;Ben's Fractal Formulas
;Here are the results of my experimentation with fractals.
;All of these are original formulas, although often I used
;the Mset or another common fractal as a "starting point."

Batwings {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Here is one of the first formulas I wrote.
;See the Julia Sets around (.2,0) when Param is .7.
;A weird-looking Mset appears when Param is 0
global:
  
init:
z=(0,0)

loop:

z = (@par-z)*(@par+z)*cabs(@par+(@mult*z)) + #pixel
 
bailout:
|z| < @bail
default:
periodicity=0
  title = "Wings of Bat"
    param par
    caption = "Param"
    default = 1.0
  endparam
   param bail
    caption = "Bailout"
    default = 40
  endparam
  param mult
    caption = "Mult"
    default = (1.0,0.0)
  endparam
switch:
type="Batjulia"
seed=#pixel
par=par
bail=bail
mult=mult
}

Batjulia {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Julia form of "Batwings"
global:
 
init:
z=#pixel

loop:

z = (@par-z)*(@par+z)*cabs(@par+(@mult*z)) + @seed 
bailout:
|z| < @bail
default:
periodicity=0
  title = "z Batwing Julia Set"
    param seed
    caption = "Julia Seed"
    default = (0.0,0.0)
  endparam
      param par
    caption = "Param"
    default = 1.0
  endparam
     param bail
    caption = "Bailout"
    default = 40
  endparam
  param mult
    caption = "Mult"
    default = (1.0,0.0)
  endparam
}

Angular {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;This formula uses DeMoivre's Theorem to break the power into three parts.
;Of course, when all of these parts are the same you get the standard Mset.
;The larger "Magnitude" is, the more "smooth" the shape will be.
;The "Coolness" factors can make cool variations and "decapitate" the Mset.
;Try negative values!
init:
  z = #pixel
  angle = 0.03
  a = 0.03
  b = (.3,.3)
  magnitude = 0.03
  theI = (0,1)
  
loop:
  angle = atan2(z)
  a = real(z)+@pert1
  b = imag(z)+(@pert2*(0,1))
  magnitude = sqrt((a^2)+(b^2))^@power
  a = (magnitude*cos(angle*@pow1))
  b = theI*(magnitude*sin(angle*@pow2))
  z = a + b + #pixel

bailout:
|z| < @bailout

default:
  title = "Angular Mandel!"
  maxiter = 149
  param power
    caption = "Magnitude"
    default = 1.5
  endparam
  param pow1
    caption = "Cos"
    default = 2.0
  endparam
  param pow2
    caption = "Sin"
    default = 2.0
  endparam
  param pert1
    caption = "Coolness"
    default = 0.0
  endparam
  param pert2
    caption = "More Coolness"
    default = 0.0
  endparam
  param bailout 
    caption = "Bailout value"
    default = 40.0
    min = 1.0
  endparam
switch:
  type = "AngularJ"
seed=#pixel
power=power
pow1=pow1
pow2=pow2
pert1=pert1
pert2=pert2
}

AngularJ {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Julia set of Angular Mandelbrot
init:
  z = #pixel
  angle = 0.03
  a = 0.03
  b = (.3,.3)
  magnitude = 0.03
  theI = (0,1)
  
loop:
  angle = atan2(z)
  a = real(z)+@pert1
  b = imag(z)+(@pert2*(0,1))
  magnitude = sqrt((a^2)+(b^2))^@power
  a = (magnitude*cos(angle*@pow1))
  b = theI*(magnitude*sin(angle*@pow2))
  z = a + b + @seed

bailout:
|z| < @bailout

default:
  title = "z Angular Julia Set"
  maxiter = 149
   param seed
    caption = "Seed"
    default = (0.3583333334,-0.0625)
  endparam
  param power
    caption = "Magnitude"
    default = 1.5
  endparam
  param pow1
    caption = "Cos"
    default = 2.0
  endparam
  param pow2
    caption = "Sin"
    default = 2.0
  endparam
  param pert1
    caption = "Coolness"
    default = 0.0
  endparam
  param pert2
    caption = "More Coolness"
    default = 0.0
  endparam
  param bailout 
    caption = "Bailout value"
    default = 40.0
    min = 1.0
  endparam
}
FviewDisco  {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Use the Switch to find some sweet Julia sets.
;Look for the "Mushrooms," you'll know what I mean when you see them.
;Bailout is an important parameter.
init:
z =(0,0)

