comment {

  This file contains standard coloring algorithms for Ultra Fractal 3.
  Many of the coloring algorithms here were written by other formula
  authors, as noted in the comments with each formula. All formulas
  have been edited and simplified by Frederik Slijkerman.
  
}


BinaryDecomposition {
;
; Classic binary decomposition. Can give quite abstract effects.
; Use low bail-out values in the fractal formula (if possible) for
; best effects. This coloring algorithm uses just two colors from
; the gradient: one from the left end and one from the middle.
;
final:
  if @type == "Type 1"
    if real(#z) * imag(#z) >= 0 
      #index = 0.5
    else
      #index = 0
    endif
  else
    if atan2(#z) > 0
      #index = 0.5
    else
      #index = 0
    endif
  endif  
default:
  title = "Binary Decomposition"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/binarydecomposition.html"
  param type
    caption = "Decomposition Type"
    enum = "Type 1" "Type 2"
    default = 0
    hint = "Toggles between two types of binary decomposition. Type 2 \
            reproduces the coloring used with many images in the classic \
            Beauty of Fractals book."
  endparam
}


Gradient {
;
; Shows the entire gradient in various ways. The fractal formula
; is ignored. Use zooming, panning and rotating to get the desired
; gradient. Make sure that Repeat Gradient is enabled.
;
final:
  if @type == "Linear"
    #index = 16.5 + 0.25 * real(#pixel)
  elseif @type == "Radial"
    #index = 0.2 * |#pixel|
  else
    #index = 0.5 - atan2(#pixel) / (2 * #pi)
  endif
default:
  title = "Gradient"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/gradient.html"
  param type
    caption = "Gradient Type"
    enum = "Linear" "Radial" "Cone"
    hint = "Specifies the shape of the gradient."
  endparam
}


Default {
;
; Reproduces the iterations coloring algorithm found in most fractal
; software. This is the coloring algorithm that is used by default in
; Ultra Fractal when no coloring algorithm is loaded. See also the
; Basic coloring algorithm.
;
final:
  #index = 0.01 * #numiter
default:
  title = "None"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/none.html"
}


Basic(OUTSIDE) {
;
; Four basic and classic ways to color a fractal. Other classic
; algorithms are Decomposition, Binary Decomposition, and
; Distance Estimator.
;
final:
  if @type == "Iteration"
    #index = 0.01 * #numiter
  elseif @type == "Real"
    #index = 0.05 * (4 + real(#z))
  elseif @type == "Imaginary"
    #index = 0.05 * (4 + imag(#z))
  else
    #index = 0.05 * (4 + real(#z) + imag(#z))
  endif  
default:
  title = "Basic" 
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/basic.html"
  param type
    caption = "Coloring Type"
    enum = "Iteration" "Real" "Imaginary" "Sum"
    hint = "Specifies how the fractal is colored. Most options work best \
            with low bail-out values for the fractal formula, like 4. \
            The Iteration option is the classic way to color fractals."
  endparam
}


Decomposition {
;
; Decomposes the angle of the Z variable after iteration
; and distributes it over the gradient. See also the
; Binary Decomposition coloring algorithm.
;
; Written by Damien M. Jones
;
final:
  float d = atan2(#z); get angle of z
  IF (d < 0); it's negative
    d = d + #pi * 2; make it positive
  ENDIF
  #index = d / (#pi * 2)

default:
  title = "Decomposition"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/decomposition.html"
}


Triangle {
;
; Variation on the Triangle Inequality Average coloring method 
; from Kerry Mitchell. The smoothing used here is based on the
; Smooth formula, which only works for z^n+c and derivates.
;
; Written by Damien M. Jones
;
init:
  float sum = 0.0
  float sum2 = 0.0
  float ac = cabs(#pixel)
  float il = 1/log(@power)
  float lp = log(log(@bailout)/2.0)
  float az2 = 0.0
  float lowbound = 0.0
  float f = 0.0
  BOOL first = true
loop:
  sum2 = sum
  IF (!first)
    az2 = cabs(#z - #pixel)
    lowbound = abs(az2 - ac)
    sum = sum + ((cabs(#z) - lowbound) / (az2+ac - lowbound))
  ELSE
    first = false
  ENDIF
final:
  sum = sum / (#numiter)
  sum2 = sum2 / (#numiter-1)
  f = il*lp - il*log(log(cabs(#z)))
  #index = sum2 + (sum-sum2) * (f+1)  
default:
  title = "Triangle Inequality Average"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/triangleinequalityaverage.html"
  param power
    caption = "Exponent"
    default = 2.0
    hint = "This should be set to match the exponent of the \
            formula you are using. For Mandelbrot, this is 2."
  endparam
  param bailout
    caption = "Bailout"
    default = 1e20
    min = 1
    hint = "This should be set to match the bail-out value in \
            the Formula tab. Use a very high value for good results."
  endparam
}


Lighting {
;
; Coloring algorithm for the Slope family of fractal types.
; This coloring algorithm performs 3D lighting for these
; fractals.
;
; Written by Damien M. Jones
;
final:
  float vz = -sqrt(1-|#z|); extract implied portion of normal
  float d2r = #pi/180; degrees to radians conversion factor

  ; create vector for light direction
  float lx = cos((270-@angle)*d2r) * cos(@elevation*d2r)
  float ly = sin((270-@angle)*d2r) * cos(@elevation*d2r)
  float lz = -sin(@elevation*d2r)

  ; compute cosine of angle between these vectors
  ; (this is the amount of lighting on the surface)
  float l = lx*real(#z) + ly*imag(#z) + lz*vz
  IF (l < @ambient); light is below the ambient level
    l = @ambient; set it to the ambient level
  ENDIF
  IF (@ambient < 0); the ambient level is negative
    l = l + 1; offset to prevent clipping at 0
  ENDIF
  #index = l*0.99; reduce it just a bit to prevent
  ; the colors from wrapping

default:
  title = "Lighting"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/lighting.html"
  
  param @angle
    caption = "Light Rotation"
    default = 90.0
    hint = "Gives the rotation of the light source, in degrees. With 0 \
            degrees, the light comes from above. Positive values give \
            clockwise rotation."
  endparam
  param @elevation
    caption = "Light Elevation"
    default = 30.0
    hint = "Gives the elevation of the light source, in degrees."
  endparam
  param @ambient
    caption = "Ambient Light"
    default = 0.0
    min = -1.0
    max = 1.0
    hint = "Specifies the level of ambient light.  Use -1.0 to \
            color all surfaces."
  endparam
}


