AttractorBasinsColoring {
; by Etienne Saint-Amant, july 2009
; intended to be used with either, Dubeau Phi 0, Dubeau Phi 1,
; Dubeau Phi Mixture, Dubeau Phi Mixture With Functions, Dubeau Psi,
; Dubeau Psi With Functions or Newton's method.
global:
  ;$define DEBUG
final:
  float angle;
  angle = atan2(#z);
  ;print(angle);
  if @noIter
    #index = (angle + #pi)/(2*#pi)
  else
    #index = 0.01 * #numiter + (angle + #pi)/(2*#pi)
  endif
default:
  title = "Attractor Basins Coloring"
  bool param noIter
    caption = "Don't use iteration number"
    default = false
  endparam
}

ESAFractalTree() {
;
; version 1.0
; By Etienne Saint-Amant, 2002/07/02
;
; Go to http://ESAfractal.com for examples and tutorial
;
; Based on FractalTree
; By Samuel Monnier, 11.1.00
; Modified with his kind permission
;
init:
  z = 0
  float arg = 0
  int i = 0
  float j = 0
  float d = 0
  float dist = 1e5
  float x = 0
  float y = 0
  float imagCof = @imaginaryCoefficient
  if @mode == 0
    z = #pixel
  endif

  float dr = pi/@rotincrCoefficient*@rotincr/@altitudeTree
  
loop:
  if @mode == 1
    i = i + 1
    if i == @itertr
      z = #z
    endif
  endif 
final:
  ; Performs translation, rotation
  ; and magnification
  z = z - @center
  z = z*exp(-1i*@rot*pi/@rotationchange)
  z = z/@size
  i = 0

  while i < @niter
    i = i + 1
    
    imagCof = imagCof + @alterimaginary

    x = abs(real(z))
    y = imag(z)
    z = x + imagCof * 1i * y
    arg = -atan2(z) + pi/@weirdness            
    ; Estimate distance
    if y >= -1 && y <= 0
      d = x^@power
    elseif y < -1
      d = cabs(z + imagCof * 1i)^@power
    elseif y > 0
      d = cabs(z)^@power
    endif
    
    if d < dist
      dist = d
    endif
    
    ; Computes the rotation to apply 
    j = @order-1
    rotincr = j*dr
    while j > 0
      j = j - 2
      if arg < (j+1)*dr
        rotincr = j*dr
      endif
    endwhile
    
    ; Performs transformation
    z = z*exp(imagCof*1i*rotincr)
    z = z*@magnincr
    z = z - imagCof*1i
    
  endwhile
  
  #index = dist 
   
default:
  title = "ESA Fractal Tree"
  param mode
    caption = "Mode"
    default = 0
    enum = "Pixel" "Distance Estimator"
  endparam
  param power
    caption = "Dist. Est. Power"
    default = 1.0
  endparam
  param order
    caption = "Tree Order"
    default = 4.0
  endparam
  param rotincr
    caption = "Angle Between Branches"
    default = 40.0
  endparam
  param magnincr
    caption = "Tree Magnification Increment"
    default = 1.9
  endparam
  param center
    caption = "Center"
    default = (0,0)
  endparam
  param rot
    caption = "Rotation"
    default = 0.0
  endparam
  param size
    caption = "Size"
    default = 1.0
  endparam
  param niter
    caption = "Number of Iteration"
    default = 10
  endparam
  param itertr
    caption = "Iteration to observe"
    default = 1
  endparam
 
  ;parameter added by ESA
  param imaginaryCoefficient
    caption = "Imaginary Coefficient"
    default = 0.75
    hint = "Imaginary Coefficient to change the shape of the branches (default .75)"
  endparam

  ;parameter added by ESA
  param alterimaginary
    caption = "Alter Imaginary Coefficient"
    default = 0.1
    hint = "Alter the Imaginary Coefficient for each iteration (default 0.1)"
  endparam

  ;parameter added by ESA
  param altitudeTree
    caption = "Altitude Tree"
    default = 2.0
    hint = "Create a tree developing more vertically (default 2.0)"
  endparam
  
  ;parameter added by ESA
  param weirdness
    caption = "Weirdness"
    default = 2.2
    hint = "Weirdness (default 2.2)"
   endparam
   
  ;parameter added by ESA
  param rotincrCoefficient
    caption = "Rotation Incrementation"
    default = 120
    hint = "Rotation Incrementation Coefficient (default 120)"
   endparam
   
  ;parameter added by ESA
  param rotationchange
    caption = "Rotation Change"
    default = 50
    hint = "Rotation Change (default 50)"
   endparam
}