Love at first sight

Rupert  Russell

Ballarat, Australia

Artist's Description


counter from “feedjit”: http://feedjit.com/joinimg/

Created with Ultra Fractal 3.02

MandelbrotBuilt-in {
formula:
maxiter=10000 filename=“Standard.ufm” entry=“FastMandel” p_start=0/0
p_bailout=4.0
}

BackgroundLocation {
location:
center=-0.889111733/-0.0550393425 magn=1.2130613
}

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
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
}

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