DistanceEstimator(OUTSIDE) {
;
; Distance-estimator coloring algorithm for Mandelbrot and
; other z^n fractal types (Phoenix, Julia). This coloring
; algorithm estimates the distance to the boundary of the
; fractal (for example the Mandelbrot set) and colors points
; accordingly.
;
; Written by Damien M. Jones
;
init:
  complex dz = (0,0)
loop:
  dz = @power * #z^(@power-1) * dz + 1
final:
  #index = (@power*log(cabs(#z)) * cabs(#z) / cabs(dz))^(1/@power)
default:
  title = "Distance Estimator"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/distanceestimator.html"
  param power
    caption = "Exponent"
    default = 2.0
    hint = "This should be set to match the exponent of the \
            formula you are using. For Mandelbrot, this is 2."
  endparam
}


Emboss {
;
; Coloring algorithm for the Embossed family of fractal types.
; This coloring algorithm performs 3D lighting for these fractals.
;
; Uses 3 colors from the gradient, at index values of 0.2, 0.5, 
; and 0.8. With Color Density set to 1, Transfer Function set to
; Linear, and Gradient Offset set to 0, these index values 
; corresponding to the gradient positions 80, 200, and 320.
;
; Written by Kerry Mitchell.
;
final:
  if(real(#z)<imag(#z))
    #index=0.2
  elseif(imag(#z)<real(#z))
    #index=0.8
  else
    #index=0.5
  endif
default:
  title="Emboss"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/emboss.html"
}


GaussianInteger {
;
; Colors by the relationship of the orbit of Z to Gaussian 
; Integers. 
;
; Written by Kerry Mitchell.
;
init:
  float r=0.0
  float rmin=1.0e12
  float rmax=0.0
  float rave=0.0
  float total=0.0
  float t=0.0
  int iter=0
  int itermin=0
  int itermax=0
  zmin=(0.0,0.0)
  zmax=(0.0,0.0)
  if(@norm==1)                       ; pixel normalization
    normfac=#pixel
  elseif(@norm==2)                   ; factor normalization
    normfac=@fac
  elseif(@norm==3)                   ; f(z) normalization
    normfac=@normfunc(#z)
  else                               ; no normalization
    normfac=(1.0,0.0)
  endif
  float logfac=@logseed
loop:
  iter=iter+1
  temp2=#z
  if @randomize
    logfac=4*logfac*(1-logfac)
    temp2=temp2*(1-@randomsize*logfac)
  endif
  if(@inttype==1)                    ; trunc
    temp=trunc(temp2/normfac)
  elseif(@inttype==2)                ; floor
    temp=floor(temp2/normfac)
  elseif(@inttype==3)                ; ceil
    temp=ceil(temp2/normfac)
  else                               ; round
    temp=round(temp2/normfac)
  endif
  remain=temp2-temp*normfac
  r=cabs(remain)
  total=total+r
  rave=total/iter
  if(r<rmin)
    rmin=r
    zmin=temp2
    itermin=iter
  endif
  if(r>rmax)
    rmax=r
    zmax=temp2
    itermax=iter
  endif
final:
  if(@colorby==1)            ; iteration @ min
    #index=0.01*itermin
  elseif(@colorby==2)        ; angle @ min
    t=atan2(zmin)
    t=t/pi
    if(t<0.0)
      t=t+2.0
    endif
    #index=0.5*t
  elseif(@colorby==3)        ; maximum distance
    #index=rmax
  elseif(@colorby==4)        ; iteration @ max
    #index=0.01*itermax
  elseif(@colorby==5)        ; angle @ max
    t=atan2(zmax)
    t=t/pi
    if(t<0.0)
      t=t+2.0
    endif
    #index=0.5*t
  elseif(@colorby==6)        ; average distance
    #index=rave
  elseif(@colorby==7)        ; min/mean/max angle
    zmax=(rave-rmin)+flip(rmax-rave)
    t=atan2(zmax)
    t=t/pi
    if(t<0.0)
      t=t+2.0
    endif
    #index=0.5*t
  elseif(@colorby==8)        ; max/min ratio
    #index=rmax/(rmin+1.e-12)
  else                       ; minimum distance
    #index=rmin
  endif
default:
  title="Gaussian Integer"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/gaussianinteger.html"
  param inttype
    caption="Integer Type"
    default=0
    enum="round(z)" "trunc(z)" "floor(z)" "ceil(z)"
  endparam
  param colorby
    caption="Color By"
    default=0
    enum="minimum distance" "iteration @ min" "angle @ min" \
      "maximum distance" "iteration @ max" "angle @ max" "average distance"\
      "min/mean/max angle" "max/min ratio"
  endparam
  param norm
    caption="Normalization"
    default=0
    enum="none" "pixel" "factor" "f(z)"
  endparam
  param fac
    caption=" Factor"
    default=(2.0,1.0)
    hint = "Normalization factor."
    visible = @norm == "factor"
  endparam
  func normfunc
    caption=" Function"
    default=ident()
    hint = "Normalization function."
    visible = @norm == "f(z)"
  endfunc
  param randomize
    caption="Randomize"
    default=false
    hint="Applies a random factor to z every iteration before \
      finding the Gaussian integer."
  endparam
  param randomsize
    caption="Random Size"
    default=(0.1,0)
    hint="Size of random factor. Larger values give more randomization."
    visible = @randomize
  endparam
  param logseed
    caption="Random Seed"
    default=0.1
    min=0.0
    max=1.0
    hint="Randomize seed, between 0 and 1. Every seed gives a different \
          image."
    visible = @randomize
  endparam
}


ExponentialSmoothing {
;
; This coloring method provides smooth iteration
; colors for all fractal types, convergent or
; divergent (or both).  It combines the two methods
; developed by Ron Barnett.  It doesn't map
; precisely to iterations, but it's close.
;
; Written by Damien M. Jones
;
init:
  float sum = 0.0
  float sum2 = 0.0
  complex zold = (0,0)
  
loop:
  IF (@diverge)
    sum = sum + exp(-cabs(#z))
  ENDIF
  IF (@converge)
    sum2 = sum2 + exp(-1/cabs(zold-#z))
  ENDIF
  zold = #z

final:
  IF (|#z - zold| < 0.5); convergent bailout.
    IF (@converge)
      #index = sum2
    ELSE
      #index = 0
    ENDIF
    
  ELSE; divergent bailout.
    IF (@diverge)
      #index = sum * @divergescale
    ELSE
      #index = 0
    ENDIF
  ENDIF
  
default:
  title = "Exponential Smoothing"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/exponentialsmoothing.html"

  param diverge
    caption = "Color Divergent"
    default = FALSE
    hint = "If set, points which escape to infinity will be \
            colored."
  endparam
  param converge
    caption = "Color Convergent"
    default = TRUE
    hint = "If set, points which collapse to one value will be \
            colored."
  endparam
  param divergescale
    caption = "Divergent Density"
    default = 1.0
    hint = "Sets the divergent coloring density, relative to the \
            convergent coloring.  If set to 1.0, they will use \
    the same color density."
  endparam
}


