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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today, for a change, I did not goof. The pleasant scene is sliced through the Z^2+C Julibrot in the Parabolic direction. The slice is located near the Seahorse Valley of one of the Mandelbrot midgets in Elephant Valley. As a result, we have a Seahorse-looking Julia midget surrounded by Elephant-looking features. The name "The Phantom Gift", which I gave to the image, has no relation to the image's appearance. I chose it on a total whim because it sounds artistic. The rating of a 7, however, is well earned. The coloring, at least on my monitor, comes as close as possible, without checkerboarding, to the smooth appearance of true-color. The bands are there, but to see them, one must look carefully. Images of midgets sliced in the odd directions often have a rather unpleasant stretched appearance, but sometimes, as in today's FOTD, they appear totally undistorted. There is a catch however. To achieve today's undistorted image, it was necessary to stretch the image in the vertical direction by a factor of 380, and skew it by a factor of almost 90. This manipulation is part of the fun of the odd planes, getting something from nothing as it were, and if it were not done, today's image would consist of nothing more than a screen filled with multi-colored horizontal stripes. The render time of 4 minutes may be avoided by downloading the completed GIF image from the FOTD web site at: I have just received a copy of the book "Schrodingers Rabbits", which discusses the many-worlds interpretation of quantum theory. I can already see that it contains things that will need to be worked into the next installment of my philosophy. This means a further delay, but anything worth having is worth waiting for. Partly cloudy skies, biting winds, and a high temperature of only freezing kept the fractal cat duo safely indoors all day Wednesday. In mid-afternoon, the intruder from up the hill showed up and left his mark in the yard. The duo somehow knew the other cat was in the yard, and kept careful watch until he casually walked away. Today is starting with hazy sun and continued cold temperatures. The forecast calls for possible snow later this evening, but by then the duo will have finished whatever they have planned for the day. The next FOTD will appear at this same spot 24 hours from now. Until then, take care, and don't get lost in Fractal Land. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Phantom_Gift { ; time=0:03:54.70--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multirot-XZ-YW-new passes=1
center-mag=+0.00000312419553334/-0.000000002198513\
13/4.551921e+010/0.002633/0.627306089407922651/89.\
4765892407080514 params=0/0/2/0/0.265019899971/0.0\
03084106765/0.265019899971/0.003084106765 float=y
maxiter=5000 inside=0 logmap=383 periodicity=10
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wAuwBuwDuwEuwGuwHuwJuwIuw }
frm:multirot-XZ-YW-new {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
z=z^(p2)+c,
|z| <= 36 }
END PARAMETER FILE=========================================
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times.
