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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The magnitude of today's fractal is 2e+14, making it most likely the deepest I have yet gone with the MandelbrotMix4 formula. True, the image is a bit past Fractint's limit of resolution, but UltraFractal's more precise math routine should resolve it. I had to set the math tolerance to /1 to reach such a magnitude in Fractint, but the little midget is unusual enough to be worth the effort. The breakdown of resolution actually adds a rather artistic effect to the picture. I named the picture "A Deep-down Midget" because the central midget lies so deep down in its parent fractal. The formula that created the image is (-1/Z)-(Z^1.1)+(1/C) -- another formula that does more than it's appearance would suggest. The render time is a nominal 6 minutes on a P200; the download time is an even more nominal 1 minute or so. That download may be found on the Usenet network at: The fractal weather today was perfect, with blue skies, a few clouds, and no noisy fireworks. The temperature of 86F (30C) lured the fractal cats into the yard, where they enjoyed as nice a romp as nine-year-old cats can manage. The philosophy sleeps while I recharge my philosophical energies. The charge cycle might be a lengthy one, so be patient fans of wisdom, and eventually your patience will be rewarded. That's it for today, but tomorrow is near, and it will bring a new and greater fractal. And it's also about time I returned to one of my favorite diversions -- higher dimensions. So tomorrow could be interesting. Check then to find out. Until next time, take care, and stay solidly grounded in the third dimension. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Deep-down_Midget { ; time=0:06:01.96 -- SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+0.12844758295825350/+0.02991434375250009\
/1.993294e+014 params=-1/-1/-1/1.1/0/0 float=y
maxiter=300 bailout=25 inside=0 logmap=123
symmetry=none periodicity=10 mathtolerance=/1
colors=000bWn<3>j_ol`pnapobp<4>M9SG3O<3>CPdBUhAZl<2>\
8nx<6>LOhNKfOGd<3>V1XPNGKg0<7>IaJI`LH_N<3>HYW<3>nHL<\
3>b9V_8YX6_<2>P1f<3>r4K<3>hGIfIIdLH<3>WWG<3>gSPiSRlR\
T<2>tPZ<3>aXLXZIS`FObC<3>bNLeJNiFPlBR<4>TGH<3>RTh<3>\
OeVOhSNkPNnLMqIMtF<9>O`HOZHOXH<3>OPH<8>VRAWR9XR8<3>Z\
R6c4v<3>Ij_RnT<3>SpWSqWSqX<3>SsZ<4>PWbOSbONc<2>M9eM5\
eN7f<6>TLjUNkUPk<3>XXm<3>UMhTJgSHfREeRCd<4>PQOPSLPVI\
<3>Od5<5>OW7OU7OT8OR8OQ8<10>WDDXBEXAE<3>_6GKUb4pxOlZ\
fhAnoQuud<10>eVU
}
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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