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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image shows the type of fractal I was fascinated with about 15 years ago. It is a scene on the northern shoreline of the Mandelbrot set, just west of the large northern bud. But it does not resemble this area as we know it. (To see a more familiar view of the same scene, change both parameters to zero and recalculate the image.) The strange appearance indicates that the image is a scene in a perturbed M-set. The fossilized buds that form the ghostly remains of the 'true' M-set are plainly visible as background shadows, but they are partly obscured by the surging low-iteration 'perturbed' stuff that is swiftly overwhelming the scene. If the parameters are changed ever so slightly, the purplish foreground stuff will shift position dramatically. But if the fossil buds in the background are visible at all, they will be in the same position. The background buds do not change position when the starting point is changed because in perturbed sets, regardless of where points begin, their travels, if they do not escape first, will eventually settle into the same orbits as points that start at zero. There is much more to tell about the fossil buds visible in today's image, but that will have to wait until a slower day. For now, I must point out that today's scene is neither named nor rated. And its calculation time is just under 15 minutes. But as always, the completed image is or soon will be available for quick viewing on the FOTD web site at: The weather continued most un-springlike here at Fractal Central on Easter Sunday, with cloudy skies, temperatures hovering around 36F 2C, and flurries of snow throughout the day. The fractal cats noted the snowflakes, but were more interested in seeing how much turkey they could beg. They were courteous at first, but when Cassie leaped onto the table and started helping herself to the turkey, they were banned from the dining room for the duration. Guests don't appreciate cats of any variety snatching slices of turkey from their plates. I managed to get through the whole dinner affair somehow. And now that it is behind me, I can look forward to things returning to normal in the upcoming week. The next grand FOTD will appear in 24 hours. Check back then to enjoy or ignore it. Jim Muth jamth@mindspring.com jimmuth@aol.com |
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