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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's listed render time of under 5 minutes is the time it takes for the image to calculate on my fastest machine, a P4-2300, which goes like lightning with the Mandel formula. On the old warhorse P200, the image takes almost 1 hour to finish. The image is another scene very deep in a valley, this time the valley of the period-4 bud on the northeast shoreline of the main bay. The 'mystic' point of this valley, where the two branches join at infinitesimal infinity, is 0.25,0.5. This valley, along with its mirror twin at -0.25,0.5, Seahorse Valley at -0.75, and Scepter Valley at -1.25, are the only valleys I know of with rational and therefore easy-to-find 'mystic points'. The limit of East Valley of the M-set lies at 0.25, and the limit of the East Valley of the largest midget is found at -1.75. But these 'east' valleys simply come to an end at these points. They have no opposite branches to join with. What we see so deep in today's valley is more of what we saw in Seahorse Valley -- lots of cut-off elements resembling sickle-shaped leaves with scalloped edges, and peanut-shaped holes surrounded by vast areas of chaos, which I call 'sand'. I could have brought some degree of order to these chaotic areas by rendering the image with the logmap in effect, but this would have reduced all but a tiny part of the image to areas of flat color. The coloring is more intense in today's image, but the image borders on a repeat, and this holds the rating to a 6. I named today's image "Deep Northeast". The name is a simple description of the scene's location. Depending on the computer, the render time could be anywhere from around 4 minutes to many hours. Regardless of the machine, the image may be seen nearly instantly by going to the FOTD web site at: Light rain in the afternoon and a temperature of only 46F 8C spoiled the cats' day Friday. They consoled themselves watching the squirrels from their shelf by the window. Today is starting no better. I expect the cats' day will be no better either. I'll finish the little bit of work, then see what I can find deep in another valley of the M-set. Hopefully, all the valleys will not be the same. The next FOTD will appear in 24 hours. Until then, take care, and speak softly but carry a big fractal. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
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reset=2004 type=mandel passes=1
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bailout=9 inside=0 periodicity=10
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END PARAMETER FILE=========================================
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times.
