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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: With today's image we tunnel quite deep into the Mandelbrot set. At the end of our trip we find ourselves in a remote valley just off the northwest shoreline of the main bud of the large midget on the negative X-axis. This area consists of areas of wild chaos interspersed with relatively orderly and almost straight filaments. The nature of the general area, with its mixture of order and chaos, is reflected quite well in today's image, which I have named "Order from Chaos". The magnitude of the image is really in the range of arbitrary precision math, but I have forced the program to use the conventional math routine by including the 'mathtolerance=/1' entry in the parameter file. In such a chaotic image, the resulting breakdown in resolution is barely noticeable, and the time saved is a sizable part of a day. One result of forcing the use of conventional math is the unwanted stretching and skewing, which is reported on the 'tab' screen of the image. This distortion is barely noticeable, but those who wish to render the image marginally more accurately may re-enable arbitrary precision math by striking the 'g' key and entering the command 'mathtolerance=/0'. The 'logmap' method of coloring does not work with today's image. The 'tdis' option runs very slowly. The other outside coloring options either create too much chaos or run far too slowly. The best method I found of coloring today's image is also the simplest -- outside=iter logmap=0. When the time came to rate the image, I was undecided whether to consider the overworked nature of the M-set. Is today's image really that unusual? After almost 20 years of exploration, is there anything truly new to be found in the M-set within the range of conventional math? One would think so. At the magnitude of today's image, the entire M-set would be about as large as the solar system. And except for the X-axis symmetry, no two spots of the M-set are identical. But the differences are often infinitesimal, and for all practical purposes, the major variations have long since been found. Considering all this, I rated today's image at an above-average 6, which, with the render time of just under 5 minutes, gives an overall value of 125. I must get a machine fast enough to make arbitrary precision math practical. Way down deep is where the undiscovered M-set goodies lie. To see the image, run the included parameter file and sit back to watch the fun, or go to Paul's FOTD web site at: The clouds moved in quickly here at Fractal Central on Monday, but the temperature reached 46F 8C, which was mild enough for the fractal cats to enjoy a full 90 minutes in the yard. They must have enjoyed their outing. When the day ended, they were content to settle down without a special treat. Today brings both work and fractals for me. The work I will finish; the fractals will never be finished. I shall return in 24 hours with more goodies, some concrete, some abstract. Until then, take care, and the search for truth is all too often hindered by the difficulty in recognizing and accepting it. Jim Muth jamth@mindspring.com jimmuth@aol.com |
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END 20.0 PAR-FORMULA FILE==================================
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