loop:
z=fn2(z+fn1(#pixel))^@power
  
bailout:
  |z|<= @bailout
default:
  title = "Sweet Julias - Inside the Disco ball"
  maxiter = 149
      complex func fn1
  caption="X Coordinate Func"
  default=ident()
  endfunc
  complex func fn2
  caption="Y Coordinate Func"
  default=abs()
  endfunc
  param power
    caption = "power"
    default = (-1.0,0.0)
  endparam
    param bailout 
    caption = "Bailout value"
    default = 40.0
    min = 1.0
  endparam
  switch:
  type="FviewJ"
  fn1=fn1
  bailout=bailout
  power=power
  fn2=fn2
  c=#pixel
}
  
FviewNeon  {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Use the Switch to find some sweet Julia sets.
;Try changing the X Coord Function
;Bailout is an important parameter.
init:
z =(0,0)
loop:
z=fn2(z+fn1(#pixel))^@power
bailout:
  |z|<= @bailout
default:
  title = "Sweet Julias - Neon Designs"
  center=(-1.492653526,-2.88352521885) 
  magn=0.47204969
  maxiter = 149
      complex func fn1
  caption="X Coordinate Func"
  default=exp()
  endfunc
  complex func fn2
  caption="Y Coordinate Func"
  default=abs()
  endfunc
  param power
    caption = "power"
    default = (0.0,-1.0)
  endparam
    param bailout 
    caption = "Bailout value"
    default = 20.0
    min = 1.0
  endparam
  switch:
  type="FviewJ"
  fn1=fn1
  bailout=bailout
  power=power
  fn2=fn2
  c=#pixel
}
FviewTan  {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Use the Switch to find some sweet Julia sets.
;Look to the Left of the Julia sets for more detail!!!
;To see "hyper veggies," look at Jset seed 1.50599060533,-0.0179266675506
init:
z =(0,0)
loop:
z=fn2(z+fn1(#pixel))^@power
bailout:
  |z|<= @bailout
default:
  title = "Sweet Julias - Tangent Veggies"
  center=(1.50813869522,-0.01317965409039)
   magn=157.11633

  maxiter = 149
      complex func fn1
  caption="X Coordinate Func"
  default=tan()
  endfunc
  complex func fn2
  caption="Y Coordinate Func"
  default=abs()
  endfunc
  param power
    caption = "power"
    default = (1.0,1.0)
  endparam
    param bailout 
    caption = "Bailout value"
    default = 200.0
    min = 1.0
  endparam
  switch:
  type="FviewJ"
  fn1=fn1
  bailout=bailout
  power=power
  fn2=fn2
  c=#pixel
}

FviewExp  {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Use the Switch to find some sweet Julia sets.
;Bailout is an important parameter.
init:
z =(0,0)
loop:
z=fn2(z+fn1(#pixel))^@power
bailout:
  |z|<= @bailout
default:
  title = "Sweet Julias - Absolute Madness eXP"
  center=(2.27217665905,1.64814078)
  magn=3.9261823
  maxiter = 149
      complex func fn1
  caption="X Coordinate Func"
  default=exp()
  endfunc
  complex func fn2
  caption="Y Coordinate Func"
  default=abs()
  endfunc
  param power
    caption = "power"
    default = (0.0,-2.0)
  endparam
    param bailout 
    caption = "Bailout value"
    default = 530.0
    min = 1.0
  endparam
  switch:
  type="FviewJ"
  fn1=fn1
  bailout=bailout
  power=power
  fn2=fn2
  c=#pixel
}
FviewJ  {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Julia form of Function viewers
init:
z =#pixel
loop:
z=fn2(z+fn1(@c))^@power
  
bailout:
  |z|<= @bailout
default:
  title = "z Julia Function Viewer"
  maxiter = 149
      complex func fn1
  caption="X Coordinate Func"
  default=ident()
  endfunc
  complex func fn2
  caption="Y Coordinate Func"
  default=abs()
  endfunc
  param power
    caption = "power"
    default = (-1.0,0.0)
  endparam
   param c
    caption = "Seed"
    default = (-0.1875,0.1166666667)
  endparam 
    param bailout 
    caption = "Bailout value"
    default = 40.0
    min = 1.0
  endparam
}