Smooth(OUTSIDE) {
;
; This coloring method provides smooth iteration
; colors for Mandelbrot and other z^2 formula types
; (Phoenix, Julia).  Results on other types may be
; unpredictable, but might be interesting.
;
; Thanks to F. Slijkerman for some tweaks.
; Thanks to Linas Vepstas for the math.
;
; Written by Damien M. Jones
;
init:
  complex il = 1/log(@power); Inverse log (power).
  float lp = log(log(@bailout)); log(log bailout).

final:
  #index = 0.05 * real(#numiter + il*lp - il*log(log(cabs(#z))))

default:
  title = "Smooth (Mandelbrot)"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/smooth.html"

  param power
    caption = "Exponent"
    default = (2,0)
    hint = "This should be set to match the exponent of the \
            formula you are using. For Mandelbrot, this is 2."
  endparam
  param bailout
    caption = "Bail-out value"
    default = 128.0
    min = 1
    hint = "This should be set to match the bail-out value in \
            the Formula tab. This formula works best with bail-out \
            values higher than 100."
  endparam
}


OrbitTraps {
;
; General Orbit Traps coloring algorithm, suitable for almost
; all fractal types.
;
; Originally written by Damien M. Jones.
;
init:
; OrbitTraps and OrbitTrapsDirect are exactly the same. The DIRECT symbol
; is used to switch between the two formulas.
; don't $DEFINE DIRECT
  float d = 0.0
  float d2 = 0.0
  complex z2 = (0,0)
  int iter = 0
  float diameter2 = sqr(@diameter)
  complex r = (0,1) ^ (@angle / 90.0)
  complex r0 = (0,0)
  complex rh = (0,1) ^ (@traporder / 8); heart rotation value
  complex zh = (0,0)
  complex trapcenter2 = @trapcenter

  if @trapshape == "ring ripples" || @trapshape == "grid ripples" || \
     @trapshape == "radial ripples"
    diameter2 = #pi / @diameter
  endif

$IFDEF DIRECT
  color accumulator = @startcolor; initialize color accumulator
  color current = rgb(0,0,0); holds current iteration's color
  
$ELSE
  float closest = 1e38
  float closest1 = 1e38
  complex point = (0,0)
  complex point1 = (0,0)
  complex point2 = (0,0)
  complex point3 = (0,0)
  bool done = false
  int i = 0
  int i1 = 0
  
  if @traptype == "farthest" || @traptype == "sum" || \
     @traptype == "average" || @traptype == "sign average" || \
     @traptype == "alternating average" || @traptype == "alternating average 2" || \
     @traptype == "inverted sum" || @traptype == "exponential average" || \
     @traptype == "average change" || @traptype == "inverted sum squared" || \
     @traptype == "trap only"
    closest = 0.0
  elseif @traptype == "product"
    closest = 1.0
  elseif @traptype == "second farthest" || @traptype == "two farthest"
    closest = 0.0
    closest = 0.0
  endif
$ENDIF  

  bool usesolid = true   ; assume a solid color

loop:
  iter = iter + 1        ; iteration counter

$IFDEF DIRECT
  z2 = #z
$ELSE
  if @traptype == "trap only"   ; trap only, work on unadulterated pixel
    z2 = #pixel
  else
    z2 = #z
  endif
$ENDIF
  
  z2 = (z2 - trapcenter2) * r; rotate  
  
  if @aspect != 1.0
    z2 = real(z2) + flip(imag(z2) * @aspect) ; apply aspect
  endif
  
  ; determine distance from trap -- different for each shape
  if @trapshape == "point"
    d = cabs(z2)
  elseif @trapshape == "ring"
    d = abs(cabs(z2) - @diameter)
  elseif @trapshape == "ring 2"
    d = abs(|z2| - diameter2)
  elseif @trapshape == "egg"
    d = (cabs(z2-flip(@diameter)*2) + cabs(z2)*@traporder*0.5) * 0.25
  elseif @trapshape == "hyperbola"
    d = abs(imag(z2) * real(z2) - @diameter)
  elseif @trapshape == "hypercross"
    d = abs(imag(z2) * real(z2))
  elseif @trapshape == "cross"
    d = abs(real(z2))
    d2 = abs(imag(z2))
    if d2 < d
      d = d2
    endif
  elseif @trapshape == "astroid"
    d = abs(real(z2))^@traporder + abs(imag(z2))^@traporder
    if @traporder < 0
      d = 1/d
    endif
  elseif @trapshape == "diamond"
    d = abs(real(z2)) + abs(imag(z2))
  elseif @trapshape == "rectangle"
    d = abs(real(z2))
    d2 = abs(imag(z2))
    if d2 > d
      d = d2
    endif
  elseif @trapshape == "box"
    d = abs(real(z2))
    d2 = abs(imag(z2))
    if d2 > d
      d = d2
    endif
    d = abs(d - @diameter)
  elseif @trapshape == "lines"
    d = abs(abs(imag(z2)) - @diameter)
  elseif @trapshape == "waves"
    d = abs(abs(imag(z2) + sin(real(z2)*@trapfreq)*@traporder*0.25) - @diameter)
  elseif @trapshape == "mirrored waves"
    d = abs(abs(imag(z2)) - @diameter + sin(real(z2)*@trapfreq)*@traporder*0.25)
  elseif @trapshape == "mirrored waves 2"
    d2 = @diameter - sin(real(z2)*@trapfreq)*@traporder*0.25; compute wave height
    d  = abs(abs(imag(z2)) - d2); distance to each wave
    d2 = abs(abs(imag(z2)) + d2)
    if d2 < d
      d = d2
    endif
  elseif @trapshape == "radial waves"
    d2 = atan2(z2)
    d = abs(cabs(z2) * (1 - sin(d2*@trapfreq)*@traporder*0.125) - @diameter)
  elseif @trapshape == "radial waves 2"
    d2 = atan2(z2)
    d2 = sin(d2*@trapfreq)*@traporder*0.125
    d = abs(cabs(z2) * (1 - d2) - @diameter)
    d2 = abs(cabs(z2) * (1 + d2) - @diameter)
    if d2 < d
      d = d2
    endif
  elseif @trapshape == "ring ripples"
    d = cabs(z2)
    if d < @traporder
      d = cos(d * diameter2 * @trapfreq) * sqr(1-d/@traporder)
    else
      d = 0
    endif
  elseif @trapshape == "grid ripples"
    d = cabs(z2)
    if d < @traporder
      d = (cos(real(z2)*diameter2*@trapfreq) + cos(imag(z2)*diameter2*@trapfreq)) * sqr(1-d/@traporder) * 0.5
    else
      d = 0
    endif
  elseif @trapshape == "radial ripples"
    d = atan2(z2)
    d2 = cabs(z2)
    if d2 < @traporder
      d = cos(4 * d * @trapfreq) * sqr(1-d2/@traporder)
    else
      d = 0
    endif
  elseif @trapshape == "pinch"
    d2 = atan2(z2)
    if d2 < 0
      d2 = d2 + 2*#pi
    endif
    d = sqrt(cabs(z2)) / abs(sin(d2*@traporder*0.5))
  elseif @trapshape == "spiral"
    d = 1/(cabs(z2)) * @diameter
    r0 = (0,1) ^ d
    z2 = z2 * r0
    d = atan(abs(imag(z2)/real(z2)))
  elseif @trapshape == "heart"
    zh = real(z2) + flip(abs(imag(z2)))
    zh = zh*rh * 3 / @diameter
    d = abs(real(zh) - sqr(imag(zh)) + 3)
  endif

