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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I consider myself a fractal purist -- that is I see fractals as the same things they were considered to be when they were originally discovered. I do not see fractals as a means of expressing one's latent artistic talent. There are countless other ways to do this. When they were discovered 20 or so years ago, fractals were seen as a means of visualizing the things numbers do when taken far beyond the limit of human calculating ability. The most common means of coloring those early images was to leave the area of trapped points black and color the outside area according to how many iterations were needed for the points to pass beyond a certain escape radius. We realized even then that other coloring methods were possible, but this equal-iteration-band method became the unofficial fractal reference standard. This is the method I still use for nearly all my images. I use it because it eliminates much of what I have done and shows more of what the numbers are doing. True, even I am not perfect, so I express a little of my creativeness when I color the images. I do the FOTD for fun, not profit, though if profit came along, I would not turn it down. I mention fractal purity because today's image digresses a bit from my ideals. In today's image, the outside area has been set to <summ> rather than <iter>. I did this because the <summ> outside option in this case makes the better picture -- an image filled with delicate detail compared to the flat areas created by the traditional equal-iteration-bands rendering method. The formula behind the image, (1/Z)-Z^300+(1/C), is a surprisingly simple formula for such a detailed image. But that's the way it is when chaos raises its head. I named the image "Fringed Minibrot" as a description, and rated it at an 8 because I like it. The parameter file takes 20 minutes to render. The GIF-format image takes only one minute to download from: But give Paul and Scott a chance to render and post the image before attempting the download. The fractal weather today was the typical stagnant summer pattern, with hazy sunshine and lots of ozone. The fractal cats didn't worry about the ozone, but the temperature of 93F (34C) was a bit too warm for their delicate constitutions. As for myself, it's time to get busy and make some money. But I'll return within 24 hours with another fractal to go 'WOW!' at. Until then, take care, and I'm still searching for one of those elusive Herman Rings. I went to the jewelers, but they had never heard of them. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fringed_Minibrot { ; time=0:20:31.10--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-13.06399625631058/+10.40371429338124/1\
91811.7/1/-172.499 params=1/-1/-1/300/0/0 float=y
maxiter=2400 inside=0 outside=summ periodicity=10
colors=000EXUDWTCVRBUQBTPAURAVT9WV9XX8YZ8Z`7_b7`d6\
af6bg9ecCg_FjWIlSLoOOqKRsGUoEXkD_gCbcAe_9hW8kS6nO5\
qK4sH3pGBmFIjFPgEWdEbaDi_DpaEocEneEmgEliFlkFkmFjoF\
iqGisGhuGgwGfyGfvKdsNbpQ`mUZjXYg_WebUbfS_iQXlPUpNR\
sLOvJMyIKxOJxUIx_GxdFxjExpDxuHrsLlqPgoSanWWl_RjcLh\
fGghJciM`kPYlRVnUSoXPpZMmXPjVShTUeRXcPZ`NaYLcWJfTH\
hRFkODmLBpJ9rG7uE6wSRpdjiSchGYg4SgBUeHWcNYaUZ__`Ye\
bWkcVlgZlkamoensinwlnwlmvkmvklvjlujkujktijtijthjsh\
isgirghrghrfgqfgqefqefpeepdeodeocdocdnbcnbcmbbmabm\
aal`al`MTgNVfOWfPXeQYeR_dS`dTacUbcVdcWebXfbYgafhti\
jtfelc`e`XYYSRVNJSJCTMFUPHVSKWVMXYPY`RZcUal__fW`iZ\
BwjItgPqeWnbdBLcJPbRSbYVaeYRJUTOVVSWWWXY`YZdZ`h_Fq\
AGpCHpDIpEaRm`PmZNmYLmWJmVImYJo`KpbLqeMrhNsjOtlSon\
VkpYgr`ctdZvgVxjRzmNxlQvlTtlVrlYpk_nkblkejkghjjfjl\
djobjqjfcrcQz`CrWDkSEcOFXKGQFHIBIB7J43J7CS9L`BTiDU\
hEUhFUhGUhHUhIUhJUhKUhLUh
}
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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