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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Curiously, now that I know how to control the inflow of junk e-mail when I don't want it, I actually have fun, when I'm in the mood, reading some of the pathetic stuff. Much of my junk e-mail informs me (presumably by law) that I have opted in to a mailing list to receive absolutely unwanted things such as free passwords to dirty web sites. And I would like to have a dollar for every time I have been relieved of the non-existent debt that I cannot pay.  This flood of e-mail concerns me. I fear I might be developing amnesia, or perhaps even a multiple personality, for I have no memory of opting in to receive anything whatsoever. In fact, I would not know where to go to opt in even if I wanted to. Where are all these opt-in lists found? Wait! I know what happened! The cats did it! Now we can get on to the fractal business. Yesterday's fractal rated a lowly 4, so today I have doubled my effort and produced a fractal that, despite the somewhat gaudy background, still rates an 8. By doing so, I have atoned for my misdeed of losing the image that was supposed to be the FOTD for October 19. The high rating of today's image comes largely from the coloring, which I spent extra time in doing, and also because, unlike yesterday's image, which looked like just another M-set midget, today's image is unlike anything that, as far as I know, exists in the classic M-set. The parent fractal consists of a large cluster of Mandeloid-shaped bays with some huge fractal rings much farther to the east. Today's image lies in the center of a valley of one of the Mandeloids. The formula behind the image combines negative portions of Z^(-1.23), Z^(-12.3), and (1/C). For some reason, combining powers of Z whose absolute value differs by a factor of 10 seems to result in unusually interesting fractals. Of course, it could also be chance. I have named the image "Four Legs", because the four prominent appendages somewhat resemble barbecued chicken legs. The render time of 26 minutes is a bit too much, so a download of the completed GIF image is recommended. The GIF file may be found at: The weather Saturday here at the Fractal Eclectic Emporium was cloudy, with a temperature of 61F 16C and just enough rain to keep the grass too wet for its final trimming of the season. That made me happy, but the cats complained loudly that they could not go into the yard without getting their paws wet. They must think that, because I control their food supply, I also control the weather. I stifled their complaints with a treat of tuna. Today is once again starting cloudy, but so far it has not rained. With the breeze drying the grass, the dynamic duo might manage a trip into the yard with dry paws before the day is finished. As for me, I feel lazy. Most likely for the rest of the day, I'll do little but forget the grass and explore for fractals. But I shall return on schedule in 24 or so hours. Until then, take care, and be at one with your fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Four_Legs { ; time=0:26:04.16--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+3.84799783165988600/-0.020054445050299\
35/3.936102e+007/1/50/1.36853965361505292e-006
params=-6/-1.23/-1/-12.3/0/0 float=y maxiter=3600
inside=0 logmap=561 periodicity=10
colors=000xIcwJdwKewLfwMgwNgwOiwPhwQkwRiwSmwTjwUow\
VjwWnvWivXlvXkuYjuZitZht_gt_fs`es_dsadqZbpX`nUZmSX\
lQWjNUiLSgIQfGOeENk9Wq5cv1kr4in6hj8fgAecDc_FbXHaTJ\
_PLZLOXIQWESUAUT7WSCXTGYULZVP_WU`XY`XZbZZd_Ze`Zga_\
hb_jc_kd_me`og`ph`ri`sjaukavlaxmaynbqhcicjFKeUTfMO\
gEJh7Ef8Fd9Fb9G`AGZAGXBHVCHUCISDIQDIOEJMFJKFKIGKHG\
KIFJJEIJDHKCHKBGLAFM9FM8EN7DN7DPPCReCTvCWuBZuBauAd\
uAgtAjt9mt9ot9ntAk``k``k`akaakablablbblbclbclcdlcd\
lcdTOeUPdUPdUQdUQcURcVRcVScVScVSbVTbVTbWTbWRaWPaWL\
aWMaWN`XO`XP`XQ_XR_XS_YT_YVZYWZYYZYZZZ`YZ`YZaYZaYZ\
bXZbX_bX_cW_cW_dW_dW`eV`ZV`fV`fV`gUagUagUahUahTaiT\
aeTbjSbjSbkSbkSblRcmRcnRcpRcqQcsQdrQdrQdwPdyPdzPcw\
AbtBaqB`nC_kCZhDYeDZdEZcEZcFZcF_cG_c__c``ca`cb`cc`\
cdaceacfadgbehbfibgjbhkcjmckoclqdmsdnudowBnzDmzEmz\
FmzGmzHmzImzJmzKmzLmzNmzOmzPmzQmzRmzSmzTmzUmzVmzXm\
zYmzZmz_mz`mzJmzQmzWmzamz }
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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