Trapinsky
From Ultrafractal Wiki
Trapinsky is a Fractal Formula in sam.ufm.
Contents |
What is it?
This formula divide the complex plane into squares of length 1/2^n at the nth iteration. The point bails out if it is inside (or outside) a shape centered in this square. It can gives some Sierpinski-like patterns.
Parameters
Shape
Define the shape of the trap
Shape parameter
A parameter of the equation of the trap. The default value is set so that it works well with the Astroïd. So you might have to change it if you are using another shape. If you use the Pinch, change this value to 5 or 6 (or the number of "petals" you want the pinch to have). On some shape like the Circle or the Square, this parameter has no effect.
Threshold
Define how far from the curve a point is considered as inside. No effect on some shapes. If the points aren't bailed out fast enough (ie the image is messy and long to calculate) or are bailed out too fast, changing this value can help. In this case, you can also try changing the size of the shape.
Rotation Step
Enables you to rotate the trap at each iteration.
Invert z
Apply z -> 1/z before trapping. This can change the shape of the trap.
Graph functions
Only with the Graph shape. The graph shape is defined by f(x) = g(y). Set the y function to ident to get a "standard" graph.
Examples
Copyright 1999 Samuel Monnier
trap2 {
; Copyrights 1999 S. Monnier
; http://www.crosswinds.net/~s31415/index/index.htm
fractal:
title="trap2" width=600 height=600 author="Samuel"
created="December 25, 1999" numlayers=9
layer:
caption="New Layer 9" opacity=12 visible=yes alpha=no mergemode=screen
mapping:
center=0.5/0.5 magn=4 angle=0
formula:
filename="mt.ufm" entry="mt-pixel" maxiter=100 percheck=normal
p_inside=no
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-Smooth2" density=0.100000000000000006
transfer=linear repeat=yes
gradient:
smooth=yes numnodes=5 index=202 color=0 index=317 color=0 index=357
color=0 index=358 color=16777215 index=398 color=16777215
layer:
method=multipass caption="New Layer 4" opacity=100 visible=yes alpha=no
mergemode=multiply
mapping:
center=0.5/0.5 magn=4 angle=0
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Squares" p_size=0.25 p_rot=0 p_r=1 p_n=0.5 p_thresh=0.2
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-Smooth2" density=0.100000000000000006
transfer=linear repeat=yes
gradient:
smooth=yes numnodes=5 index=202 color=0 index=317 color=0 index=357
color=0 index=358 color=16777215 index=398 color=16777215
layer:
method=multipass caption="New Layer 8" opacity=52 visible=yes alpha=yes
mergemode=color
mapping:
center=0.5/0.5 magn=4 angle=0
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Squares" p_size=0.25 p_rot=0 p_r=1 p_n=0.5 p_thresh=0.2
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-Decomp" transfer=linear repeat=yes
p_portion=256
gradient:
smooth=yes numnodes=1 index=357 color=6513507
alpha:
smooth=yes numnodes=8 index=106 alpha=255 index=107 alpha=0 index=200
alpha=0 index=201 alpha=255 index=292 alpha=255 index=293 alpha=0
index=398 alpha=0 index=399 alpha=255
layer:
caption="New Layer 7" opacity=83 visible=yes alpha=no
mergemode=saturation
mapping:
center=-0.147381756756756768/1.88456805019305024
magn=0.945713878191413504 angle=0
formula:
filename="mt.ufm" entry="mt-pixel" maxiter=100 percheck=normal
p_inside=no
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-fBm" transfer=linear repeat=yes p_scale=0.5
p_angle=0 p_step=0.7 p_anglestep=37 p_octaves=10 p_power=2
gradient:
smooth=yes numnodes=2 index=111 color=14811207 index=325 color=6974058
layer:
method=multipass caption="New Layer 6" opacity=100 visible=yes alpha=no
mergemode=overlay
mapping:
center=0.5/0.5 magn=4 angle=0
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Squares" p_size=0.25 p_rot=0 p_r=1 p_n=0.5 p_thresh=0.2
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-fBm" density=0.5 transfer=linear repeat=yes
p_scale=1 p_angle=0 p_step=0.1 p_anglestep=37 p_octaves=7 p_power=2
gradient:
smooth=yes numnodes=3 index=0 color=1354460 index=103 color=1655227
index=327 color=12194381
layer:
method=multipass caption="New Layer 5" opacity=100 visible=yes alpha=no
mergemode=softlight
mapping:
center=0.5/0.5 magn=4 angle=0
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Squares" p_size=0.25 p_rot=0 p_r=1 p_n=0.5 p_thresh=0.2
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-Lyapunov" density=0.5 transfer=linear
repeat=yes p_trackvariable="magnitude of z" p_negative="absolute value"
p_power=2 p_bailout=1E20 p_smooth=no
gradient:
smooth=yes numnodes=3 index=106 color=4524387 index=224 color=12187903
index=294 color=2239281
layer:
method=multipass caption="New Layer 3" opacity=100 visible=yes alpha=no
mergemode=hardlight
mapping:
center=0.5/0.5 magn=4 angle=0
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Squares" p_size=0.25 p_rot=0 p_r=1 p_n=0.5 p_thresh=0.2
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-fBm" transfer=linear repeat=yes p_scale=0.5
p_angle=0 p_step=0.5 p_anglestep=37 p_octaves=7 p_power=2
gradient:
smooth=yes numnodes=2 index=98 color=14015681 index=268 color=4274990
layer:
method=multipass caption="New Layer 2" opacity=100 visible=yes alpha=no
mergemode=difference
mapping:
center=0.502/0.503 magn=4 angle=0
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Squares" p_size=0.25 p_rot=0 p_r=1 p_n=0.5 p_thresh=0.2
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-fBm" density=0.5 transfer=linear repeat=yes
p_scale=0.2 p_angle=0 p_step=0.5 p_anglestep=37 p_octaves=7 p_power=4
gradient:
smooth=yes numnodes=2 index=68 color=0 index=221 color=16777215
layer:
method=multipass caption="New Layer 1" opacity=0 visible=yes alpha=no
mergemode=difference
mapping:
center=0.5/0.5 magn=4 angle=0
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Squares" p_size=0.25 p_rot=0 p_r=1 p_n=0.5 p_thresh=0.2
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-fBm" density=0.5 transfer=linear repeat=yes
p_scale=0.2 p_angle=0 p_step=0.5 p_anglestep=37 p_octaves=7 p_power=4
gradient:
smooth=yes numnodes=2 index=27 color=0 index=180 color=16777215
}
Copyright 1999 Samuel Monnier
sq1 {
; Copyrights 1999 S. Monnier
; http://www.crosswinds.net/~s31415/index/index.htm
fractal:
title="sq1" width=600 height=600 author="Samuel"
created="December 23, 1999" numlayers=7
layer:
method=multipass caption="New Layer 2" opacity=100 visible=yes alpha=no
mergemode=overlay
mapping:
center=-0.124978194286819/0.499943244382454521 magn=7.27608641340130458
angle=134.895794878437078
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Strophoïd" p_size=0.25 p_rot=0 p_r=1 p_n=100 p_thresh=0.5
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
density=1000012 transfer=linear repeat=yes
gradient:
smooth=no numnodes=6 index=0 color=4933396 index=75 color=7968129
index=93 color=9608079 index=142 color=11595514 index=196 color=6910817
index=245 color=12643832
layer:
method=multipass caption="New Layer 7" opacity=0 visible=yes alpha=no
mergemode=overlay
mapping:
center=-0.124878194286818983/0.503943244382454525
magn=7.27608641340130458 angle=134.895794878437078
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Strophoïd" p_size=0.1 p_rot=0 p_r=1 p_n=100 p_thresh=0.5
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
density=1000012 transfer=linear repeat=yes
gradient:
smooth=no numnodes=4 index=2 color=4999189 index=153 color=11661050
index=211 color=2502431 index=348 color=12709368
layer:
method=multipass caption="New Layer 4" opacity=100 visible=yes alpha=no
mergemode=softlight
mapping:
center=-0.124978194286819/0.499943244382454521 magn=7.27608641340130458
angle=134.895794878437078
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Strophoïd" p_size=0.25 p_rot=0 p_r=1 p_n=100 p_thresh=0.5
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-fBm" density=0.400000000000000022
transfer=linear repeat=yes p_scale=2 p_angle=0 p_step=0.5 p_anglestep=37
p_octaves=7 p_power=2
gradient:
smooth=no numnodes=5 index=15 color=8289918 index=48 color=7500402
index=60 color=5131854 index=132 color=263219 index=331 color=11789802
layer:
method=multipass caption="New Layer 3" opacity=100 visible=yes alpha=no
mergemode=overlay
mapping:
center=-0.124978194286819/0.499943244382454521 magn=7.27608641340130458
angle=134.895794878437078
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Strophoïd" p_size=0.25 p_rot=0 p_r=1 p_n=100 p_thresh=0.5
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-fBm" density=5 transfer=linear repeat=yes
p_scale=0.1 p_angle=0 p_step=0.5 p_anglestep=37 p_octaves=7 p_power=2
gradient:
smooth=yes numnodes=2 index=83 color=5131854 index=277 color=10340067
layer:
method=multipass caption="New Layer 5" opacity=100 visible=yes alpha=no
mergemode=difference
mapping:
center=-0.124878194286818983/0.500943244382454523
magn=7.27608641340130458 angle=134.895794878437078
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Strophoïd" p_size=0.25 p_rot=0 p_r=1 p_n=100 p_thresh=0.5
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
density=2 transfer=linear repeat=yes
gradient:
smooth=no position=-6 numnodes=2 index=156 color=0 index=356
color=16777215
layer:
method=multipass caption="Layer 1" opacity=100 visible=yes alpha=no
mergemode=multiply
mapping:
center=-0.124978194286819/0.499943244382454521 magn=7.27608641340130458
angle=134.895794878437078
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Strophoïd" p_size=0.25 p_rot=0 p_r=1 p_n=100 p_thresh=0.5
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
density=2 transfer=linear repeat=yes
gradient:
smooth=no numnodes=2 index=129 color=0 index=329 color=16777215
layer:
method=multipass caption="New Layer 1" opacity=100 visible=yes alpha=no
mergemode=overlay
mapping:
center=-0.124978194286819/0.499943244382454521 magn=7.27608641340130458
angle=134.895794878437078
formula:
filename="sam.ufm" entry="trapinski" maxiter=100 percheck=off
p_shape="Strophoïd" p_size=0.25 p_rot=0 p_r=1 p_n=100 p_thresh=0.5
p_rotst=0 p_inside="Outside" p_invert=no f_g1=sin f_g2=ident f_f1=ident
f_f2=ident f_f3=ident
inside:
transfer=none repeat=yes
outside:
filename="mt.ucl" entry="mt-magnitude" density=0.100000000000000006
transfer=linear repeat=yes p_mode="Final magnitude"
gradient:
smooth=yes numnodes=2 index=80 color=16777215 index=363 color=0
}