DynamicCloud {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Originally an IFS type fractal that I modified to make this.
;See this: a = (2,0)  b = (-1.7,1.7)
;Weird eyeballs: a = (2,0)  b = (-1.1,1.2)
init:
  z=(0,0)
loop:
x=real(z)
y=imag(z)
w=(@a*x+@b*fn1(x))
z=y+w+((w-x)*(0,1))+#pixel

bailout:
  |z| <= @bailout
default:
  title = "Dynamic Cloud"
  maxiter = 100
  periodicity = 0
  method = guessing
  param a
    caption = "a"
    default = (2, 0.0)
  endparam
  param b
    caption = "b"
    default = (-3, 0.0)
  endparam
  param bailout
    caption = "Bailout value"
    default = 64.0
    min = 1
  endparam
  func fn1
  caption="F"
  default=sin()
  endfunc
switch:
type = "DynamicCloud"
a =#pixel
bailout = bailout
b=b
power=power
fn1 = fn1
}

Flipped {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Uses the "flip" function to make things interesting.
;Asin() gives good results when bailout is low. And change mult to 0.
global:
  
init:
z=(0,0)

loop:
z = fn1(flip(z^@power))+ z*@mult + #pixel
bailout:
|z| < @bail
default:
  title = "Flipped Fractal"
 complex func fn1
  caption="Func"
  default=ident()
  endfunc
  param power
  hint="Power"
  default=2.0
  endparam
     param mult
  hint="Mult"
  default=(-1.0,0.0)
  endparam
    param bail
  hint="Bailout"
  default=400
  endparam
switch:
type="FlippedJ"
seed=#pixel
bail=bail
power=power
fn1=fn1
mult=mult
}
FlippedAsin {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Asin() gives good results when bailout is low. And change mult to 0.
global:
  
init:
z=(0,0)

loop:
z = fn1(flip(z^@power))+ z*@mult + #pixel
bailout:
|z| < @bail
default:
  title = "Sweet Julias - Insane Asin"
 complex func fn1
  caption="Func"
  default=asin()
  endfunc
  param power
  hint="Power"
  default=-2.0
  endparam
     param mult
  hint="Mult"
  default=(0.0,0.0)
  endparam
    param bail
  hint="Bailout"
  default=10
  endparam
switch:
type="FlippedJ"
seed=#pixel
bail=bail
power=power
fn1=fn1
mult=mult
}
HyperPetals {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Asin() gives good results when bailout is low. And change mult to 0.
global:
  
init:
z=(0,0)

loop:
z = fn1(flip(z^@power))+ z*@mult + #pixel
bailout:
|z| < @bail
default:
  title = "HyperPetals"
 complex func fn1
  caption="Func"
  default=sin()
  endfunc
  param power
  hint="Power"
  default=-2.0
  endparam
     param mult
  hint="Mult"
  default=(1.0,0.0)
  endparam
    param bail
  hint="Bailout"
  default=400
  endparam
switch:
type="FlippedJ"
seed=#pixel
bail=bail
power=power
fn1=fn1
mult=mult
}

FlippedJ {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Uses the "flip" function to make things interesting.
global:
init:
z=#pixel

loop:
z = fn1(flip(z^@power))+ z*@mult + @seed
bailout:
|z| < @bail
default:
  title = "z Flipped Fractal Julia"
 complex func fn1
  caption="Func"
  default=asin()
  endfunc
  param power
  hint="Power"
  default=-2.0
  endparam
  param seed
  hint="Julia Seed"
  default=(-0.0170092189,0.565024819)
  endparam
     param mult
  hint="Mult"
  default=(0.0,0.0)
  endparam
    param bail
  hint="Bailout"
  default=10
  endparam
}
cburst {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/

global:

  
init:
z=(0,0)
float rea = 0.0
float imagi = 0.0
float mag = 0.0

loop:
rea = real(z)
imagi = imag(z)
angle = atan2(z)+(@c2*(0,1))
mag = sqrt(rea^2+imagi^2)
z = (mag^@power2)*(z^@power)*cos(angle*@mult)*sin(angle*@mult) + #pixel
 
bailout:
|z| < @bail
default:
  title = "Color Burst"
param c2
    caption = "Sweet Adjust"
    default = 0.0
  endparam
 param power
    caption = "Z Power"
    default = 2.0
    endparam
 param power2
    caption = "Magnitude Power"
    default = -3.0
  endparam
    param mult
    caption = "Angle Multiplier"
    default = 3.0
  endparam
    param bail
    caption = "Bailout"
    default = 4.0
  endparam
switch:
  type = "cburstj"
seed=#pixel
c2 =c2
power=power
power2=power2
bail=bail
mult=mult
}

