;These formulas have been taken from Standard.ufm and
;have been modified by Michael W. Brown and Sharon S.
;Schultz. The credit for making the new functions work
;goes to Sharon herself.


MandelbrotChanged+SSS {
;
; This is an experiment on the M-Set by Michael W. Brown.
; Modified by Sharon S. Schultz, June, 2004.

init:
  z = @start

loop:
  z = fn1(fn2(fn3(z^@power + #pixel)* @factor/(@divisor)))
bailout:
  |z| <= @bailout

default:
  title = "Mandelbrot Changed + SSS"
  method = multipass
  periodicity = 0
  maxiter = 100
  center = (-0.5, 0)
  helpfile = "Uf3.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
  
heading
  caption = "Parameters"
endheading  

param bailout
  caption = "Bailout value"
  default = 4.0
  min = 0
  hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
         to the Mandelbrot set anymore."
endparam
param start
  caption = "Starting Point"
  default = (0.0,0.0)
  hint = "Perturbation. Use (0,0) for the standard Mandelbrot set."
endparam
param divisor
  caption = "Divisor"
  default = (1.0,0.0)
  hint = "A parameter"
endparam
param factor
  caption = "Factor"
  default = 1.0
  hint = "Does *something*"
endparam
param power
  caption = "Power"
  default = (2.0,0.0)
  hint = "This defines the power of the Mandelbrot set. Use (2,0) \
         for the standard Mandelbrot set."
endparam

heading
  caption = "Functions"
endheading

func fn1
  caption = "Change"
  default = ident()
  hint = "Select a function to change the formula."
endfunc
func fn2
  caption = "Change More"
  default = ident()
  hint = "Select a function to change the formula more."
endfunc
func fn3
  caption = "Total change"
  default = ident()
  hint = "Select a function to totally change the formula."
endfunc 

switch:
  type = "JuliaChanged+SSS"
  seed = #pixel
  power = power
  factor = factor
  bailout = bailout
  divisor = divisor
  fn1 = fn1
  fn2 = fn2
  fn3 = fn3
}

JuliaChanged+SSS {
;
; Modified Julia Set.
; Modified by Sharon S. Schultz, June, 2004.

init:
  z = #pixel

loop:
  z = fn1(fn2(fn3(z^@power + @seed)*@factor/(@divisor)))

bailout:
  |z| <= @bailout

default:
  title = "Julia Changed + SSS"
  method = multipass
  periodicity = 0
  maxiter = 100
  helpfile = "Uf3.chm"
  helptopic = "Html\formulas\standard\julia.html"
  
heading
  caption = "Parameters"
endheading

float param bailout
  caption = "Bailout value"
  default = 4.0
  min = 1.0
  hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
         to the Mandelbrot set anymore."
endparam
complex param seed
  caption = "Julia Seed"
  default = (-1.25, 0.00)
  hint = "Use this to create many different Julia sets. You can \
         also set this value using the Switch feature."
endparam
complex param power
  caption = "Power"
  default = (2.0,0.0)
  hint = "This defines the power of the Julia set. Use (2,0) \
         for the standard Julia set."
endparam
float param factor
  caption = "Factor"
  default = 1.0
  hint = "Does *something*"
endparam
float param divisor
  caption = "Divisor"
  default = 1.0
  hint = "A parameter"
endparam

heading
  caption = "Functions"
endheading

func fn1
  caption = "Change"
  default = ident()
  hint = "Select a function to change the formula."
endfunc
func fn2
  caption = "Change More"
  default = ident()
  hint = "Select a function to change the formula more."
endfunc
func fn3
  caption = "Total change"
  default = ident()
  hint = "Select a function to totally change the formula."
endfunc 

switch:
  type = "MandelbrotChanged+SSS"
  power = power
  factor = factor
  divisor = divisor
  bailout = bailout
  fn1 = fn1
  fn2 = fn2
  fn3 = fn3
}


