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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image shows the outline of a large twisted minibrot in East Valley of the Mandelbrot set, which in itself is nothing unusual. But inside this East Valley minibrot lies a smaller minibrot from Seahorse Valley, which at first is quite puzzling. The puzzle is solved when we see that the image was created by the type=hypercomplex formula, which draws four-dimensional Mandeloids consisting of two overlapping classic M-sets. By changing the cj and ck parameters, the two sets may be made to overlap at any two points chosen. Today's parent fractal was drawn with East Valley overlapping Seahorse Valley in such a way that a small Seahorse Valley minibrot shows through a larger minibrot in East valley. (The c and ci parameters of the formula are fixed to the screen and cannot be changed, but the z, zi, zj, zk axes are all perpendicular to the screen. It would be nice to have a way to perturb the images in these four directions, and also to rotate the orientation of the images through the entire 4-D Mandeloid.) Since it took a bit of effort to find the overlapping midgets, I decided to add an extra point to the rating in recognition of my effort. The image itself is perhaps a bit above average, though similar images have been seen in some earlier FOTD's. The name "Minibrot Minibrot" accurately describes the image. The rather slow calculation time of 5-3/4 minutes is due to the maxiter of 14400, but it was needed to get full definition inside the outer minibrot. And all but a minute or so of this time may be saved by viewing the finished image on the FOTD web site at: Full sun could not offset a temperature of only 25F -4C here at Fractal Central on Monday. The fractal cats avoided the more drafty windows to keep warm on their shelf by the window over the radiator. My M.L.K. holiday was reasonably slow. The next FOTD will come from nowhere in 24 hours. Until then, take care, and if free will is but an illusion, why is it such a convincing one? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
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END PARAMETER FILE=========================================
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