cburstj {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/

global:
init:
z=#pixel
float rea = 0.0
float imagi = 0.0
float mag = 0.0

loop:
rea = real(z)
imagi = imag(z)
angle = atan2(z)+(@c2*(0,1))
mag = sqrt(rea^2+imagi^2)
z = (mag^@power2)*(z^@power)*cos(angle*@mult)*sin(angle*@mult) + @seed
bailout:
|z| < @bail
default:
  title = "z Bursting Julia"
  param seed
    caption = "Julia Seed"
    default = (0.0,0.0)
  endparam
param c2
    caption = "Sweet Adjust"
    default = 0.0
  endparam
 param power
    caption = "Z Power"
    default = 2.0
    endparam
 param power2
    caption = "Magnitude Power"
    default = -3.0
  endparam
    param mult
    caption = "Angle Multiplier"
    default = 3.0
  endparam
    param bail
    caption = "Bailout"
    default = 4.0
  endparam
}
rainbowbrot {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;A variation on the Mset.
global:
init:
z=(0,0)
a = @ai

loop:
a = a+(a/@blur)
z = a*z*((1-z)^(@power-1)) + #pixel
 
bailout:
|z| < @bail
default:
  title = "Rainbow Mandelbrot"
  periodicity=0
   param ai
    caption = "Param"
    default = (0.4,0.0)
  endparam
  param blur
    caption = "Blur/Swirl"
    default = (100,0.0)
  endparam
    param power
    caption = "power"
    default = 2.0
  endparam
     param bail
    caption = "Bail"
    default = 75.0
  endparam
switch:
type="rainbowbrotJ"
seed=#pixel
ai=ai
blur=blur
power=power
bail=bail
}
rainbowbrotJ {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;A variation on the Jset.
global:
init:
z=#pixel
a = @ai
loop:
a = a+(a/@blur)
z = a*z*((1-z)^(@power-1)) + @seed
bailout:
|z| < @bail
default:
 periodicity=0
  title = "z Rainbow Julia Set"
   param seed
    caption = "Julia Seed"
    default = (1.9125,0.1125)
  endparam
   param ai
    caption = "Param"
    default = (0.4,0.0)
  endparam
  param blur
    caption = "Blur/Swirl"
    default = (100,0.0)
  endparam
    param power
    caption = "power"
    default = 2.0
  endparam
     param bail
    caption = "Bail"
    default = 75.0
  endparam
}
RandomShape {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Change the Seed to get a different picture.
;Also try different coloring formulas.
global:

init:
z= 0
int seed = @theseed
float a = 4

loop:
seed = random(seed)
a = abs(seed)/#randomrange
if a>0.2
if a>0.4
if a>0.6
if a>0.8
z = z^4 + #pixel
endif
z = z^3 + #pixel
endif
z = z^2 + #pixel
endif
z = z + #pixel
endif

bailout:
|z| < @bail
default:
periodicity=0
  title = "Random Shape Generator"
  param theseed
    caption = "Random Seed"
    default = 45
  endparam
   param bail
    caption = "Bailout"
    default = 400
  endparam
}

secantsketch {
;Original formula at http://astronomy.swin.edu.au/~pbourke/fractals/thorn/
;Made cool by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
global:
  
init:
z=(0,0)
value=0.0
loop:
x=real(z)
y=imag(z)
tempx= (x/cos(y))*@mult+real(#pixel)
tempy = (y/cos(x))*@mult+imag(#pixel)
z=tempx + tempy*(0,1)
if @bailmode
value=|z|
else
value=x+y
endif
bailout:
value < @bail
default:
periodicity = 0
angle=0.001
  title = "Secant Sketch!"
   param mult
    caption = "Multiplier"
    default = (1.0,0.0)
    endparam
     param bail
    caption = "Bail"
    default = 10000
  endparam
   param bailmode
 caption = "Bail Mode"
 default=true
 endparam
switch:
type="secantsketchJ"
seed=#pixel
mult=mult
bail=bail
bailmode=bailmode
}
secantsketchJ {
;Original formula at http://astronomy.swin.edu.au/~pbourke/fractals/thorn/
;Made cool by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
global:
  
