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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I seem to have just invented, or at least discovered, the wheel. Today's image certainly does resemble a chariot wheel, with its 8 spokes and various decorations. But actually, it's a midget in the fractal that is created by the iterated formula: -0.6(Z^(-1.3))-0.006(Z^(-3))+(1/C). Regardless of what it is, the name "The Wheel" serves well as a description of the picture. The parent fractal is a routine shape created by combining negative portions of Z^(-1.3) and Z^(-3). Today's scene is located very deep in a tiny valley, just inland of the conventional buds, near to a larger midget. I rated it at a 6 because of the unusually brilliant colors, though at times I think that the colors are a bit too brilliant. The magnitude of the image is so great that I needed to include an entry in the parameter file telling the program to render the scene at the correct magnitude regardless of whether it is fully resolved. I do not intentionally go beyond the limits of the math routine as I did today, but sometimes the midget that I am chasing doesn't appear until the resolution limit has been reached. The parameter file of the scene requires almost one hour to render on my 200MHZ once-a-fireball-but-now-a-clunker computer. A hasty trip to one of the two web sites where the image is posted will be well worth the effort. But give Paul and Scott a chance to render and post the image before visiting. The URL's of those sites are: The fractal weather today was cloudy with light rain and a temperature of 75F (24C). Later in the afternoon however, the rain stopped, the clouds blew away and the fractal cats ventured out of doors. When they returned to the house, I found a freshly-killed and half-eaten sparrow on the pathway. I have no way of knowing for sure who did it, though Tippy had the more satisfied attitude after the event. It's now time to get on to other things. So until next time, which will be here before you know it, take care, and why do fractals exist in a world where so much does not exist? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
The_Wheel { ; time=0:56:22.09--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-14.27546797101664000/-10.1681352980652\
0000/5.003527e+011/1/-98.994/1 mathtolerance=/1
params=-0.6/-1.3/-0.006/-3/0/800 float=y
maxiter=6000 inside=0 logmap=1000 periodicity=10
colors=000OOFMMFKKFJIFHGFFEGECGCAGA8G96G74G52G41G9\
DGDOGHZGPXGWWGcUGjTGrRGyQGrVHl_HfcH_hHUmHOqHLmHJjH\
HgHFcHD`HBYH9VHCWIEXIGYJJYJLZJN_KQ_KS`KUaLXaLZbM`c\
MccMedNgeNjeNlfOngOpgOkiTfkXam`XndWkaVi_VgYUdWTbUT\
`SSZPSWNRULQSJQPHPNFPLCOJANG8NE6MC4MA2PHAROHTVOV`V\
XgaZnh`toWkhScaOWVKOOGGHC8BDACEBCECCFDCFFDGGDGHDHI\
DIJDILEJMEJNEKOEKPEMQCOQBPRARR8SS7US6WT4XT3ZU2_U1a\
S5bQ8cPCdNFeLJfKMgIQhHTiFWjD_kCblAfm9in7mo5pp4tq2w\
r1zp2xo3vn3tm4rl4qj5oi5mh6kg6jf7he7fc8db9ba9a`A__A\
YYBWXBVWCTVCRUDPTDOWENZEM`FMcFLeGKhGKkHJmHIpIIrIHu\
JGwJGwIFvHDvGBvGAvF8uE7uD5uC4uB2uB1tD2sF2sH2rJ2qL2\
qN2pP3pR3oV3nZ3na3md3me3o`3qU3pR8oMDnGHmFMlERkEVjD\
_iCdhChgBmfAreAvgEpiHkkKflNanRXpUSrXNs_InYJjWJfVKb\
TKZSLVQLRPMNNMJMMMLKOKJRKHTJGWJEYID_ICaJEcKGeKIgLJ\
iMLkMNmNPoOQqOSsPUuPVwQXyRZzR`zSazTczCSzDTzFTzHTzI\
UzKUzMUzNVzPVzRVzUFzSFzQF
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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times.