{
; Here, you can describe the fractal formula. This text
; will appear in the browsers as comments.
; For more information about fractal formulas, look up
; "writing fractal formulas" in the online help index.
global:
; This section is executed once per image. This is a good
; place for initializing variables and precalculating tables.
; Variables declared here will be read-only in the rest of
; the coloring algorithm.
  
init:
; The code in this section is executed once per pixel, before
; the iteration loop is entered. It should set up variables
; used in the loop: section.
  
loop:
; The code in this section is repeatedly executed, until
; either the maximum iteration count has been reached (then
; the pixel being computed is considered to be inside), or
; the boolean expression in the bailout: section becomes
; false (then the pixel is considered to be outside).
  
bailout:
; This section should contain a boolean expression, such as
; |z| < 4. When this expression becomes false, the iteration
; loop is stopped, and the pixel is considered to be outside.
  
default:
; This section contains default settings that make the
; fractal formula and its parameters easier to use.
  title = "odified by Sharon S. Schultz, June, 2004."
switch:
; This section is optional and can be used to specify a formula
; in the same file that forms a switch pair with this formula.
; This is the case for example with Mandelbrot and Julia sets.
}

Formula1J {
;Written March 2005 for UF3 by Michael W. Brown
;A modified version of the Julia Set.
;Change "Operator" to None to get the standard set.
global:

init:

  z = #pixel
    
loop:
 
  IF(@oper==0)
  z = z^@power + @seed + z^@fn1(z)
  ELSEIF(@oper==1)
  z = z^@power + @seed - z^@fn1(z)
  ELSEIF(@oper==2)
  z = z^@power + @seed * z^@fn1(z)
  ELSEIF(@oper==3)
  z = z^@power + @seed / z^@fn1(z)
  ELSEIF(@oper==4)
  z = z^@power + @seed
  ENDIF
  
  IF(@use_inv == true)
  invZ = 1/z
  ELSE
  invZ = 0
  ENDIF
  z = z + invZ
  
bailout:
  
  |z| < @bailout

default:

    param seed
    caption = "Julia Seed"
    default = (-1.25,0)
    endparam

    float param bailout
      caption = "Bailout"  
      default = 4
      min = 0
    endparam
  
    func fn1
    caption = "Primary Function"
    default = ident()
    endfunc
    
    param power
      caption = "Power"
      default = (2,0)
    endparam
    
    param oper
      caption = "Operator"
      default = 0
      enum = "+""-""*""/""None (Mandelbrot)"
    endparam
    
    bool param use_inv
      caption = "Add inverse?"
      default = false
    endparam
    
switch:
type = "Formula1M"
power = power
bailout = bailout
fn1 = fn1
use_inv = use_inv
oper = oper
}

Formula1M {
;Written March 2005 for UF3 by Michael W. Brown
;A modified version of the Mandelbrot Set.
;Change "Operator" to None to get the standard set.
global:

init:
;Z Initialization testing
  IF(@zINIT==0)
    z = #pixel
  ELSEIF(@zINIT==1)
    z = @start
  ENDIF
loop:
 
  IF(@oper==0)
  z = z^@power + #pixel + z^@fn1(z)
  ELSEIF(@oper==1)
  z = z^@power + #pixel - z^@fn1(z)
  ELSEIF(@oper==2)
  z = z^@power + #pixel * z^@fn1(z)
  ELSEIF(@oper==3)
  z = z^@power + #pixel / z^@fn1(z)
  ELSEIF(@oper==4)
  z = fn1(z^@power) + #pixel
  ENDIF
  
  IF(@use_inv == true)
  invZ = 1/z
  ELSE
  invZ = 0
  ENDIF
  z = z + invZ
  
bailout:
  
  |z| < @bailout

default:
  
    param zINIT
    caption = "z Initialization"
    default = 0
    enum = "#pixel""Starting Point"
    endparam

    float param bailout
      caption = "Bailout"  
      default = 4
      min = 0
    endparam
  
    func fn1
    caption = "Primary Function"
    default = ident()
    endfunc
    
    param power
      caption = "Power"
      default = (2,0)
    endparam
    
    param oper
      caption = "Operator"
      default = 0
      enum = "+""-""*""/""None (Mandelbrot)"
    endparam
    
    bool param use_inv
      caption = "Add inverse?"
      default = false
    endparam
    
    param start
    visible = (@zINIT==1)
    caption = "Starting Point"
    default=(0,0)
    endparam    
switch:
type = "Formula1J"
seed = #pixel
fn1 = fn1
use_inv = use_inv
oper = oper
power = power
bailout = bailout
}