$IFDEF DIRECT
  ; Compute direct color. This code is very similar to the normal processing
  ; in the final section.
  IF (d < @threshold); orbit is close enough to shape
    IF (@trapcolor == "distance"); distance
      current = gradient(d/@threshold)
    ELSEIF (@trapcolor == "magnitude"); magnitude
      current = gradient(cabs(z2))
    ELSEIF (@trapcolor == "real"); real
      current = gradient(abs(real(z2)))
    ELSEIF (@trapcolor == "imaginary"); imaginary
      current = gradient(abs(imag(z2)))
    ELSEIF (@trapcolor == "angle to trap"); angle to trap
      d2 = atan2(z2)
      IF (d2 < 0)
        d2 = d2 + #pi * 2
      ENDIF
      current = gradient(d2 / (#pi * 2))
    ELSEIF (@trapcolor == "angle to origin"); angle to origin
      d2 = atan2(#z)
      IF (d2 < 0)
        d2 = d2 + #pi * 2
      ENDIF
      current = gradient(d2 / (#pi * 2))
    ELSEIF (@trapcolor == "angle to origin 2") ; angle to origin 2 (old ReallyCool)
      current = gradient(0.02 * abs(atan(imag(#z) / real(#z)) * 180/#pi))
    ELSEIF (@trapcolor == "iteration"); iteration
      current = gradient(iter / #maxiter)
    ENDIF

    IF (@trapmergemodifier == "distance")
      current = rgba(red(current), green(current), blue(current), alpha(current) * (1 - d / @threshold))
    ENDIF
    IF (@trapmergeorder == "bottom-up")
      accumulator = compose(accumulator, blend(current, @trapmergemode(accumulator, current), alpha(accumulator)), @trapmergeopacity)
    ELSEIF (@trapmergeorder == "top-down")
      accumulator = compose(current, blend(accumulator, @trapmergemode(current, accumulator), alpha(current)), @trapmergeopacity)
    ENDIF
  ENDIF

$ELSE
  ; now adjust closest/point/i as needed
  IF (@traptype == 0); closest
    IF (d < closest)
      i = iter
      point = #z
      point2 = z2
      closest = d
    ENDIF
    IF (d < @threshold)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 1); farthest (within threshold)
    IF (d > closest && d < @threshold)
      i = iter
      point = #z
      point2 = z2
      closest = d
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 2); first (within threshold)
    IF (d < @threshold && done == false)
      i = iter
      point = #z
      point2 = z2
      closest = d
      done = true
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 3); last (within threshold)
    IF (d < @threshold)
      i = iter
      point = #z
      point2 = z2
      closest = d
      done = true
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 4); sum (within threshold)
    IF (d < @threshold)
      i = iter
      point = point + #z
      point2 = point2 + z2
      closest = closest + d
      usesolid = false
   ENDIF
  ELSEIF (@traptype == 5); average (within threshold)
    IF (d < @threshold)
      i = iter
      i1 = i1 + 1
      point = point + #z
      point2 = point2 + z2
      closest = closest + d
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 6); product (within threshold)
    IF (d < @threshold)
      i = iter
      point = point * #z / @threshold
      point2 = point2 * z2 / @threshold
      closest = closest * d / @threshold
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 7); sign average
    IF (d < d2)
      i = i + 1
      point = point + #z
      point2 = point2 + z2
      closest = closest + 1
      usesolid = false
    ELSE
      i = i - 1
    ENDIF
    d2 = d
  ELSEIF (@traptype == 8 || @traptype == 10) ; second/two closest
    IF (d < closest)
      i1 = i
      point1 = point
      point3 = point2
      closest1 = closest
      i = iter
      point = #z
      point2 = z2
      closest = d
    ELSEIF (d < closest1)
      i1 = iter
      point1 = #z
      point3 = z2
      closest1 = d
    ENDIF
    IF (d < @threshold)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 9 || @traptype == 11) ; second/two farthest
    IF (d > closest && d < @threshold)
      i1 = i
      point1 = point
      point3 = point2
      closest1 = closest
      i = iter
      point = #z
      point2 = z2
      closest = d
      usesolid = false
    ELSEIF (d > closest1 && d < @threshold)
      i1 = iter
      point1 = #z
      point3 = z2
      closest1 = d
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 12); funky average
    IF (d < @threshold)
      i = i + 1
      point = #z - point
      point2 = z2 - point2
      closest = @threshold - abs(closest - d)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 13); funky average 2
    IF (d < @threshold)
      i = i + 1
      point = #z - point
      point2 = z2 - point2
      closest = abs(d - @threshold + closest)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 14); funky average 3 (Luke Plant)
    IF (d < @threshold)
      i = i + 1
      d2 = d/@threshold
      point = #z + (point-#z) * d2
      point2 = z2 + (point2-z2) * d2
      closest = closest + d
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 15); funky average 4 (exponential average)
    IF (d < @threshold)
      i = i + 1
      point = #z - point
      point2 = z2 - point2
      closest = closest + exp(-d)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 16); funky average 5 (average distance change)
    IF (d < d2)
      point = point + #z
      point2 = point2 + z2
      closest = closest + d2-d
      usesolid = false
    ENDIF
    d2 = d
  ELSEIF (@traptype == 17); funky average 6 (Luke Plant, 1/squared)
    IF (d < @threshold)
      i = i + 1
      usesolid = false
    ENDIF
    d2 = sqr(d/@threshold)
    point = #z + (point-#z) * d2
    point2 = z2 + (point2-z2) * d2
    closest = closest + 1/d2
  ELSEIF (@traptype == 18); trap only, do first iteration
    IF (iter == 1)
      point = #z
      point2 = z2
      closest = d/@threshold
      IF (d < @threshold)
        usesolid = false
      ENDIF
    ENDIF
  ENDIF
$ENDIF  
  
final:
  ; Apply solid color, if it is allowed.
  if @solidcolor
    #solid = usesolid
  else
    #solid = false
  endif
  
