Title: Second iterate to third iterate of the Mandelbrot set Post by: Tater on June 02, 2016, 10:01:21 PM Second iterate to third iterate of the Mandelbrot set (http://nocache-nocookies.digitalgott.com/gallery/19/3614_02_06_16_10_01_18.gif) http://www.fractalforums.com/index.php?action=gallery;sa=view;id=19267 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. |