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Author Topic: Second iterate to third iterate of the Mandelbrot set  (Read 667 times)
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« on: June 02, 2016, 10:01:21 PM »

Second iterate to third iterate of the Mandelbrot set


This is an animation of the transition of the second iterate of the Mandelbrot set (M set) to its third iterate.

Points in the M set are either periodic of period n or chaotic. Periodic points may be attracting or repelling. Points in the boundary are always repelling. By iterating points in the M set by the map z->z^2+c we get their images under the map, which, in general, are not in the M set. However, the nth iterate of a periodic point of period n is in the M set. Because there are periodic points of all periods, the iterates of the entire M set never repeat, so there is an infinite chain or Mandelbrot cousin sets. Higher iterates seem to look more like the original.

This was done using Maple.
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