comment {
  Fractal formulae by Mike Williams
}

Kellett {
; Becomes a Mandelbrot set when Initial Exponent=2
; and the two parameters are zero
;
; Parameters 1 and 2 cause the distinctive patterns
; of this fractal to appear. When Threshold is low
; Prameter 2 predominates and Parameter 1 has little
; effect, when Threshold is high Parameter 1 predominates.
;
; Use low values of parameters (e.g. 0.002) to obtain
; regular fractal shapes that are similar to Mandelbrots.
; Use higher values (e.g. 0.1) for more irregular chaotic
; effects.
;
; The "control shape" does not often appear visible in the
; final image, but affects the results at a deeper level.
;
; The "All outside" switch can be used to force all pixels
; to be outside. You can use it instead of copying the outside
; colouring to the inside.
; 
init:
  z=0
  a=@a
  bool up = false
  float iter = 0
loop:
  iter = iter + 1
  z=z^a+#pixel
  if @Shape == "Square"
    up = (abs(real(z))<=@thresh && abs(imag(z))<=@thresh)
  elseif @Shape == "Round"
    up = (|z| < @thresh)
  elseif @Shape == "Diamond"
    up = (abs(real(z))+abs(imag(z)) < @thresh)
  elseif @Shape == "Horizontal"
    up = (abs(imag(z)) < @thresh)
  elseif @Shape == "Vertical"
    up = (abs(real(z)) < @thresh)
  elseif @Shape == "Hyperbola"
    up = (abs(imag(z) * real(z)) < @thresh)
  elseif @Shape == "Wave"
    up = (abs(imag(z)+sin(real(z))) < @thresh)
  elseif @Shape == "Wave2"
    up = (abs(real(z)+sin(imag(z))) < @thresh)
  elseif @Shape == "Thingy"
    up = (abs(sin(imag(z)) * sin(real(z))) < @thresh)
  endif
  
  if up  
    a=a-@dec1
  else
    a=a-@dec2  
  endif
bailout:
  (iter < #maxiter && @outside == true) || (|z| < @bailout && @outside == false)
default:
  title = "Kellett"
  center = (0,0)
  magn = 1
  angle = 90
  periodicity = 0
  method = onepass
  maxiter = 300

  param bailout
    caption = "Bailout"
    default = 200
  endparam
  param Shape
    caption = "Control Shape"
    enum = "Square" "Round" "Diamond" "Vertical" "Horizontal" \
           "Hyperbola" "Wave" "Wave2" "Thingy"
    default = 5
  endparam
  float param a
    caption = "Initial Exponent"
    default = 2.0
  endparam
  float param dec1
    caption = "Parameter 1"
    default = 0.1
  endparam
  float param dec2
    caption = "Parameter 2"
    default = 1.0
  endparam
  float param thresh
    caption = "Threshold"
    default = 1.0
    min = 0
  endparam
  bool param outside
    caption = "All outside"
    default = false
  endparam
switch:
  type = "KellettJulia"
  power = power
  bailout = bailout
  Shape = Shape
  a = a
  dec1 = dec1
  dec2 = dec2
  thresh = thresh
  seed = #pixel
  outside = outside
}

KellettJulia {
; Becomes a Julia set when Initial Exponent=2
; and the two parameters are zero
;
; Parameters 1 and 2 cause the distinctive patterns
; of this fractal to appear. When Threshold is low
; Prameter 2 predominates and Parameter 1 has little
; effect, when Threshold is high Parameter 1 predominates.
;
; Use low values of parameters (e.g. 0.002) to obtain
; regular fractal shapes that are similar to Mandelbrots.
; Use higher values (e.g. 0.1) for more irregular chaotic
; effects.
;
; The "control shape" does not often appear visible in the
; final image, but affects the results at a deeper level.
; 
; The "All outside" switch can be used to force all pixels
; to be outside. You can use it instead of copying the outside
; colouring to the inside.
; 
init:
  z=#pixel
  a=@a
  bool up = false
  float iter = 0
loop:
  iter = iter + 1
  z=z^a+@seed
  if @Shape == "Square"
    up = (abs(real(z))<=@thresh && abs(imag(z))<=@thresh)
  elseif @Shape == "Round"
    up = (|z| < @thresh)
  elseif @Shape == "Diamond"
    up = (abs(real(z))+abs(imag(z)) < @thresh)
  elseif @Shape == "Horizontal"
    up = (abs(imag(z)) < @thresh)
  elseif @Shape == "Vertical"
    up = (abs(real(z)) < @thresh)
  elseif @Shape == "Hyperbola"
    up = (abs(imag(z) * real(z)) < @thresh)
  elseif @Shape == "Wave"
    up = (abs(imag(z)+sin(real(z))) < @thresh)
  elseif @Shape == "Wave2"
    up = (abs(real(z)+sin(imag(z))) < @thresh)
  elseif @Shape == "Thingy"
    up = (abs(sin(imag(z)) * sin(real(z))) < @thresh)
  endif
  
