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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is named "The Cube-Root of 2". The reason is simple -- the exponent of Z is 1.26, which is approximately the cube root of 2. I have complicated things a bit by drawing the fractal as it exists 70 levels down the hyper-something created by multi-valued complex-logarithms. (This something might or might not be an actual spiral.) The parent fractal is the nearly shapeless thing that would be expected to be created by exponents in this low range. Its most interesting part lies on its west border, where a nest of filaments appear to be trying to form a theme. Today's image lies near a node in this nest of loosely-organized filaments. Filaments. This is one thing that fractals in this range have an abundance of. They are easy sources of midgets, but the midgets have a tendency to all look the same -- like spiny undersea creatures. Today's midget, if that is what a theoretical but invisible object at the center of the image can be called, is surrounded by filaments different enough to almost create a theme pattern. The effect is striking enough to make the image worthy of being declared FOTD for July 7. The rating of a 6 and render time of four minutes (on my tired old fractal machine) combine into an overall value of 146. It is up to the individual fractalist to decide whether to run the attached parameter file and wait a couple minutes or to download the completed image from the FOTD web site at: Monday was 95F 35C hot here at Fractal Central, until a brief heavy thunder-squall cooled things notably at 6pm. Tuesday was sunny and cooler, but the strong sun and high temperature of 88F 31C still made things uncomfortably warm. The cats made the best of the conditions. Today is starting sunny and warmer. It looks like another day of overheated cats. For me, it looks like a lot of work, so my intuition tells me it's time to get started working. Until next FOTD in a day or a few, take care, and be fair. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
The_Cube-Root_of_2 { ; time=0:04:07.00--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 passes=1 center-mag=-1.46\
8655458749068/+0.9535213132151095/2446642/1/75/1.16\
947064154049318e-005 params=1.26/0/-70/100 float=y
maxiter=1200 inside=0 periodicity=10
colors=000nNrf_qcXqaVqZSqWPqTMqRKqOHqLEqKAsJCqJEoJ\
GnJIlIKkIMiIOhIQfISdHUcHWaHY`H_Z7fPHaYRYe`UmgOwiQu\
jSskUqlWomYnn_loajpchqefrgesictkaum_voYwqXxpWxpWxo\
WxoWynVynVynVymVymVzlUzlUzkUzkUzkUxjSvjQtiOriNphLn\
hJmgIkgGifEgfCeeBce9ad7`d6ab7aa8a`8a_9aZAaYAaWBaVB\
aUCbTDbSDbREbPEbOFbNGbMGbLHbKH`MGZNFYOFWPEUQETRDRS\
DQTCOUCMVBLXBJYAHZAG_9E`9Da8Bb89c78d76e64h35f65e86\
dA6bD7aF7`H8_K8AY8A_9Aa9AcAAeAAgBAiBAkBAmCAoCBqDCs\
DDuEEwEFvEGzCFfBHQDKSFNUHQWJTYLWaOZeQaiTdmVgqYjs`m\
uboweqxhszkuzmwzpxzryztzznqwnpwnovnnuomuoltoksojso\
irphqpgqpfppeorcqpdoodnndmmdkldjkdijdgidfheegecfeb\
eeade_ceZbeYcdVaeX`eZ_e_ZfaYfbWfdVgfUggTgiSgjQhlPh\
nOhoNiqMirKitJjvIjwHjy5gzGjzRmzapzYjtUdoQZjMTeHL`I\
N`JP`JR`KT`KV`LX`LY`M_`Ma`Nc`Ne`Og`Oi`Pj`Pl`Qn`Qp`\
Rr`Rt`Sv`Sw`LvVEuQ7tK1sF4qI7oKAmMCkOFjQIhTLfVNdXQb\
ZTa`W_cYYe`WgcUifTkhRnkPp }
frm:MandelbrotBC2 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*floor(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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