)
elseif @eqselection == 6
	zcos = cos(zworking + jc1)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp + jc3)
elseif @eqselection == 7
	zcos = cos(zworking * jc1)
	zexp = exp(zworking)
	zsin = sin(zexp)
elseif @eqselection == 8
	zcos = cos(zworking)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp)
elseif @eqselection == 9
	zcos = cos(zworking)
	zexp = exp(zworking)
	zsin = sin(zexp * jc3)
elseif @eqselection == 10
	zcos = cos(zworking * jc1)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp)
elseif @eqselection == 11
	zcos = cos(zworking)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp * jc3)
elseif @eqselection == 12
	zcos = cos(zworking * jc1)
	zexp = exp(zworking)
	zsin = sin(zexp * jc3)
elseif @eqselection == 13
	zcos = cos(zworking * jc1)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp * jc3)
elseif @eqselection == 14
	zcos = cos(zworking + jc1)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp)
elseif @eqselection == 15
	zcos = cos(zworking)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp * jc3)
elseif @eqselection == 16
	zcos = cos(zworking + jc1)
	zexp = exp(zworking)
	zsin = sin(zexp * jc3)
elseif @eqselection == 17
	zcos = cos(zworking * jc1)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp)
elseif @eqselection == 18
	zcos = cos(zworking)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp + jc3)
elseif @eqselection == 19
	zcos = cos(zworking * jc1)
	zexp = exp(zworking)
	zsin = sin(zexp + jc3)
elseif @eqselection == 20
	zcos = cos(zworking + jc1)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp * jc3)
elseif @eqselection == 21
	zcos = cos(zworking + jc1)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp * jc3)
elseif @eqselection == 22
	zcos = cos(zworking + jc1)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp + jc3)
elseif @eqselection == 23
	zcos = cos(zworking * jc1)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp + jc3)
elseif @eqselection == 24
	zcos = cos(zworking * jc1)
	zexp = exp(zworking + jc2)
	zsin = sin(zexp * jc3)
elseif @eqselection == 25
	zcos = cos(zworking * jc1)
	zexp = exp(zworking * jc2)
	zsin = sin(zexp + jc3)
endif ; @eqselection

zmexp = exp(-z)
zmsin = sin(zmexp)
funcresult = zsin * zmsin - zcos + @const
derivresult = zexp*cos(zexp)*zmsin - zmexp*zsin*cos(zmexp) + zsin
zquotient = funcresult/derivresult
zworking = zworking - zquotient

#z = 1/zquotient

bailout:
|#z| < @bailout

default:
title = "sin(exp(z))*sin(exp(-z)) - cos(z) + c"
maxiter = 1000
periodicity = 0
method = multipass
center = (0,0)
magn = 1.0
angle = 0.0

param const
	caption = "Constant Term"
	default = (0,0)
	hint = "This parameter is the constant term of the equation."
endparam
param explore
	caption = "Explore Mode"
	default = FALSE
	hint = "When enabled, the 'Equation Selection' options use the values set in parameters \
		'Seed 1', 'Seed 2', and 'Seed 3' rather than the default, built-in \
		values.  Use the Explore tool to find interesting values.  Not \
		all 'Equation Selection' options are affected by every 'Seed' \
		constant."
endparam
param eqselection
	caption = "Equation Selection"
	enum = "0" "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"
	default = 0
	hint = "This parameter selects which modification of the equation to iterate.  \
		If 'Explore Mode' is NOT enabled, then all these 'Equation Selection' options \
		use the same internal defaults and yield the same results."
	visible = @explore
endparam
param jconstant1
	caption = "Seed 1"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 1' is used in 'Equation \
		Selection' options 0, 3, 5, 6, 7, 10, 12, 13, 14, 16, 17, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant2
	caption = "Seed 2"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 2' is used in 'Equation \
		Selection' options 1, 3, 4, 6, 8, 10, 11, 13, 14, 15, 17, 18, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param jconstant3
	caption = "Seed 3"
	default = (0,0)
	hint = "This seed is used for some of the 'Equation Selection' options \
		if parameter 'Explore Mode' is enabled.  'Seed 3' is used in 'Equation \
		Selection' options 2, 4, 5, 6, 9, 11, 12, 13, 15, 16, 18, 19, 20, \
		21, 22, 23, 24, and 25."
	visible = @explore
endparam
param bailout
	caption = "Bailout Value"
	default = 100.0
	min = 0.0
	hint = "Use a large bailout value."
endparam
}