  if up  
    a=a-@dec1
  else
    a=a-@dec2  
  endif
bailout:
  (iter < #maxiter && @outside == true) || (|z| < @bailout && @outside == false)
default:
  title = "Kellett Julia"
  center = (0,0)
  magn = 1
  periodicity = 0
  method = onepass
  maxiter = 300
  param seed
    caption = "Julia seed"
    default = (-1.25, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  param bailout
    caption = "Bailout"
    default = 200
  endparam
  param Shape
    caption = "Control Shape"
    enum = "Square" "Round" "Diamond" "Vertical" "Horizontal" \
           "Hyperbola" "Wave" "Wave2" "Thingy"
    default = 5
  endparam
  float param a
    caption = "Initial Exponent"
    default = 2.0
  endparam
  float param dec1
    caption = "Parameter 1"
    default = 0.1
  endparam
  float param dec2
    caption = "Parameter 2"
    default = 1.0
  endparam
  float param thresh
    caption = "Threshold"
    default = 1.0
    min = 0
  endparam
  bool param outside
    caption = "All outside"
    default = false
  endparam
switch:
  type = "Kellett"
  power = power
  bailout = bailout
  Shape = Shape
  a = a
  dec1 = dec1
  dec2 = dec2
  thresh = thresh
  outside = outside
}

mjw_Marvin {
;
; 
;
init:
  z = (0,0)
loop:
  z = (z^2 + #pixel)*@marv + z*(1-@marv)
bailout:
  |z| <= @bailout
default:
  title = "Marvin"
  float param marv
    caption = "Marvinness"
    default = 0.5
    min = 0
    max = 1
  endparam
  float param bailout
    caption = "Bailout value"
    default = 1e20
    hint = "Defines how soon an orbit bails out, i.e. doesn't belong \
            to the Mandelbrot set anymore."
  endparam
switch:
  type = "mjw_Marvin_Julia"
  seed = #pixel
  bailout = bailout
  marv=marv
}


mjw_Marvin_Julia {
;
; 
;
init:
  z = #pixel
loop:
  z = (z^2 + @seed)*@marv + z*(1-@marv)
bailout:
  |z| <= @bailout
default:
  title = "Marvin Julia"
  param seed
    caption = "Julia seed"
    default = (-1.25, 0)
    hint = "Use this to create many different Julia sets. You can \
            also set this value using the Switch feature."
  endparam
  float param marv
    caption = "Marvinness"
    default = 0.5
    min = 0
    max = 1
  endparam
  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 Julia set anymore."
  endparam
switch:
  type = "mjw_Marvin"
  bailout = bailout
  marv=marv
}

mjw_PollyM {
init:
  z = (0,0)
loop:
  z = @five*z^5 + @four*z^4 + @cube*z^3 + @square*z^2 + @unit*z + #pixel
bailout:
  |z| <= @bailout
default:
  title = "Polly Mandelbrot"
  float param bailout
    caption = "Bailout value"
    default = 100
    min = 0
  endparam
  float param five
    caption = "fifth power"
    default = 0.0
  endparam
  float param four
    caption = "fourth power"
    default = 0.0
  endparam
  float param cube
    caption = "cube"
    default = 1.0
  endparam
  float param square
    caption = "square"
    default = 2.0
  endparam
  float param unit
    caption = "unit"
    default = 2.2
  endparam
switch:
  type = "mjw_PollyJ"
  five = five
  four = four
  cube = cube
  square = square
  unit = unit
  seed = #pixel
  bailout = bailout
}

mjw_PollyJ {
init:
  z = #pixel
loop:
  z = @five*z^5 + @four*z^4 + @cube*z^3 + @square*z^2 + @unit*z + @seed
bailout:
  |z| <= @bailout
default:
  title = "Polly Julia"
  float param bailout
    caption = "Bailout value"
    default = 100
    min = 0
  endparam
  param seed
    caption = "Julia seed"
    default = (-0.14375,-0.3)
  endparam
  float param five
    caption = "fifth power"
    default = 0.0
  endparam
  float param four
    caption = "fourth power"
    default = 0.0
  endparam
  float param cube
    caption = "cube"
    default = 1
  endparam
  float param square
    caption = "square"
    default = 2
  endparam
  float param unit
    caption = "unit"
    default = 2.2
  endparam
switch:
  type = "mjw_PollyM"
  five = five
  four = four
  cube = cube
  square = square
  unit = unit
  bailout = bailout
}

mjw_KaptainKrunch {
;
; I suggest keeping the Maximum Iterations set low
; and using the same colouring inside and outside
;
init:
  #z=@fn1(@fn2(@A/#pixel*@B/pixel))
  c=flip(#pixel)-@c
loop:
  #z=#z-(@fn3(#pixel/#z))/c-(@fn3(#pixel/c))
bailout:
  |real(z)| <= 4
default:
  title = "Kaptain Krunch"
  maxiter = 10
  float param A
    caption = "Openness"
    default = 1.0
  endparam
  float param B
    caption = "Width"
    default = 5.0
  endparam
  float param C
    caption = "Control"
    default = 0.0
  endparam
  func fn1
    caption = "Function 1"
    default = cos()
  endfunc
  func fn2
    caption = "Function 2"
    default = cos()
  endfunc
  func fn3
    caption = "Function 3"
    default = sin()
  endfunc
}

mjw_Wurlitzer {
init:
  #z = (0,0)
  d = #pixel
loop:
  #z = @fn1(#z) - d
  d = 1 / (z * @B)
bailout:
  |z| < @Bailout  
default:
  title = "Wurlitzer"
  float param B
    caption = "Whirliness"
    default = 10
  endparam
  param Bailout
    caption = "Disruption"
    default = 4
  endparam
  func fn1
    caption = "Function"
    default = tanh()
    hint = "Try sin, cosh, tanh, sqr, exp"
  endfunc
}