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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With all the news about storms on the TV, it seemed only proper that we should have a stormy fractal. Once again the Fractint program and the world of math obliged, and we got our stormy fractal. There are two images in today's parameter file. The first one is named "Graph", and it is exactly what its name implies. The 'Graph' image is a graph of the function entered into the formula. The critical points are now obvious. They are the imaginary values of the tips of the arabolic curves, the points where the tangents to the curve are vertical, the points where the derivative is zero. The problem lies in determining the exact Y-values of these points, but this can be done by repeatedly compressing the imaginary direction and thereby sharpening the parabolic curves. The graph shows three critical points -- 9.3944253327, 6.0457442391 and -0.4401695778. Today's image lies in the parent Mandeloid determined by the first critical point. I named today's image "Storm Clouds". With a little stretch of the imagination it could be a dark and stormy sky. The image is half-inside and half-outside. The inside parts have been rendered with the 'fmod' option, with the proximity set to 27. The image appears to be at least slightly above average, though the coloring could certainly use more work. I rated it at a 6. With its maxiter of 2, the "Graph" image renders instantly. The "Storm Clouds" image requires 1/2 hour to complete on my tired old fractal machine. The stormy image is posted on the FOTD web site at: Philosophy fans take heart. I expect to have an outburst ready in time to appear in the philofractal version of tomorrow's FOTD. It remained warm and very humid here at Fractal Central on Tuesday. The temperature reached 84F 29C, but no rain fell and the fractal cats enjoyed a full afternoon in the holly patch. Today is starting much the same. If the rain holds off again, it will be another good day. For me, it will be an average day. The next FOTD fractal will appear in 24 hours. Until then, take care, and some mysteries are more easily answered than others. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Graph { ; time=0:00:00.24--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=ParabolicMix3 function=ident
center-mag=1.8579/4.2739/0.1162964 params=1/2/-0.2\
/3/1/1/0.01/4/0/0 float=y maxiter=2 inside=0
symmetry=none periodicity=10
colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\
zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\
zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\
00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\
VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\
lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\
lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\
E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\
OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\
OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\
SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\
G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\
G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\
G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\
GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\
G000000000000000000000000 }
Storm_Clouds { ; time=0:30:30.30--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix3a function=ident passes=1
center-mag=-5.09875460590885100/+0.991687004724402\
60/2.341077e+009/1/-32.5/-7.09176330104810404e-007
params=1/2/-0.2/3/1/1/0.01/4/9.3944253327/525
float=y maxiter=1500 inside=fmod proximity=27
symmetry=none periodicity=10
colors=00085C5592560537C8EICKOGRUKY`PcfTjlXqr`wxdi\
t`XpYJlU6iRIjPTkOdkMolLzlKxjLvhLufLsdLqbLpaMn_MmYM\
kWMiUMhTNfRNdPNcNNaLN`KNYNLVQKSTJPVHMYGJ`FGbDDeCAh\
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vpuwTww5tu8rtBpsDnqGlpJioLgmOelQckTaiWZhYXg`VecTde\
RchPbjUchYdfaeeefcjgbnh`ri_vjYzjXui_qhbmhdiggdgi`f\
lXfnTeqPesNgpLinJkkImiJlhJkhJkgJjgJifJifJhfJgeJgeJ\
fdJedJedKdfLcgMbhNaiO`jP_kPZmQYnRXoSWpTVqUUrUTsVMg\
VGXW9LW3AbLRUbfTevRiuQktOmsNkrLjqKhpIfoHdnFcmEalC_\
kBYjAXi9SeN5SK5PH5ME5JB5F }
frm:ParabolicMix3 {; Jim Muth
z=imag(pixel)+flip(real(p5)),
c=fn1(real(pixel))+flip(imag(p5)),
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=real(p3), h=imag(p3), j=real(p4), k=imag(p4):
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <= 100 }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END PARAMETER FILE=========================================
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times.
