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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: In the most recent FOTD, the Z^1.003+C fractal that appeared two days ago, I mentioned that the large Mandeloid filling the frame has a tiny area of chaos on its northeast shore, but that the iteration count in this chaotic area is too high for exploring to be practical. For today's FOTD, I accomplished the impractical. The image I found takes over 4 hours to render. Today's image is a scene in this narrow area of chaos, which appears to consist entirely of discontinuities. The unbroken features themselves, if such things exist, consist only of equal-iteration bands with smoothly curving boundaries. It is the way these boundaries are broken up that makes the image. The image shows a series of incomplete spirals with exaggerated colors -- the kind of thing that might be expected. But behind the spirals lies an 'inside' area with a perfectly straight edge, and this edge cuts uninterrupted across all the discontinuities that would normally be expected to disrupt it. A few thumbnail excursions into the detail along this straight edge have shown that the chaos there is totally unorganized, with areas having totally differing characteristics lying side-by-side. (I might explore this area in the near future.) I named the today's image "Whirling Devilish", a play on words that takes note of its prominent spirals. The over-exaggerated color palette permits a rating of no higher than a 6, which, combined with the 244-minute render time, gives an overall value of a pathetic 2.4. Wise fractalists will find a far better value by downloading the finished image from Paul's web site at: I e-mailed the image to Paul several hours ago, so there should be no unusual wait for it to be rendered and posted. Friday was far too cold here at Fractal Central for dignified cats to be outdoors. The temperature never rose beyond 19F -7C, and the wind blew at a brisk pace all afternoon. The dynamic duo satisfied themselves curled by the radiator, catching up on sleep. This morning the ground is covered with about 3cm of powdery snow, and it is as cold as yesterday. It's no mystery how the cats will pass the day. I hope to pass the day uneventfully. I'll start by sweeping the sidewalk, and then . . . . Until next time, take care, and who knows what fractals lurk in the world of numbers? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Whirling_Devilish { ; time=4:04:39.54--SF5 on a P200
reset=2003 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.84148491609888050/-0.080629287046106\
61/527.1442/1/117.5/-5.21221954485895367e-013
params=1.003/0/1040/1500 float=y maxiter=60000
inside=0 logmap=-4386 periodicity=10
colors=000L0HL0IM0IM0JN0JN0KO0KO0LP0LP0MQ0MQ0NR0NR\
0OS0OS0PT0PT0QU0QU0RV1RV2SW3SW4TW5TW6UW7UW6UV6SU6R\
T6PR6OQ6MP6LO6JM6HL6GK6EJ6DH6BG6AF68A48E67I87M97QB\
7UD6YE6cG6iI6mJ6qJ5nJ5kJ4iJ4gJ3dJ3aJ2ZJ2WJ1VJ1XO3Z\
S4`W5c_6ec7hg8jk9moAqtAosBmsCkrDirDgqEeqFcpFapG_pH\
YqIWqIUrJSrKPtLRtKSuKTvKUuKWtJXsJYrJZqJ_pJaoIbnIcm\
IdmIfmHgmHhmHimHjmHlmGmmGnmGomGqmFrmFsmFtmFumFvnHw\
oJxpLyqMzrOzsQztSzuTzvVzwXzxZzy_zzczzgzzlzzkzzjzzi\
zzhzzgzzfzzezzdzzczzbzzazz`zz_zzZzzYzzZzzXzzWzzVzz\
TzzSzzRzzPzzOzzNzzMzzKzzJzzIzzGzzFzzEzzDzzBzzAzz9z\
z7zz6zz5zz5zz4zz4zz4zz3zz3zz3zz3zz2zz2zz2zz2zz1zz1\
zz1zz1zz0zz0zz0zz0zz3zz6zz8zzBzzDzzGzzIzzLzzOzzQzz\
TzzVzzYzz_zzbzzezzgzzjzzlzzozzqzztzzwzzvzzuzzuzztz\
zszzszzrzzqzzqzzpzzozzozznzzmzzmzzlzzkzzkzzjzzizzi\
zzgzzezzdzzbzz`zz_zz`zzazzbzzbzzczzdzzdzzezzfzzfzz\
gzzhzznzzmzzlzzjzzizzgzzf }
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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