Formula2J {
global:
  
init:
  z = #pixel
  

loop:

    IF(@numeroper==0)
    numerator = (@n1+z)
  ELSEIF(@numeroper==1)
    numerator = (@n1-z)
  ELSEIF(@numeroper==2)
    numerator = (z-@n1)
  ELSEIF(@numeroper==3)
    numerator = (@n1*z)
  ELSEIF(@numeroper==4)
    numerator = (@n1/z)
  ELSEIF(@numeroper==5)
    numerator = (z/@n1)
  ELSEIF(@numeroper==6)
    numerator = (@n1^z)
  ELSEIF(@numeroper==7)
    numerator = (z^@n1)
  ELSE
    numerator = 0
  ENDIF
  
    IF(@denomoper==0)
    denominator = (@n2+z)
  ELSEIF(@denomoper==1)
    denominator = (@n2-z)
  ELSEIF(@denomoper==2)
    denominator = (z-@n2)
  ELSEIF(@denomoper==3)
    denominator = (@n2*z)
  ELSEIF(@denomoper==4)
    denominator = (@n2/z)
  ELSEIF(@denomoper==5)
    denominator = (z/@n2)
  ELSEIF(@denomoper==6)
    denominator = (@n2^z)
  ELSEIF(@denomoper==7)
    denominator = (z^@n2)
  ELSE
    denominator = 0
  ENDIF

  
  z = @fn1(numerator)/@fn2(denominator) + @seed

  
bailout:
  |z| <= real(@bailout)
default:
  title = "Formula2J"
  
  param seed
  caption = "Julia Seed"
  default = (-1.25,0)
  endparam
  
  float param bailout
  caption = "Bailout"
  default = 50
  min = 0
  endparam
  
  param numeroper
  caption = "Numerator Operator"
  enum = "n1+z""n1-z""z-n1""n1*z""n1/z""z/n1""n1^z""z^n1"
  default = 0
  endparam
  
  param denomoper
  caption = "Denomiator Operator"
  enum = "n2+z""n2-z""z-n2""n2*z""n2/z""z/n2""n2^z""z^n2"
  default = 0
  endparam
  
  func fn1
  caption = "Numerator Function"
  default = ident()
  endfunc
  
  func fn2
  caption = "Denomerator Function"
  default = ident()
  endfunc
  
  float param n1
  caption = "Numerator Binomial (n1)"
  hint = "Specifies the number in the numerator"
  default = 1.0
  endparam
  
  float param n2
  caption = "Denominator Binomial (n2)"
  hint = "Specifies the number in the denominator"
  endparam  
switch:
type = "Formula2M"
n1 = n1
n2 = n2
fn1 = fn1
fn2 = fn2
bailout = bailout
numeroper = numeroper
denomoper = denomoper
}

Formula2M {
global:
  
init:
  z = #pixel
  

loop:

    IF(@numeroper==0)
    numerator = (@n1+z)
  ELSEIF(@numeroper==1)
    numerator = (@n1-z)
  ELSEIF(@numeroper==2)
    numerator = (z-@n1)
  ELSEIF(@numeroper==3)
    numerator = (@n1*z)
  ELSEIF(@numeroper==4)
    numerator = (@n1/z)
  ELSEIF(@numeroper==5)
    numerator = (z/@n1)
  ELSEIF(@numeroper==6)
    numerator = (@n1^z)
  ELSEIF(@numeroper==7)
    numerator = (z^@n1)
  ELSE
    numerator = 0
  ENDIF
  
