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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's formula is not strictly an escape-time formula, but the type of image it draws (it draws only one image) is close enough to escape-time images to be included in the Fractint tour. We learned in high school that the graph of X^2+Y^2 is a circle, but we never learned that it could be a fractal. (At least I didn't.) As today's image shows, X^2+Y^2 makes a striking fractal. All that is necessary to bring out the latent fractal is to make the journey to unity a bit difficult, as has been done in the 'unity' formula. (An interested fractalist is also a help.) The fractal is a strange one. Features that are clear on the surface vanish mysteriously as we zoom in on them. When today's image is rendered at a resolution of 640x480, there is an obvious but very narrow circle of radius 1 around the origin. At a resolution of 800x600 only a few scattered traces of this circle are visible. And when we try to zoom in on the circle, it vanishes completely. It is not only this delicate circle that vanishes when it is enlarged; nearly every feature in the interior of the circular fractal itself is unstable, almost as though the entire fractal were a moire pattern. Today's image shows the entire unity fractal rotated -135 degrees. By setting the outside to 'atan' and turning on the 'decomp' feature, I was able to divide the fractal into two contrasting semi-circles and come up with an image worthy of FOTD status. The name "Un-Unity" implies that the two halves of the image are so different as to be separate entities. The image is extremely fast, rendering in less than 6 seconds on my 7-year-old machine. Since the 'unity' formula has no parameters to tweak, and the fractal is unstable when it is zoomed into, I could take no credit for finding a great image. But today's FOTD is a fine rendering of the basic fractal, well worth the rating of an average 5 that I gave it. And when the hyper-fast render time is considered, the overall worth measures an astounding 5102. Of course, such numbers are meaningless. All fractals that complete in less that a minute should be considered 'instant' fractals. Today's fractal can be seen by running the included parameter file or by downloading it from the FOTD web site at: The warm sun continued all afternoon here at Fractal Central on Sunday, while the temperature reached a mild 54F 12C, giving the fractal cats all the time they wanted in the yard. It was one of the best days in the past several weeks. The day was so good in fact that no special treat was needed to keep the duo happy in the evening. This morning is starting cloudy however, and it is colder. Rain is also threatening, so I doubt that the good day will be repeated. For me it will be just another workday. When I finish, I will have to decide what kind of fractal theme to tackle next. Check back tomorrow to see what I dream up. Until then, take care, and be at unity with both yourself and the cosmos. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Un-Unity { ; time=0:00:05.88--SF5 on a P200
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outside=atan logmap=yes decomp=256
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7HK9HKAHKCHKDHKFHKGHKIHKJ }
END PARAMETER FILE=========================================
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