$IFDEF DIRECT
  ; Return direct color.
  #color = accumulator
  
$ELSE
  ; Calculate index value.
  ; Un-fudge anything that was fudged.
  IF (@traptype == 5); traptype average
    point = point / i1
    point2 = point2 / i1
    closest = closest / i1
  ELSEIF (@traptype == 6); traptype product
    closest = abs(closest)
  ELSEIF (@traptype == 7); traptype sign average
    point = point / iter
    point2 = point2 / iter
    closest = closest / iter
  ELSEIF (@traptype == 8 || @traptype == 9) ; second closest or farthest
    i = i - i1
    point = point - point1
    point2 = point2 - point3
    closest = closest - closest1
  ELSEIF (@traptype == 10 || @traptype == 11) ; two closest or farthest
    i = round((i + i1) / 2)
    point = (point + point1) / 2
    point2 = (point2 + point3) / 2
    closest = (closest + closest1) / 2
  ELSEIF (@traptype == 14); funky average 3
    closest = @threshold * i - closest
  ENDIF

  ; choose coloring based on method
  IF (@trapcolor == 0); distance
    IF (@traptype == 2 || @traptype == 3) ; first or last type
      #index = closest / @threshold
    ELSE; any other trap type
      #index = closest
    ENDIF
  ELSEIF (@trapcolor == 1); magnitude
    #index = cabs(point2)
  ELSEIF (@trapcolor == 2); real
    #index = abs(real(point2))
  ELSEIF (@trapcolor == 3); imaginary
    #index = abs(imag(point2))
  ELSEIF (@trapcolor == 4); angle to trap
    d = atan2(point2)
    IF (d < 0)
      d = d + #pi * 2
    ENDIF
    #index = d / (#pi * 2)
  ELSEIF (@trapcolor == 5); angle to trap 2 (no aspect)
    point = point - @trapcenter
    d = atan2(point)
    IF (d < 0)
      d = d + #pi * 2
    ENDIF
    #index = d / (#pi * 2)
  ELSEIF (@trapcolor == 6); angle to origin
    d = atan2(point)
    IF (d < 0)
      d = d + #pi * 2
    ENDIF
    #index = d / (#pi * 2)
  ELSEIF (@trapcolor == 7); angle to origin 2 (old ReallyCool)
    #index = 0.02 * abs(atan(imag(point) / real(point)) * 180/#pi)
  ELSEIF (@trapcolor == 8); iteration
    d = i
    #index = d / #maxiter
  ENDIF
$ENDIF  
  
default:
  title = "Orbit Traps"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/orbittraps.html"
  
  param trapshape
    caption = "Trap Shape"
    default = 0
    enum = "point" "ring" "ring 2" "egg" "hyperbola" "hypercross" \
           "cross" "astroid" "diamond" "rectangle" "box" "lines" \
    "waves" "mirrored waves" "mirrored waves 2" \
   "radial waves" "radial waves 2" "ring ripples" \
   "grid ripples" "radial ripples" "pinch" "spiral" "heart"
    hint = "This is the shape of the orbit trap."
  endparam
  param diameter
    caption = "  Diameter"
    default = 1.0
    hint = "This is the diameter of the trap (for ring, box, and \
            line shapes)."
    visible = @trapshape != "point" && @trapshape != "hypercross" && \
              @trapshape != "cross" && @trapshape != "astroid" && \
              @trapshape != "diamond" && @trapshape != "rectangle" && \
              @trapshape != "radial ripples" && @trapshape != "pinch"
  endparam
  param traporder
    caption = "  Order"
    default = 4.0
    hint = "Number of leaves for the pinch trap shape, the \
            exponent to use for astroid curves (try 0.66667), \
            'egginess', or the height of waves."
    visible = @trapshape != "point" && @trapshape != "ring" && \
              @trapshape != "ring 2" && @trapshape != "hyperbola" && \
              @trapshape != "hypercross" && @trapshape != "cross" && \
              @trapshape != "diamond" && @trapshape != "rectangle" && \
              @trapshape != "box" && @trapshape != "lines" && \
              @trapshape != "spiral"
  endparam
  param trapfreq
    caption = "  Frequency"
    default = 1.0
    hint = "The frequency of ripples or waves."
    visible = @trapshape == "waves" || @trapshape == "mirrored waves" || \
              @trapshape == "mirrored waves 2" || @trapshape == "radial waves" || \
              @trapshape == "radial waves 2" || @trapshape == "ring ripples" || \
              @trapshape == "grid ripples" || @trapshape == "radial ripples"
  endparam
  param trapcolor
    caption = "Trap Coloring"
    default = 0
    enum = "distance" "magnitude" "real" "imaginary" "angle to trap" \
           "angle to trap 2" "angle to origin" "angle to origin 2" "iteration"
    hint = "This is the information used to produce a color."
  endparam

$IFDEF DIRECT
  param threshold
    caption = "Threshold"
    default = 0.25
    min = 0
  endparam

  heading
    caption = "Merging"
  endheading
  color param startcolor
    caption = "Base Color"
    default = rgb(0,0,0)
    hint = "Specifies the 'base', or starting color with which all iterations' \
            colors will be merged."
  endparam
  color func trapmergemode
    caption = "Trap Color Merge"
    default = mergenormal()
    hint = "This chooses the merge mode used to blend colors at each iteration."
  endfunc
  param trapmergemodifier
    caption = "Additional Alpha"
    default = 0
    enum = "none" "distance"
    hint = "Specifies an additional alpha value to incorporate during merging."
  endparam
  param trapmergeopacity
    caption = "Trap Merge Opacity"
    default = 0.2
    hint = "Sets the opacity of each trap shape. Even if you set this value to 1 \
        (forcing all traps to be fully opaque) you can still control opacity \
        using the alpha channel in the gradient."
  endparam
  param trapmergeorder
    caption = "Trap Merge Order"
    default = 0
    enum = "bottom-up" "top-down"
    hint = "Sets the order in which traps will be merged. Bottom-up merges new \
    traps on top of previous ones. Top-down merges new traps underneath \
    previous ones."
  endparam

$ELSE
  param traptype
    caption = "Trap Mode"
    default = 0
    enum = "closest" "farthest" "first" "last" "sum" "average" "product" \
           "sign average" "second closest" "second farthest" "two closest" \
           "two farthest" "alternating average" "alternating average 2" "inverted sum" \
           "exponential average" "average change" "inverted sum squared" \
           "trap only"
    hint = "This is how points will be chosen to use for coloring."
  endparam
  param threshold
    caption = "  Threshold"
    hint = "This is the width of the trap area, used for most trap modes."
    visible = @traptype != "sign average" && @traptype != "average change"
    default = 0.25
    min = 0
  endparam
$ENDIF

  heading
    caption = "Options"
  endheading
  param trapcenter
    caption = "Trap Center"
    default = (0,0)
    hint = "This is the location of the trap in the complex plane."
  endparam
  param aspect
    caption = "Aspect Ratio"
    default = 1.0
    min = 0.0000000001
    hint = "This is how square the trap is.  You can distort the \
            trap by using a value other than 1.0."
  endparam
  param angle
    caption = "Rotation"
    default = 0.0
    hint = "This is the angle, in degrees, that the trap should \
            be rotated."
  endparam
  param solidcolor
    caption = "Use Solid Color"
    default = false
    hint = "If enabled, areas 'outside' the trap area will be colored \
            with the 'solid color' on the coloring tab."
  endparam
}