    IF(@denomoper==0)
    denominator = (@n2+z)
  ELSEIF(@denomoper==1)
    denominator = (@n2-z)
  ELSEIF(@denomoper==2)
    denominator = (z-@n2)
  ELSEIF(@denomoper==3)
    denominator = (@n2*z)
  ELSEIF(@denomoper==4)
    denominator = (@n2/z)
  ELSEIF(@denomoper==5)
    denominator = (z/@n2)
  ELSEIF(@denomoper==6)
    denominator = (@n2^z)
  ELSEIF(@denomoper==7)
    denominator = (z^@n2)
  ELSE
    denominator = 0
  ENDIF

  
  z = @fn1(numerator)/@fn2(denominator) + #pixel

  
bailout:
  |z| <= real(@bailout)
default:
  title = "Formula2M"
  
  float param bailout
  caption = "Bailout"
  default = 50
  min = 0
  endparam
  
  param numeroper
  caption = "Numerator Operator"
  enum = "n1+z""n1-z""z-n1""n1*z""n1/z""z/n1""n1^z""z^n1"
  default = 0
  endparam
  
  param denomoper
  caption = "Denomiator Operator"
  enum = "n2+z""n2-z""z-n2""n2*z""n2/z""z/n2""n2^z""z^n2"
  default = 0
  endparam
  
  func fn1
  caption = "Numerator Function"
  default = ident()
  endfunc
  
  func fn2
  caption = "Denomerator Function"
  default = ident()
  endfunc
  
  float param n1
  caption = "Numerator Binomial (n1)"
  hint = "Specifies the number in the numerator"
  default = 1.0
  endparam
  
  float param n2
  caption = "Denominator Binomial (n2)"
  hint = "Specifies the number in the denominator"
  endparam  
switch:
type = "Formula2J"
n1 = n1
n2 = n2
seed = #pixel
fn1 = fn1
fn2 = fn2
bailout = bailout
numeroper = numeroper
denomoper = denomoper
}

Formula3J {
global:
  
init:
  z = #pixel
loop:
    IF(@op1==0)
      z = @fn1(z+@c)^@power
    ELSEIF(@op1==1)
      z = @fn1(z-@c)^@power
    ELSEIF(@op1==2)
      z = @fn1(z*@c)^@power
    ELSEIF(@op1==3)
      z = @fn1(z/@c)^@power
    ELSEIF(@op1==4)
      z = @fn1(@c/z)^@power
    ELSEIF(@op1==5)
      z = @fn1(z^@c)^@power
    ELSEIF(@op1==6)
      z = @fn1(@c^z)^@power
    ENDIF
    
    IF(@invSwitch==1)
      z = 1/z
    ELSEIF(@invSwitch==2)
      z = z + (1/z)
    ELSE
      z = z
    ENDIF
    
bailout:
  |z| <= @bail
default:
  title = "Formula3J"
  
  param bail
  default = 50.0
  min = 0.0
  caption = "Bailout"
  endparam
  
  param op1
  caption = "Method"
  enum = "+""-""*""z/pix""pix/z""z^pix""pix^z"
  default = 0
  endparam
  
  param power
  caption = "Power"
  default = (2,0)
  endparam
  
  func fn1
  caption = "Function 1"
  default = ident()
  endfunc
  
  param invSwitch
  caption = "Inversion Options"
  enum = "None""Invert Z""Add Inversion to Z"
  default = 0
  endparam
switch:
type = "Formula3M"
bail = bail
op1 = op1
power = power
fn1 = fn1
invSwitch = invSwitch
}

Formula3M {
global:
  
init:
  z = #pixel
loop:
    IF(@op1==0)
      z = @fn1(z+#pixel)^@power
    ELSEIF(@op1==1)
      z = @fn1(z-#pixel)^@power
    ELSEIF(@op1==2)
      z = @fn1(z*#pixel)^@power
    ELSEIF(@op1==3)
      z = @fn1(z/#pixel)^@power
    ELSEIF(@op1==4)
      z = @fn1(#pixel/z)^@power
    ELSEIF(@op1==5)
      z = @fn1(z^#pixel)^@power
    ELSEIF(@op1==6)
      z = @fn1(#pixel^z)^@power
    ENDIF
    
