Mandelbrot Images
I've been fascinated by Mandelbrot images since before I had a computer. A favorite benchmark for a new system is to see how fast it can compute a new image -- until the Pentium, not very fast :).
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To see a very large version of these images, download the MBWIN program from my software page. These images and many more are encapsulated in small description files that can be used to recompute them to a desired resolution. The program also provides coloring and exploration tools.
The Mandelbrot set was discovered by Benoit Mandelbrot in 1960. The color of each pixel is based on the number of iterations before z(n) leaves the circle of radius 2 about the origin, using the pixel's complex value c as a parameter in z(n+1) = z(n)*z(n) + c, z(0)=0. The Mandelbrot set is the set of points for which the number of iterations is infinite, and those (and other) pixels are colored black in these images. The colors in the image are a measure of the rapidity with which the iteration leaves the circle for each possible parameter c.
