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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is very slow. In fact it's the second slowest FOTD of all time. It's so slow because we've gone a long way -- we've followed the largest midget of the M-set until it is finally ready to be absorbed into the infinite ocean of trapped points of its parent, the god-like place where midgets go when they cease to exist. It's the same midget that appeared in the N-D-E image of July 8, but what a change lowering the exponent of Z from 1.066 to 1.05 has made. The N-D-E image renders in 6 minutes, while today's takes 11 hours. The big difference is that the midget, or what remains of it, has been absorbed into the high-iteration random chaos that stretches (invisibly at normal maxiters) along the shoreline of the parent fractal, the nearest part of which lies just beyond the upper right corner of the frame. Most of the elements in the N-D-E image had iterations in the hundreds; the blue elements in today's image have iterations in the hundreds of thousands. The original negative tail of the M-set is still vaguely visible as the broad, featureless area of blue stretching from the midget toward the left edge of the screen. The midget itself has degenerated until it is little more than a distorted circle. The only remaining recognizable feature is East Valley, the point on the midget's lower edge, where the features converge. No elephants are in the scene however. The elephants have long since vanished, to be replaced by scalloped features that seem to be shedding fractal debris. The reddish area at the lower left, which eventually leads into the midget's valley, seems almost not to belong there. It has an iteration in the 150 range compared to the 100,000 range of most of the scene, and is an actual part of the shoreline of the parent fractal, which is little more than a crooked circle. To see how today's midget lies in relation to its parent, lower the maxiter to 300, turn off the logmap, and back out a few zooms. It will be immediately apparent that, when viewing the parent, there is no evidence of the midget's existence. The only way to find today's midget is to follow it as the exponent of Z is reduced. And even this is difficult, for the exponent of C in the iterated formula must be adjusted by just the right amount to keep the midget from slipping out of sight beyond some branch-cut discontinuity. I could have taken the process even further, but at lower exponents of Z, the render time increases apparently without limit. Since as far as I can tell, the appearance of the midget does not change at lower exponents, I decided that Z^1.05 and a render time of almost 12 hours was a good place to stop. And that's the story of how a midget came to its end. I named the picture "The End of a Midget" and rated it a 6. For those wise fractalists who decide not to render, but to download the finished GIF image instead, that image will soon be available on paul's web site at: The fractal weather today (yesterday) was summer-like, with hot sun, a temperature of 90F (32C), and happy cats. The work today is piling up, so I'd better get busy. I'll return in the allotted time with a fractal that is guaranteed to be faster. And I might even have some philosophy to cause one to wonder about things they would rather forget. Until then, take care, and don't forget to wonder about those fractals. Jim Muth jamth@mindspring.com |
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