    IF(@invSwitch==1)
      z = 1/z
    ELSEIF(@invSwitch==2)
      z = z + (1/z)
    ELSE
      z = z
    ENDIF
    
bailout:
  |z| <= @bail
default:
  title = "Formula3M"
  
  param bail
  default = 50.0
  min = 0.0
  caption = "Bailout"
  endparam
  
  param op1
  caption = "Method"
  enum = "+""-""*""z/pix""pix/z""z^pix""pix^z"
  default = 0
  endparam
  
  param power
  caption = "Power"
  default = (2,0)
  endparam
  
  func fn1
  caption = "Function 1"
  default = ident()
  endfunc
  
  param invSwitch
  caption = "Inversion Options"
  enum = "None""Invert Z""Add Inversion to Z"
  default = 0
  endparam
switch:
type = "Formula3J"
bail = bail
op1 = op1
power = power
fn1 = fn1
invSwitch = invSwitch
c = #pixel
}


Formula4M {
init:
  z = #pixel
loop:

  IF (@addpix) && (@beforepix)
  z = z + #pixel
  ENDIF
  z = 1 / z    ;Invert Z
  IF (@addpix) && (@beforechange)
  z = z + #pixel
  ENDIF
  z = fn1(z)   ;Change Z
  IF (@addpix) && (@afterchange)
  z = z + #pixel
  ENDIF
  z = 1 / z    ;Flip Z back
  IF (@addpix) && (@afterrev)
  z = z + #pixel
  ENDIF
bailout:
  |z| <= @bail
default:
  title = "Formula4M"
  
  param bail
    caption = "Bailout"
    default = 4.0
    min = 0
  endparam
  
  func fn1
     caption = "Inversion Function"
     default = ident()
  endfunc
  
  Heading
    caption = "#pixel Options"
  endheading
  param addpix
    caption = "Add #pixel"
    default = false
  endparam
  param beforepix
    caption = "Before Invert"
    visible = @addpix
    default = false
  endparam
  param beforechange
    caption = "After Invert"
    visible = @addpix
    default = false
  endparam
  param afterchange
    caption = "After Change"
    visible = @addpix
    default = false
  endparam
  param afterrev
    caption = "After Revert"
    visible = @addpix
    default = false
  endparam
  
    
switch:
type = "formula4j"
bail = bail
fn1 = fn1
addpix = addpix
beforepix = beforepix
beforechange = beforechange
afterchange = afterchange
afterrev = afterrev
c = #pixel
}

Formula4J {
init:
  z = #pixel
loop:

  IF (@addpix) && (@beforepix)
  z = z + @c
  ENDIF
  z = 1 / z    ;Invert Z
  IF (@addpix) && (@beforechange)
  z = z + @c
  ENDIF
  z = fn1(z)   ;Change Z
  IF (@addpix) && (@afterchange)
  z = z + @c
  ENDIF
  z = 1 / z    ;Flip Z back
  IF (@addpix) && (@afterrev)
  z = z + @c
  ENDIF
bailout:
  |z| <= @bail
default:
  title = "Formula4J"
  
  param bail
    caption = "Bailout"
    default = 4.0
    min = 0
  endparam
  
  func fn1
     caption = "Inversion Function"
     default = ident()
  endfunc
  
  param c
    caption = "Julia Seed"
    default = (0,0)
  endparam
  
  Heading
    caption = "Seed Options"
  endheading
  param addpix
    caption = "Add Seed"
    default = false
  endparam
  param beforepix
    caption = "Before Invert"
    visible = @addpix
    default = false
  endparam
  param beforechange
    caption = "After Invert"
    visible = @addpix
    default = false
  endparam
  param afterchange
    caption = "After Change"
    visible = @addpix
    default = false
  endparam
  param afterrev
    caption = "After Revert"
    visible = @addpix
    default = false
  endparam
  
    
switch:
type = "formula4M"
bail = bail
fn1 = fn1
addpix = addpix
beforepix = beforepix
beforechange = beforechange
afterchange = afterchange
afterrev = afterrev
}