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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I enjoy finding well-defined fractal 'objects', such as the mathematical dead-ends for wandering points known as 'midgets' or sometimes 'atoms'. The assemblage illustrated in today's image might or might not be considered a fractal 'object', but it is an interesting collection of fractal things regardless, and it is invisibly filled with the true well-defined 'objects' known as midgets. I named the image "Seeing Triple". The name is an exaggeration of the more common phrase 'seeing double'. The name came about when I noticed that the image had left-right symmetry. Then I looked again and discovered that the opposites were reflections of reflections. They were identical. A third look revealed that the opposites are not reflections or rotations at all -- they are totally different, and no reflection or rotation can ever make them coincide. The parent fractal combines negative portions of Z^(-1.26) and Z^(-12.6). It is a variation of the parent which produced the series of FOTD images that ended about a week ago. The coloring features pastel tints inside the non-symmetrical objects, which contrasts with the intense deep blues of the surrounding environment. I am not sure the rating of 7 is totally earned, but the image does appear to be at least above the FOTD average. The render time of 7 minutes is within reason. If 7 minutes is not reasonable, the wait can be eliminated entirely by downloading the completed GIF image from: The sun broke through in mid-afternoon Tuesday here at Fractal Central, but the temperature reached only 45F 7C, which was a bit too chilly for the paws of the fractal cats, who spent only 45 minutes outside. Their evening was improved however by a generous treat of tuna. Today is starting partly cloudy and colder. It looks rather bleak for the duo. For me the day looks normal -- at least so far. The next FOTD will appear in 24 hours. Until that magnificent moment arrives, take care, but have fun. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Seeing_Triple { ; time=0:07:11.71--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+3.91423665492388400/+0.003269872083774\
09/171588.5/1.168/10.7/-2.30992197591817217e-009
params=-5/-1.26/-0.5/-12.6/0/625 float=y
maxiter=5000 inside=0 logmap=129 periodicity=10
colors=000G0MG0SG0PG0TG1UG3UG4XG4XG7`GBaGCgGGgGJnH\
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7G09E0BB0C90E60G40H10J00K }
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.