init:
z=#pixel
value=0.0
loop:
x=real(z)
y=imag(z)
tempx= (x/cos(y))*@mult+real(@seed)
tempy = (y/cos(x))*@mult+imag(@seed)
z=tempx + tempy*(0,1)
if @bailmode
value=|z|
else
value=x+y
endif
bailout:
value < @bail
default:
periodicity = 0
angle=0.001
  title = "z Secant Sketch Julia"
   param mult
    caption = "Multiplier"
    default = (1.0,0.0)
    endparam
    param seed
    caption = "Julia Seed"
    default = (0.0,0.0)
    endparam
   param bail
    caption = "Bail"
    default = 10000
  endparam
  param bailmode
 caption = "Bail Mode"
 default=true
 endparam
}
timewarp {
;Modification of Secant Sketch, but with hyperbolic secant
;by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
global:
  
init:
z=(0,0)
value=0.0
loop:
x=real(z)
y=imag(z)
tempx= (x/cos(y))*@mult+real(#pixel)
tempy = (y/cosh(x))*@mult+imag(#pixel)
z=tempx + tempy*(0,1)
if @bailmode
value=|z|
else
value=x+y
endif
bailout:
value < @bail
default:
periodicity = 0
angle=0.001
  title = "Time Warp"
   param mult
    caption = "Multiplier"
    default = (1.0,0.0)
    endparam
     param bail
    caption = "Bail"
    default = 10000
  endparam
   param bailmode
 caption = "Bail Mode"
 default=true
 endparam
switch:
type="timewarpj"
seed=#pixel
mult=mult
bail=bail
bailmode=bailmode
}
timewarpj {
;by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Modification of Secant Sketch
global:
init:
z=#pixel
value=0.0
loop:
x=real(z)
y=imag(z)
tempx= (x/cos(y))*@mult+real(@seed)
tempy = (y/cosh(x))*@mult+imag(@seed)
z=tempx + tempy*(0,1)
if @bailmode
value=|z|
else
value=x+y
endif
bailout:
value < @bail
default:
periodicity = 0
angle=0.001
  title = "z Time Warp Julia"
   param mult
    caption = "Multiplier"
    default = (1.0,0.0)
    endparam
    param seed
    caption = "Julia Seed"
    default = (0.0,2.6625)
    endparam
   param bail
    caption = "Bail"
    default = 10000
  endparam
  param bailmode
 caption = "Bail Mode"
 default=true
 endparam
}

Tangoid {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;This versitile formula allows creation of several shapes.
global:
  
init:
z=(0,0)

loop:
z=@mult*z*fn1(fn2(z))^@power+#pixel

bailout:
|z| < @bail

default:
periodicity = 0
center=(-2.2,0) 
magn=1
  title = "Tangoid"
   param power
    caption = "Power"
    default = (1.0,0.0)
    endparam
   param mult
    caption = "Multiplier"
    default = (1.0,0.0)
    endparam
     param bail
    caption = "Bail"
    default = 600
  endparam
  complex func fn1
  caption="X Coordinate Func"
  default=tan()
  endfunc
  complex func fn2
  caption="Y Coordinate Func"
  default=ident()
  endfunc
   param bailmode
 caption = "Bail Mode"
 default=true
 endparam
switch:
type="TangoidJ"
seed=#pixel
power=power
bail=bail
mult=mult
fn1=fn1
fn2=fn2
}
TangoidJ {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;This versitile formula allows creation of several shapes.
global:
  
