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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I'll soon be posting a discussion about how I choose good parameters for the MandelbrotMix4 formula. I had hoped to have it ready today, but the truth is I am not sure exactly how I find my parameters. I would have assumed that the exponents in today's formula are too close together to do much of interest, but I entered them in the M-Mix4 formula anyway. Today's parameters define a formula that combines Z^(1.95) with Z^(2.05) and adds straight C. I chose the exponents because the average of 1.95 and 2.05 is 2, and since Z2+C is the classic Mandelbrot formula, I wondered if a formula where the average of the exponents is 2 would have anything special to offer. As it turned out nothing unusual appeared. The parent fractal resembles one of the perturbed Mandelbrot sets, with a very non-critical look about it that makes the search for interior midgets almost useless. But even though there are no midgets in the parent fractal, there are many interesting nooks and crannies, with much to explore. Today's image is located very near the negative X-axis of the parent fractal, in a blunt valley centered on the axis and pointing east. I named it "Odd Fractal Out", since it has no midgets hidden within it and I could think of nothing better. The rating of a 6 might be a bit liberal, but the image really is rather striking, and the calculation time of 9-1/2 minutes is marginally within reason. Those who do not calculate Fractint parameter files may view the image on the FOTD web site at: I have updated the MandelbrotMix4 formula, and starting tomorrow I'll retire the old workhorse and switch to the new version for most of my fractals. The newer version will be able to draw the fractals that result when Z is initialized to a second critical point of the formula. Heavy clouds and continued chilly temperatures in the 40's F (around 8C) made Tuesday far less than ideal here at Fractal Central. The fractal cats must have agreed, for they were unusually sulky most of the day. It took extra tuna to raise their spirits. My day was actually quite pleasant, at least compared to the way things have been for the past couple months. And tomorrow looks to be a repeat. I already have tomorrow's FOTD fractal, and it's a pretty good one, so check back here in 24 hours for a fractal surprise. Until then, take care, and search for those patterns in the void. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Odd_Fractal_Out { ; time=0:09:25.19--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=ident inside=0
center-mag=-0.68373061187701090/-0.000464846373378\
43/3556049 params=1/1.95/1/2.05/0/0 periodicity=10
float=y maxiter=1500
colors=000WaSVaTTaURaVQ`WO`XN`YL`ZJ`_I``G`aXL_OTaF\
`b3fa5gb7gc9hdBheDifFifHigIjhKjiMkjOkkQkkSllUlmVmn\
XmoZnp`npbnqdorfosgptipukpumqvoqwqrxsrytryrqwqpvop\
unotlnsknrimqhlpflnekmcjlbjk`ij_hiYhhXggVffUfdSecR\
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HOhQQkYRnfSpnTswVvvUuuTuuTttStsSssRsrRrrQrqPqpPqpO\
poOpnNonNomMnmLnlLmkKmkKljJllKmjJliJkhIjgIifIheHgd\
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OBQNBPMAOLANKAMJ9LI9KH9KJBLLCMNENPFORHPSIQUJRWLSYM\
T_OUaPVbQWdSXfTYhVZjW_jUZkX`l_bmbdndfoghpjjqmlrons\
rpturuxtvzvtstrmsqgqoapmWnlQmjKkiEjlGenI`qJXsLSuMO\
vLMwKJxJHRV`OS_LPZKO_IMYHLWGJUFISEHQDFOCEM2AIBDLKF\
NhbJfbKebLcbMbaN`aOZaPYaQ }
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 PARAMETER FILE=========================================
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times.