DirectOrbitTraps {
;
; General Direct Orbit Traps coloring algorithm, suitable for almost
; all fractal types. Computes and combines colors at every iteration.
;
; Originally written by Damien M. Jones.
;
init:
; OrbitTraps and DirectOrbitTraps are exactly the same, except for the
; title. The DIRECT symbol is used to switch between the two formulas.
$DEFINE DIRECT
  float d = 0.0
  float d2 = 0.0
  complex z2 = (0,0)
  int iter = 0
  float diameter2 = sqr(@diameter)
  complex r = (0,1) ^ (@angle / 90.0)
  complex r0 = (0,0)
  complex rh = (0,1) ^ (@traporder / 8); heart rotation value
  complex zh = (0,0)
  complex trapcenter2 = @trapcenter

  if @trapshape == "ring ripples" || @trapshape == "grid ripples" || \
     @trapshape == "radial ripples"
    diameter2 = #pi / @diameter
  endif

$IFDEF DIRECT
  color accumulator = @startcolor; initialize color accumulator
  color current = rgb(0,0,0); holds current iteration's color
  
$ELSE
  float closest = 1e38
  float closest1 = 1e38
  complex point = (0,0)
  complex point1 = (0,0)
  complex point2 = (0,0)
  complex point3 = (0,0)
  bool done = false
  int i = 0
  int i1 = 0
  
  if @traptype == "farthest" || @traptype == "sum" || \
     @traptype == "average" || @traptype == "sign average" || \
     @traptype == "alternating average" || @traptype == "alternating average 2" || \
     @traptype == "inverted sum" || @traptype == "exponential average" || \
     @traptype == "average change" || @traptype == "inverted sum squared" || \
     @traptype == "trap only"
    closest = 0.0
  elseif @traptype == "product"
    closest = 1.0
  elseif @traptype == "second farthest" || @traptype == "two farthest"
    closest = 0.0
    closest = 0.0
  endif
$ENDIF  

  bool usesolid = true   ; assume a solid color

loop:
  iter = iter + 1        ; iteration counter

$IFDEF DIRECT
  z2 = #z
$ELSE
  if @traptype == "trap only"   ; trap only, work on unadulterated pixel
    z2 = #pixel
  else
    z2 = #z
  endif
$ENDIF
  
  z2 = (z2 - trapcenter2) * r; rotate  
  
  if @aspect != 1.0
    z2 = real(z2) + flip(imag(z2) * @aspect) ; apply aspect
  endif
  
  ; determine distance from trap -- different for each shape
  if @trapshape == "point"
    d = cabs(z2)
  elseif @trapshape == "ring"
    d = abs(cabs(z2) - @diameter)
  elseif @trapshape == "ring 2"
    d = abs(|z2| - diameter2)
  elseif @trapshape == "egg"
    d = (cabs(z2-flip(@diameter)*2) + cabs(z2)*@traporder*0.5) * 0.25
  elseif @trapshape == "hyperbola"
    d = abs(imag(z2) * real(z2) - @diameter)
  elseif @trapshape == "hypercross"
    d = abs(imag(z2) * real(z2))
  elseif @trapshape == "cross"
    d = abs(real(z2))
    d2 = abs(imag(z2))
    if d2 < d
      d = d2
    endif
  elseif @trapshape == "astroid"
    d = abs(real(z2))^@traporder + abs(imag(z2))^@traporder
    if @traporder < 0
      d = 1/d
    endif
  elseif @trapshape == "diamond"
    d = abs(real(z2)) + abs(imag(z2))
  elseif @trapshape == "rectangle"
    d = abs(real(z2))
    d2 = abs(imag(z2))
    if d2 > d
      d = d2
    endif
  elseif @trapshape == "box"
    d = abs(real(z2))
    d2 = abs(imag(z2))
    if d2 > d
      d = d2
    endif
    d = abs(d - @diameter)
  elseif @trapshape == "lines"
    d = abs(abs(imag(z2)) - @diameter)
  elseif @trapshape == "waves"
    d = abs(abs(imag(z2) + sin(real(z2)*@trapfreq)*@traporder*0.25) - @diameter)
  elseif @trapshape == "mirrored waves"
    d = abs(abs(imag(z2)) - @diameter + sin(real(z2)*@trapfreq)*@traporder*0.25)
  elseif @trapshape == "mirrored waves 2"
    d2 = @diameter - sin(real(z2)*@trapfreq)*@traporder*0.25; compute wave height
    d  = abs(abs(imag(z2)) - d2); distance to each wave
    d2 = abs(abs(imag(z2)) + d2)
    if d2 < d
      d = d2
    endif
  elseif @trapshape == "radial waves"
    d2 = atan2(z2)
    d = abs(cabs(z2) * (1 - sin(d2*@trapfreq)*@traporder*0.125) - @diameter)
  elseif @trapshape == "radial waves 2"
    d2 = atan2(z2)
    d2 = sin(d2*@trapfreq)*@traporder*0.125
    d = abs(cabs(z2) * (1 - d2) - @diameter)
    d2 = abs(cabs(z2) * (1 + d2) - @diameter)
    if d2 < d
      d = d2
    endif
  elseif @trapshape == "ring ripples"
    d = cabs(z2)
    if d < @traporder
      d = cos(d * diameter2 * @trapfreq) * sqr(1-d/@traporder)
    else
      d = 0
    endif
  elseif @trapshape == "grid ripples"
    d = cabs(z2)
    if d < @traporder
      d = (cos(real(z2)*diameter2*@trapfreq) + cos(imag(z2)*diameter2*@trapfreq)) * sqr(1-d/@traporder) * 0.5
    else
      d = 0
    endif
  elseif @trapshape == "radial ripples"
    d = atan2(z2)
    d2 = cabs(z2)
    if d2 < @traporder
      d = cos(4 * d * @trapfreq) * sqr(1-d2/@traporder)
    else
      d = 0
    endif
  elseif @trapshape == "pinch"
    d2 = atan2(z2)
    if d2 < 0
      d2 = d2 + 2*#pi
    endif
    d = sqrt(cabs(z2)) / abs(sin(d2*@traporder*0.5))
  elseif @trapshape == "spiral"
    d = 1/(cabs(z2)) * @diameter
    r0 = (0,1) ^ d
    z2 = z2 * r0
    d = atan(abs(imag(z2)/real(z2)))
  elseif @trapshape == "heart"
    zh = real(z2) + flip(abs(imag(z2)))
    zh = zh*rh * 3 / @diameter
    d = abs(real(zh) - sqr(imag(zh)) + 3)
  endif

