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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I named today's fractal image "Spokes". The name was inspired by the four straight arms radiating from the traditional midget at the center. The arms are not workable spokes however, for they are an illusion, no more than infinitely divided fractal debris arranged into roughly straight lines. The parent fractal was created by adding 3 parts of Z^4 to Z^2. Because the formula was iterated with 1/C rather than C, the fractal is inverted -- an island in an infinite ocean, rather than a lake in an infinite continent. But the island is lined with the expected Mandelbrot buds along its shoreline, and two very distorted Mandelbrot midgets lie in the marsh-lands near the western shore. Today's image lies in a valley of one of these midgets. Studying the image, I could find nothing outstanding in it. Yet it's not really a below-average image. Undecided, I rated it an average 5. The image takes 46 minutes to render on my squeaky old Pentium 200mhz machine with the fan that needs to be nudged with a toothpick before it starts turning. Waiting this long a time is a rather heavy effort for such a mediocre result, but frustration may be avoided by letting Paul and Scott do the work and downloading the completed image from one of their FOTD web sites. Paul's site is at: The fractal weather Saturday featured a raw wind and steady cold rain from morning until dusk, eventually totalling around 1/2 inch (13mm). The fractal cats hate rain, they hate wind, and they hate cold temperatures such as the 39F 4C, which was all we could reach today. Needless to say, the dynamic duo were most unhappy, and sulked most all afternoon. A treat of warm tuna followed by a turkey treat was necessary to lift their spirits. My spirits are reasonably high now that the hard part of the seasonal decoration is finished. They are high enough in fact, that I might go searching for one of those elusive fractals. If I find one, it will appear as tomorrow's FOTD. Until then, take care, and be serene in an un-serene world. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Spokes { ; time=0:46:20.55--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-1.881330206915339/+0.4805578993509941/\
843933.2/1/40/1.76137477478355287e-007 params=1/2/\
3/4/0/0 float=y maxiter=12000 inside=0 logmap=500
colors=000JHhJHiJHiJIjJIkKJkKJlKKmKKmKJnKJoLIoLIpL\
JqLKqLLrLMqKNpKOoKOnKOmKOlKOkKOjKOiKOhKOgKOfKOeKOd\
KOcFOeBOg7Oi3Ok4Oh4Nf5Md5Lb6J`6IZ7HX7GV8ET8DR9CP9B\
N77M9ALBCKCEKEGJFIIHKIIMHKOGMQGNSFPUEQWESYDT_DVaCW\
cBYeB_gA`i9bk9cm8eo7fq7hs6iu6ht7ht8hs8hs9gsAgrAgrB\
gqBfqCfqDfpDfpEeoEeoFeoGenGdnHdnIdmIdmJclJclKclLck\
LbkMbjMbjNbjOaiOaiPaiQahQ`hR`gR`gS`gT_fT_fU_eU_eVZ\
eWZdWZdXZdXccRccLccFcc9cc4cc5cc5ac6Xc6Nc7Ha7H`6H`5\
H_4H_3H_2HZ1HZ0HZ0K_1P`2U`2Za3ca4hb4rb5sc6wg6zh7ug\
7pe8hf9cf9ZgAUgBPhBKhCKiDKiDKjEKjEPkBUl8Um6Um3Um1U\
m0Um0Ul9Th8Sd7Ra6RY6QU5PR4ON3OK3QI5RG6SG7UH8VI9WJA\
XKBYLDZMFZNH_OI`PK`QMaRObSPbTRcUTcVUdWWeXYeY_fZ`g_\
bg`dhafibgicijdkjelgfhdge`hbai_cjWekTglQimNknJmoGo\
pDqqAsrTusSwtRyuRzvQzwPzxOzyOzzNzzMzzLzzJzzLzzMzzO\
zzPzzRzzSzzUzzVzzXzzYzz_zz_zz`zz`zz`zz`zz`zzazzbzz\
bzzczzdzzdzzezzfzzfzzgzzh
}
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.
