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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is one of those that owes almost its entire worth to the coloring. This is always a risky thing to do because different monitors display the same colors differently, and only a slight shift in color balance will spoil the effect of today's image. For this reason I decided to let it go un-named and unrated. The parent fractal is an indescribable thing, (as are almost all fractals), created by combining 7 negative parts of Z^(-1.4142) with -0.7 negative part of Z^(-7.7) and then adding (1/C). The reciprocal of C turns the fractal right side out. As do many fractals in this range, this parent fractal has a prominent 'fan'. Today's image is located near an odd-shaped hole at the eastern edge of the 'fan'. The image's calculation time is under 3-1/2 minutes on my tired machine, which is a reasonable time for a reasonable image. And if reason does not work, the completed GIF image is available on the FOTD web site at: The Fractal Central weather proved disappointing on Sunday. The heavy clouds, light rain and temperature of 46F 8C made things much too unpleasant for a Palm Sunday. The fractal cats must have agreed, for as far as I know, they passed the entire day without as much as a glance out the window. In my department, the pile of work that has been plaguing me for the past two months is finally finished. This means better fractals (if such things are possible) in the days to come. If the fractals don't get better, at least the discussions will get longer. The next FOTD will appear in 24 hours. Until then, take care, and we don't know what we don't know. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
FOTD_for_Apr_02_07 { ; time=0:03:24.71--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip inside=0
center-mag=+1.70772411165322400/+0.072704959182236\
64/36617.56/1/90/3.88578058618804789e-016 logmap=72
params=-7/-1.4142/-0.7/-7.7/0/0 float=y maxiter=800
outside=tdis periodicity=10
colors=000pzMhzRbsVYmYTgaOadJVhEPk9Jo4Dr7HsAKtCNuF\
QuHTvKWwNZwPaxSdyUgyXgsZgm`ggbgaegWggQigKkgFldImbK\
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_9W`8Z`8a`7ea7ha6ka6ob5rb5ub5qoOpjNoeMo`LnWKmRJlMI\
kHHkCGlFFmIFmLFnOEnREoUEpXDp_DqbDqeCrhCrjCsfCscCs`\
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YU_UU_QU_LUZHUZDUZqaPdUHSN9FG2HF3JE4LE4ND5PD6RC6SC\
7UB8WA8YA9_9Aa9Ac8Bd8BfRH }
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.
