Embedded Julia Set
From Ultrafractal Wiki
Toby Marshall wrote:
You'll see that the filament has many small "islands" spaced across its length.
These islands are embedded Julia sets. Their shape is the shape of the
Julia set that is taken from the same place on the main set, relative to
where this point is to the West Midget. Here's the corresponding Julia set;
you can see that it has the same essential structure (without the filaments,
of course).
Kerry
Copyright © 2008 by Kerry Mitchell
squareMidgetFig.5Julia {
fractal:
title="square midget fig.5 Julia" width=500 height=500 layers=1
credits="Kerry Mitchell;1/11/2009"
layer:
caption="Background" opacity=100 method=multipass
mapping:
center=0/0 magn=1.7 angle=83
formula:
maxiter=10000 percheck=off filename="Standard.ufm" entry="Julia"
p_seed=0.256030882961008/0.000753981228703686 p_power=2/0
p_bailout=1e12
inside:
density=.87 transfer=none
outside:
transfer=sqrt solid=4286722382 filename="Standard.ucl"
entry="Smooth" p_power=2/0 p_bailout=1e12
gradient:
smooth=yes index=0 color=0 index=200 color=16777215
opacity:
smooth=yes rotation=90 index=66 opacity=255 index=467 opacity=255
index=298 opacity=255
}
***
Here's a second-level embedded Julia. There's a midget off of the main set (I used the West Midget, like Toby did), off of which there's an embedded Julia. In the center of that is a midget, off of which I zoomed into another midget (in the elephant valley). In the seahorse valley of this midget is the second-level embedded Julia.
To see the progression, start with the magnification of this parameter set at 3E0. This will show the West Midget in the center of the window. Without changing the location center, just increase the exponent on the magnification by 1: 3E1, 3E2, 3E3, etc. At 3E5, you'll see the first-level embedded Julia, and its center midget at 3E8. At 3E11, the next midget will appear, and the embedded Julia at 3E15.
Kerry
Copyright © 2008 by Kerry Mitchell
jan11-a {
; second-level embedded Julia
fractal:
title="jan11-a" width=640 height=480 layers=1
credits="Kerry Mitchell;1/11/2009"
layer:
caption="Background" opacity=100
mapping:
center=-1.7494530187891835966886215/0.00009812081244531119944114343
magn=3E15
formula:
maxiter=104983 percheck=off adjust=yes filename="Standard.ufm"
entry="Mandelbrot" p_start=0/0 p_power=2/0 p_bailout=1e12
inside:
transfer=none solid=4290707456
outside:
transfer=cuberoot filename="Standard.ucl" entry="Smooth" p_power=2/0
p_bailout=1e12
gradient:
smooth=yes index=0 color=0 index=200 color=16777215
opacity:
smooth=no index=0 opacity=255
}
