comment {
Formulas by Reynard D. Fox
No spam, please.
reynard@eznet.net
}

PickoverTanVariation {
;Transcribed Mar 2001 by Reynard D. Fox
;Mad props to Paul Bourke's Fractal Introduction
;(http://astronomy.swin.edu.au/pbourke/fractals/fracintro/)
;which contains Pickering's Biomorph formula, from
;which this function is derived. Tangent function
;is substituted for sine function.
init:
z = 0
loop:
z = tan(z) + (z ^ @power) + #pixel
bailout:
|z| < @bailout
default:
title = "Pickover Tangent Variation"
center = (-1, 0)
param power
caption = "Power"
default = (2,0)
endparam
param bailout
caption = "Bailout"
default = 100000
endparam
}

Brot+Brot {
; Formula by Reynard D. Fox, May 2001
; 2 Mandelbrot sets added together or subtracted from each other.
;
; Hints: 
; To subtract sets from each other, change Mult1 or Mult2 to -1.
; Try using different exponential powers with each other in Power1 or Power2.
; Interesting results can also be obtained by using fractional multipliers
; in Mult1 or Mult2.
; A switch has been enabled with the analogous Julia+Julia formula.
;
init:
  z = @start
loop:
  z = (@mult1 * (z^@power1)) + (@mult2 * (z^@power2)) + #pixel
bailout:
  |z| <= @bailout
default:
  title = "Brot + Brot"
  center = (-1.5, 0)
  magn = 1
  param start
    caption = "Starting point"
    default = (0,0)
    hint = "Perturbation. Use (0,0) for the standard Mandelbrot set."
  endparam
   param mult1
    caption = "Mult1"
    default = (1,0)
    hint = "This is what Power1 is multiplied by (can be made negative with negative numbers)"
  endparam
  param power1
    caption = "Power1"
    default = (2,0)
    hint = "This defines the power of the first Mandelbrot set."
  endparam
  param mult2
    caption = "Mult2"
    default = (1,0)
    hint = "This is what Power2 is multiplied by (can be made negative with negative numbers)"
  endparam
  param power2
    caption = "Power2"
    default = (0,0)
    hint = "This defines the power of the second Mandelbrot set."
  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 Mandelbrot set anymore."
  endparam
switch:
  type = "Julia+Julia"
  seed = #pixel
  bailout = bailout
  mult1 = mult1
  power1 = power1
  mult2 = mult2
  power2 = power2
}

Julia+Julia {
; Formula by Reynard D. Fox, May 2001
; 2 Julia sets added together or subtracted from each other.
;
; Hints: 
; It's easiest to start with Brot+Brot, then use switch mode to
; change to Julia+Julia.
; If you insist on starting with this function, make sure to change
; Mult2 to something other than 0 (1 to add, -1 to subtract, or feel
; free to experiment with fractional multipliers.)
;
init:
  z = #pixel
loop:
  z = (@mult1 * (z^@power1)) + (@mult2 * (z^@power2)) + @seed
bailout:
  |z| <= @bailout
default:
  title = "Julia + Julia"
  magn = 1
  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 mult1
    caption = "Mult1"
    default = (1,0)
    hint = "This is what Power1 is multiplied by (can be made negative with negative numbers)"
  endparam
  param power1
    caption = "Power1"
    default = (2,0)
    hint = "This defines the power of the first Julia set."
  endparam
  param mult2
    caption = "Mult2"
    default = (0,0)
    hint = "This is what Power2 is multiplied by (can be made negative with negative numbers)"
  endparam
  param power2
    caption = "Power2"
    default = (0,0)
    hint = "This defines the power of the second Julia set."
  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 Mandelbrot set anymore."
  endparam
switch:
  type = "Brot+Brot"
  power1 = power1
  power2 = power2
  mult1 = mult1
  mult2 = mult2
  bailout = bailout
}

ModifiedMandelbrotInversion {
; Formula by Reynard D. Fox, June 2001
; A counter determines the number of iterations made before the real component is swapped with
; the imaginary component in the iterated complex point. Use the number 0 in the Switchcount
; value for the swap to occur on every pass.
init:
  z = @start
  int counter = 0
loop:
  if counter < @switchcount
    z = z^@power + #pixel
    counter = counter + 1
  else
    z = flip(z)^@power + #pixel
    counter = 0
  endif
bailout:
  |z| <= @bailout
default:
  title = "Modified Mandelbrot Inversion"
  center = (-0.5, 0)
  param start
    caption = "Starting point"
    default = (0,0)
    hint = "Perturbation. Use (0,0) for the standard Mandelbrot set."
  endparam
  param power
    caption = "Power"
    default = (2,0)
    hint = "This defines the power of the Mandelbrot set. Use (2,0) \
            for the standard Mandelbrot set."
  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 Mandelbrot set anymore."
  endparam
  param switchcount
    caption = "Switchcount"
    default = 9 ; integer value
    min = 0
    hint = "Defines how many iterations to go until real value is swapped \
            with imaginary value (use 0 for swap every time)"
  endparam
}