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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Yes, I'm late again today with the FOTD. It's getting to be a habit. My excuse is the same old one which needs no repetition. Today's fractal image, which looks like a rotten melon with a face drawn on it, being squashed, fairly cries "OOOF!". So this is what I named it. Normally, I avoid images that resemble funny faces, but today's picture is so ridiculous that I had no choice but to declare it FOTD for April 25. I displayed my disgust with comedy fractals by rating the image a lowly 3. The formula behind the image is Z^2+C -- the Mandelbrot formula. The mouth of the squashed melon-head is actually a Mandel-midget on the tip of the longest northwest filament shooting out from the fifth bud along the negative tail of the M-set. The midget is so distorted because it has been sliced in a different direction through the 4-dimensional Julibrot, which is the assemblage of all Julia sets and all perturbed Mandelbrot sets. Though the Mandelbrot formula drew the image, the image is not part of any Mandelbrot set. Nor is it part of any Julia set. It is kind of a hybrid, with both Mandelbrot and Julia characteristics, and a few entirely new characteristics, such as the stretching effect, thrown in for extra measure. I seem to have forgotten the Julibrot and the fourth dimension since becoming involved with the M-Mix4 formula and its limitless variety of midgets. But perhaps it's time to get back to basics as well as the unknown, and nothing is more unknown than the fourth dimension. Since the FOTD is so, late, the parameter file is the fastest in many months, rendering in less than a minute on a 200mhz Pentium. It will take longer than that to reach the GIF image, which is posted to: The fractal weather experts was very warm again today. The cats, comfort seekers that they are, took full advantage of the 86F (30C) temperature, by spending the entire afternoon lounging in the yard. That's it for today. It's time to rev up the fractal shoppe and get busy with other things. Until next time, take care, and life is never so good that it can't get better. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
OOOF { ; time=0:00:54.58--SF5 on a p200
reset=2001 type=formula formulafile=multirot.frm
formulaname=multirot-xz-yw passes=b
center-mag=-0.00000000002107355/-0.000000000029447\
31/8.638531e+009/14.687/-180/35.229
params=45/45/-1.4041038040019/0.00422258114480\
08/-1.4041038040019/0.0042225811448008 float=y
maxiter=600 inside=255 logmap=147 periodicity=10
colors=000Eg`JgbOgdSgfXgh`gjeglignfijckg`ldYnaVpYS\
qVPsSMtPVrJbpD_rFXsGUtIRvJOwLMxMKpQIiTGaXFV_DNbBGf\
98i81lYQN`UQbYTdaWgdZihakldmogelgZjgShgLfgEdg7bg0`\
gFcMTf091V74X67Z5A`4Db3Gd2Jf1MgJaYDaP7aG1a7TF6UO9U\
WBUdEUlGUtIQjTM`bIRmFIwNLqVNlbQfjSaqUXpSVpRTpPRpOP\
pNOjLLeJI`HFWFCQD9LB6G93B7195Y9ak8Vj7Pj6Ji6DiCKcHQ\
YNWTSaNXgIfbVoYgxUskdr_nrcgkfaeiW_lPUoJOrDIu7CkCQa\
GcbLebQfcVhcZidckdhlemneqofiofaogUogMogFoaLmWQkRVj\
L_hGdgI`cLY_NUWQQRSNNVJJXGFaJZfLrZLqRLpKLoMQpNVpO_\
pPdpQipRnpSspWrkZqfbpaepYioTlnOpmJsmFklJckNXkQPjUH\
iYAi`QfdddgsbjVac6`X5_S5_N5ZI4ZD4Y84Y3BVIHSXOPkUNz\
ZRsbUlfXej_ZnbSteEzh1daqUysYwmauhesbhqYloTpmNtkIwj\
DsbBpV9mO8iG6f84c13kPrmRlnSgpTaqUXsWStXMvYHwZCuVBt\
RAsN9rJ8qF7pB6o85k58h2Ae0CaBPZM`WXlaThgPdmM`sIXxFU\
ZPM9ZEAaFAcFBeGBgGCfEDeDEeBFdAGd8Hc7Ic6HZ7HV7GR76h\
l4ilGcdRYYaSQlMJwHCgQL000
}
frm:multirot-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=sqr(z)+c,
|z| <= 36 }
END 20.0 PAR-FORMULA FILE==================================
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