$IFDEF DIRECT
  ; Compute direct color. This code is very similar to the normal processing
  ; in the final section.
  IF (d < @threshold); orbit is close enough to shape
    IF (@trapcolor == "distance"); distance
      current = gradient(d/@threshold)
    ELSEIF (@trapcolor == "magnitude"); magnitude
      current = gradient(cabs(z2))
    ELSEIF (@trapcolor == "real"); real
      current = gradient(abs(real(z2)))
    ELSEIF (@trapcolor == "imaginary"); imaginary
      current = gradient(abs(imag(z2)))
    ELSEIF (@trapcolor == "angle to trap"); angle to trap
      d2 = atan2(z2)
      IF (d2 < 0)
        d2 = d2 + #pi * 2
      ENDIF
      current = gradient(d2 / (#pi * 2))
    ELSEIF (@trapcolor == "angle to origin"); angle to origin
      d2 = atan2(#z)
      IF (d2 < 0)
        d2 = d2 + #pi * 2
      ENDIF
      current = gradient(d2 / (#pi * 2))
    ELSEIF (@trapcolor == "angle to origin 2") ; angle to origin 2 (old ReallyCool)
      current = gradient(0.02 * abs(atan(imag(#z) / real(#z)) * 180/#pi))
    ELSEIF (@trapcolor == "iteration"); iteration
      current = gradient(iter / #maxiter)
    ENDIF

    IF (@trapmergemodifier == "distance")
      current = rgba(red(current), green(current), blue(current), alpha(current) * (1 - d / @threshold))
    ENDIF
    IF (@trapmergeorder == "bottom-up")
      accumulator = compose(accumulator, blend(current, @trapmergemode(accumulator, current), alpha(accumulator)), @trapmergeopacity)
    ELSEIF (@trapmergeorder == "top-down")
      accumulator = compose(current, blend(accumulator, @trapmergemode(current, accumulator), alpha(current)), @trapmergeopacity)
    ENDIF
  ENDIF

$ELSE
  ; now adjust closest/point/i as needed
  IF (@traptype == 0); closest
    IF (d < closest)
      i = iter
      point = #z
      point2 = z2
      closest = d
    ENDIF
    IF (d < @threshold)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 1); farthest (within threshold)
    IF (d > closest && d < @threshold)
      i = iter
      point = #z
      point2 = z2
      closest = d
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 2); first (within threshold)
    IF (d < @threshold && done == false)
      i = iter
      point = #z
      point2 = z2
      closest = d
      done = true
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 3); last (within threshold)
    IF (d < @threshold)
      i = iter
      point = #z
      point2 = z2
      closest = d
      done = true
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 4); sum (within threshold)
    IF (d < @threshold)
      i = iter
      point = point + #z
      point2 = point2 + z2
      closest = closest + d
      usesolid = false
   ENDIF
  ELSEIF (@traptype == 5); average (within threshold)
    IF (d < @threshold)
      i = iter
      i1 = i1 + 1
      point = point + #z
      point2 = point2 + z2
      closest = closest + d
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 6); product (within threshold)
    IF (d < @threshold)
      i = iter
      point = point * #z / @threshold
      point2 = point2 * z2 / @threshold
      closest = closest * d / @threshold
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 7); sign average
    IF (d < d2)
      i = i + 1
      point = point + #z
      point2 = point2 + z2
      closest = closest + 1
      usesolid = false
    ELSE
      i = i - 1
    ENDIF
    d2 = d
  ELSEIF (@traptype == 8 || @traptype == 10) ; second/two closest
    IF (d < closest)
      i1 = i
      point1 = point
      point3 = point2
      closest1 = closest
      i = iter
      point = #z
      point2 = z2
      closest = d
    ELSEIF (d < closest1)
      i1 = iter
      point1 = #z
      point3 = z2
      closest1 = d
    ENDIF
    IF (d < @threshold)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 9 || @traptype == 11) ; second/two farthest
    IF (d > closest && d < @threshold)
      i1 = i
      point1 = point
      point3 = point2
      closest1 = closest
      i = iter
      point = #z
      point2 = z2
      closest = d
      usesolid = false
    ELSEIF (d > closest1 && d < @threshold)
      i1 = iter
      point1 = #z
      point3 = z2
      closest1 = d
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 12); funky average
    IF (d < @threshold)
      i = i + 1
      point = #z - point
      point2 = z2 - point2
      closest = @threshold - abs(closest - d)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 13); funky average 2
    IF (d < @threshold)
      i = i + 1
      point = #z - point
      point2 = z2 - point2
      closest = abs(d - @threshold + closest)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 14); funky average 3 (Luke Plant)
    IF (d < @threshold)
      i = i + 1
      d2 = d/@threshold
      point = #z + (point-#z) * d2
      point2 = z2 + (point2-z2) * d2
      closest = closest + d
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 15); funky average 4 (exponential average)
    IF (d < @threshold)
      i = i + 1
      point = #z - point
      point2 = z2 - point2
      closest = closest + exp(-d)
      usesolid = false
    ENDIF
  ELSEIF (@traptype == 16); funky average 5 (average distance change)
    IF (d < d2)
      point = point + #z
      point2 = point2 + z2
      closest = closest + d2-d
      usesolid = false
    ENDIF
    d2 = d
  ELSEIF (@traptype == 17); funky average 6 (Luke Plant, 1/squared)
    IF (d < @threshold)
      i = i + 1
      usesolid = false
    ENDIF
    d2 = sqr(d/@threshold)
    point = #z + (point-#z) * d2
    point2 = z2 + (point2-z2) * d2
    closest = closest + 1/d2
  ELSEIF (@traptype == 18); trap only, do first iteration
    IF (iter == 1)
      point = #z
      point2 = z2
      closest = d/@threshold
      IF (d < @threshold)
        usesolid = false
      ENDIF
    ENDIF
  ENDIF
$ENDIF  
  
final:
  ; Apply solid color, if it is allowed.
  if @solidcolor
    #solid = usesolid
  else
    #solid = false
  endif
  
$IFDEF DIRECT
  ; Return direct color.
  #color = accumulator
  
$ELSE
  ; Calculate index value.
  ; Un-fudge anything that was fudged.
  IF (@traptype == 5); traptype average
    point = point / i1
    point2 = point2 / i1
    closest = closest / i1
  ELSEIF (@traptype == 6); traptype product
    closest = abs(closest)
  ELSEIF (@traptype == 7); traptype sign average
    point = point / iter
    point2 = point2 / iter
    closest = closest / iter
  ELSEIF (@traptype == 8 || @traptype == 9) ; second closest or farthest
    i = i - i1
    point = point - point1
    point2 = point2 - point3
    closest = closest - closest1
  ELSEIF (@traptype == 10 || @traptype == 11) ; two closest or farthest
    i = round((i + i1) / 2)
    point = (point + point1) / 2
    point2 = (point2 + point3) / 2
    closest = (closest + closest1) / 2
  ELSEIF (@traptype == 14); funky average 3
    closest = @threshold * i - closest
  ENDIF

