Fractal of the Day
by Jim Muth
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FOTD -- April 14, 2009 (Rating 7.5)
Fractal visionaries and enthusiasts:
Today's image lies on the border between the magnitude range of arbitrary precision math and conventional math. I have included two parameter files -- a slow version done with arbitrary precision math, which takes about 10 minutes to finish, and a fast version done with conventional math, which draws the image in only a few seconds. The slow version has a somewhat better resolution than the fast version, but it is up to the individual viewer to decide whether slightly better resolution is worth a calculation time about 200 times as long.
Perhaps the most unusual thing about the image is its anti-bifurcation. The outer ring around the minibrot consists of 16 lobes, while the next inner ring has reverted back to 8 lobes, from where it again begins normal bifurcation. This is a sign that the minibrot lies within the attraction basin of a larger minibrot.
The image lies deep in the East Valley of the largest minibrot on the filament network extending from the period-4 bud on the northeast shore line of the main bay of the Mandelbrot set. I named it "Chrysanthemum" because that's what it reminds me of. (This might not be the first time I have used this name.) I rated the image at a 7.5, which includes a self-awarded bonus of 1/2 point for the coloring. The coloring probably makes 3/4 of the image.
As I said earlier, a decision must be made between top quality and saved time. But this decision may be avoided by surfing out to the FOTD web site at:where the finished image is posted for total bliss. I leave it to Paul to decide whether to calculate and post the fast or slow version.
The Monday morning sun at Fractal Central faded fast as midday approached, and by afternoon was totally gone. The fractal cats, looking forward to a pleasant afternoon on their sun-shelf, were much disappointed. A short burst of artificial heat and a minor treat of tuna restored their good moods however.
My day was semi-busy; tomorrow will likely be the same. Until then, take care, and when we have faith, must we turn off our faculty of reason and our knowledge of science?
Jim Muth
jamth@mindspring.com
jimmuth@aol.com
START PARAMETER FILE=======================================
Chrysanthemum-slow { ; time=0:09:27.18-SF5 on P4-2000
reset=2004 type=mandel float=y inside=0 maxiter=2500
center-mag=0.3601037962566401851/0.6412655477927573\
511/6.016702e+013/1/132/0 logmap=-570 periodicity=10
params=0/0 bailout=16 mathtolerance=0.05/0
colors=000XePXePXePXePXePXePXePXePXePXePXeOYeNZeM_\
eL`dK_dLYeLXeMVeNUfNSfOQfPPgPNgQMgRKhRJhSHhTGhTKjU\
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8zz8zzVzzpzzgzzZzzQzzHzz8zzDzzIzzNzzSzzVzzYzz`zzcz\
zfzzhzzjzzlzzmzzozzuzzrzz }
Chrysanthemum-fast { ; time=0:00:03.88-SF5 on P4-2000
reset=2004 type=mandel float=y inside=0 maxiter=2500
center-mag=0.3601037962566401851/0.6412655477927573\
511/6.016702e+013/1/132/0 logmap=-570 periodicity=10
params=0/0 bailout=16 mathtolerance=0.05/1
colors=000XePXePXePXePXePXePXePXePXePXePXeOYeNZeM_\
eL`dK_dLYeLXeMVeNUfNSfOQfPPgPNgQMgRKhRJhSHhTGhTKjU\
OlVTmWYoXbpYgrZls_pu`tvaxxbzyczr`zkZzeWYZUSSRMMPGF\
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zzZzzZzz`zzbzzdzzfzzhzzizzczzZzzUzzOzzJzzEzz9zz8zz\
8zz8zzVzzpzzgzzZzzQzzHzz8zzDzzIzzNzzSzzVzzYzz`zzcz\
zfzzhzzjzzlzzmzzozzuzzrzz }
END PARAMETER FILE=========================================
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