init:
z=#pixel
value=0.0

loop:
z=@mult*z*fn1(fn2(z))^@power+@seed

bailout:
|z| < @bail

default:
periodicity = 0
angle=0
  title = "z Tangoid Julia"
    param seed
    caption = "seed"
    default = (-0.63534722177,-0.0015972223833)
    endparam
       param mult
    caption = "Multiplier"
    default = (1.0,0.0)
    endparam
   param power
    caption = "Power"
    default = (.4,0.0)
    endparam
       param bail
    caption = "Bail"
    default = 60
  endparam
  complex func fn1
  caption="X Coordinate Func"
  default=tan()
  endfunc
  complex func fn2
  caption="Y Coordinate Func"
  default=ident()
  endfunc
   param bailmode
 caption = "Bail Mode"
 default=true
 endparam
}
volterraKalei {
;Modified by Ben Fisher, to add artificial symmetry
;Written by Luke Plant
;The artificial symmetry forces the fractal to be symmetrical
init:
  float x = real(@mult*fn2(pixel))
  float y = imag(@mult*fn2(pixel))
  float f = 0.0
  float g = 0.0
  float p = imag(@j)
  float h = real(@j)
  float x2 = 0.0
  float y2 = 0.0
  z = pixel
loop:
  f = x - x * y
  g = -y + x * y
  x2 = x + p * f
  y2 = y + p * g 
  x = x + h/2 * (f + ( x2 - x2*y2))
  y = y + h/2 * (g + (-y2 + x2*y2))
  z = x + (y*(0,1))
bailout:
  |z| < @bailout
default:
  title = "Kaleidoscope!"
  maxiter = 149
  periodicity=0
  param j
    caption = "Julia Parameter"
    default = (0.26,0.0)
  endparam
  param mult
    caption = "Artificial Symmetry"
    default = (1,0)
  endparam
  func fn2
  caption= "Function"
  default = abs()
  endfunc
  param bailout
    caption = "Bailout value"
    default = 256.0
    min = 1
  endparam
  switch:
  type="volterraKalei"
  bailout=bailout
  fn2=fn2
  mult=mult
  j=#pixel
}
HenonFlame {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Based loosely on the Henon IFS formula.
;Uses primitive artificial symmetry.
init:
  float a = real(@j)
  float b = imag(@j)
  complex tempx=(0.0,0.0)
  complex x=(0.0,0.0)
  complex y=(0.0,0.0)
    z = fn2(#pixel)^@power
loop:
 x=real(abs(fn1(z)))
 y=imag(abs(fn1(z)))
 tempx = x
 x=(x*a)-(y-(x*x))*b
 y = (tempx*b) + (y-tempx*tempx)*a
 z = x + (y*(0,1))
bailout:
  |z| < @bailout
default:
  title = "Henon Flame"
  maxiter = 149
  periodicity=0
  param j
    caption = "Henon Parameter 1"
    default = (-0.6958333334,0.8125000001)
  endparam
    param power
    caption = "Power"
    default = (1,0)
  endparam
  func fn2
  caption="Complete Function"
  default = ident()
  endfunc
  func fn1
  caption="Variable Function"
  default = ident()
  endfunc
  param bailout
    caption = "Bailout value"
    default = 25.0
    min = 1
  endparam
switch:
type="HenonFlame"
bailout=bailout
fn1=fn1
fn2=fn2
power=power
  j=#pixel
}
Z2Z {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
;Raises Z to the Z power. Optionally makes symmetry.
global:
  
init:
z=(0,0)
c=(0.0,0.0)
c=#pixel

if (@mode==true)
if (real(c)>0)
c=(0-real(c))+((0,1)*imag(c))
endif
endif
if (@mode==false)
if (real(c)<0)
c=(real(c)*-1)+((0,1)*imag(c))
endif
endif
loop:
z = (z^@power)^(z+@plus)*@times + c
 
bailout:
|fn1(z)| < @bail
default:
center=(0,0)
magn=16
  title = "Z to the Z"
 param mode
 caption = "Symmetry Reflect"
 default=false
 endparam
  func fn1
 caption = "Bail Function"
 default = ident()
endfunc
  param plus
    caption = "Z Plus"
    default = 0.0
   endparam
   param times
    caption = "Times"
    default = -2.0
   endparam
  param power
    caption = "Z Power"
    default = (1.0,0.0)
   endparam
   param bail
    caption = "Bailout"
    default = 4.0
  endparam
switch:
type="Z2Zj"
seed=#pixel
plus=plus
times=times
power=power
bail=bail
mode=mode
fn1=fn1
}

Z2Zj {
;Formula by Ben Fisher, 2004 - http://www.angeltowns2.net/jamonben/ufanim/
global:
init:
z=#pixel
c=(0.0,0.0)
c=@seed
if (@mode==true)
if (real(z)>0)
z=(0-real(z))+((0,1)*imag(z))
endif
endif
loop:
z = (z^@power)^(z+@plus)*@times + c
bailout:
|fn1(z)| < @bail
default:
  title = "z to the z Julia"
 param mode
 caption = "Symmetry Reflect"
 default=false
 endparam
  func fn1
 caption = "Bail Function"
 default = ident()
endfunc
  param plus
    caption = "Z Plus"
    default = 0.0
   endparam
   param times
    caption = "Times"
    default = -2.0
   endparam
   param power
    caption = "Julia Seed"
    default = (0.0,0.0)
   endparam
  param power
    caption = "Z Power"
    default = (1.0,0.0)
   endparam
   param bail
    caption = "Bailout"
    default = 4.0
  endparam
}