This draws a picture of the famous Mandelbrot set, which is the set of points c in the complex plane so that the sequence of points obtained by

zn+1 = zn2 + c

remains bounded in the complex plane, where z0=0.

As usual, points near the Mandelbrot set are colored to indicate how quickly their iterates go to infinity. In this example, the limit on the number of iterations can be specified. The resolution can also be controlled: unless your machine is very fast, it seems best to work at resolution 64 and about 150 iterations until you find an interesting spot, and only then draw the picture at resolution 256 and perhaps 500 or 1000 iterations.

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