  ; choose coloring based on method
  IF (@trapcolor == 0); distance
    IF (@traptype == 2 || @traptype == 3) ; first or last type
      #index = closest / @threshold
    ELSE; any other trap type
      #index = closest
    ENDIF
  ELSEIF (@trapcolor == 1); magnitude
    #index = cabs(point2)
  ELSEIF (@trapcolor == 2); real
    #index = abs(real(point2))
  ELSEIF (@trapcolor == 3); imaginary
    #index = abs(imag(point2))
  ELSEIF (@trapcolor == 4); angle to trap
    d = atan2(point2)
    IF (d < 0)
      d = d + #pi * 2
    ENDIF
    #index = d / (#pi * 2)
  ELSEIF (@trapcolor == 5); angle to trap 2 (no aspect)
    point = point - @trapcenter
    d = atan2(point)
    IF (d < 0)
      d = d + #pi * 2
    ENDIF
    #index = d / (#pi * 2)
  ELSEIF (@trapcolor == 6); angle to origin
    d = atan2(point)
    IF (d < 0)
      d = d + #pi * 2
    ENDIF
    #index = d / (#pi * 2)
  ELSEIF (@trapcolor == 7); angle to origin 2 (old ReallyCool)
    #index = 0.02 * abs(atan(imag(point) / real(point)) * 180/#pi)
  ELSEIF (@trapcolor == 8); iteration
    d = i
    #index = d / #maxiter
  ENDIF
$ENDIF  
  
default:
  title = "Direct Orbit Traps"
  helpfile = "Uf3.chm"
  helptopic = "Html/coloring/standard/directorbittraps.html"

  param trapshape
    caption = "Trap Shape"
    default = 0
    enum = "point" "ring" "ring 2" "egg" "hyperbola" "hypercross" \
           "cross" "astroid" "diamond" "rectangle" "box" "lines" \
    "waves" "mirrored waves" "mirrored waves 2" \
   "radial waves" "radial waves 2" "ring ripples" \
   "grid ripples" "radial ripples" "pinch" "spiral" "heart"
    hint = "This is the shape of the orbit trap."
  endparam
  param diameter
    caption = "  Diameter"
    default = 1.0
    hint = "This is the diameter of the trap (for ring, box, and \
            line shapes)."
    visible = @trapshape != "point" && @trapshape != "hypercross" && \
              @trapshape != "cross" && @trapshape != "astroid" && \
              @trapshape != "diamond" && @trapshape != "rectangle" && \
              @trapshape != "radial ripples" && @trapshape != "pinch"
  endparam
  param traporder
    caption = "  Order"
    default = 4.0
    hint = "Number of leaves for the pinch trap shape, the \
            exponent to use for astroid curves (try 0.66667), \
            'egginess', or the height of waves."
    visible = @trapshape != "point" && @trapshape != "ring" && \
              @trapshape != "ring 2" && @trapshape != "hyperbola" && \
              @trapshape != "hypercross" && @trapshape != "cross" && \
              @trapshape != "diamond" && @trapshape != "rectangle" && \
              @trapshape != "box" && @trapshape != "lines" && \
              @trapshape != "spiral"
  endparam
  param trapfreq
    caption = "  Frequency"
    default = 1.0
    hint = "The frequency of ripples or waves."
    visible = @trapshape == "waves" || @trapshape == "mirrored waves" || \
              @trapshape == "mirrored waves 2" || @trapshape == "radial waves" || \
              @trapshape == "radial waves 2" || @trapshape == "ring ripples" || \
              @trapshape == "grid ripples" || @trapshape == "radial ripples"
  endparam
  param trapcolor
    caption = "Trap Coloring"
    default = 0
    enum = "distance" "magnitude" "real" "imaginary" "angle to trap" \
           "angle to trap 2" "angle to origin" "angle to origin 2" "iteration"
    hint = "This is the information used to produce a color."
  endparam

$IFDEF DIRECT
  float param threshold
    caption = "Threshold"
    default = 0.25
    min = 0
  endparam

  heading
    caption = "Merging"
  endheading
  color param startcolor
    caption = "Base Color"
    default = rgb(0,0,0)
    hint = "Specifies the 'base', or starting color with which all iterations' \
            colors will be merged."
  endparam
  color func trapmergemode
    caption = "Trap Color Merge"
    default = mergenormal()
    hint = "This chooses the merge mode used to blend colors at each iteration."
  endfunc
  param trapmergemodifier
    caption = "Additional Alpha"
    default = 0
    enum = "none" "distance"
    hint = "Specifies an additional alpha value to incorporate during merging."
  endparam
  param trapmergeopacity
    caption = "Trap Merge Opacity"
    default = 0.2
    hint = "Sets the opacity of each trap shape. Even if you set this value to 1 \
        (forcing all traps to be fully opaque) you can still control opacity \
        using the alpha channel in the gradient."
  endparam
  param trapmergeorder
    caption = "Trap Merge Order"
    default = 0
    enum = "bottom-up" "top-down"
    hint = "Sets the order in which traps will be merged. Bottom-up merges new \
    traps on top of previous ones. Top-down merges new traps underneath \
    previous ones."
  endparam

$ELSE
  param traptype
    caption = "Trap Mode"
    default = 0
    enum = "closest" "farthest" "first" "last" "sum" "average" "product" \
           "sign average" "second closest" "second farthest" "two closest" \
           "two farthest" "alternating average" "alternating average 2" "inverted sum" \
           "exponential average" "average change" "inverted sum squared" \
           "trap only"
    hint = "This is how points will be chosen to use for coloring."
  endparam
  param threshold
    caption = "  Threshold"
    hint = "This is the width of the trap area, used for most trap modes."
    visible = @traptype != "sign average" && @traptype != "average change"
    default = 0.25
    min = 0
  endparam
$ENDIF

  heading
    caption = "Options"
  endheading
  param trapcenter
    caption = "Trap Center"
    default = (0,0)
    hint = "This is the location of the trap in the complex plane."
  endparam
  param aspect
    caption = "Aspect Ratio"
    default = 1.0
    min = 0.0000000001
    hint = "This is how square the trap is.  You can distort the \
            trap by using a value other than 1.0."
  endparam
  param angle
    caption = "Rotation"
    default = 0.0
    hint = "This is the angle, in degrees, that the trap should \
            be rotated."
  endparam
  param solidcolor
    caption = "Use Solid Color"
    default = false
    hint = "If enabled, areas 'outside' the trap area will be colored \
            with the 'solid color' on the coloring tab."
  endparam
}