Iterations in the complex plane: the computation of the Mandelbrot set [Itérations dans le plan complexe: le calcul de l'ensemble de Mandelbrot].




When computing the Mandelbrot set in the complex plane, one iterates the following computation:
                    Z  = 0
                     0
                            2
                    Z    = Z  + C
                     n+1    n
where 'C' denotes the current point.

Then there are two cases: Z(n+1) stays in the vicinity of the origin (then C belongs to the Mandelbrot set -black domain-) or Z(n+1) goes to the infinity (then C does not belong to the Mandelbrot set).

This picture displays the trajectories of "current points" C located on a regular 5x5 grid and displayed as big disks.


See some interesting trajectories of points INSIDE the Mandelbrot set (possibly including this one):




See some interesting trajectories of points OUTSIDE the Mandelbrot set (possibly including this one):




See the animation:




See the pictures of the preceding animation (possibly including this one):

 
 
 
 
 
 
 
 
 
 



(CMAP28 WWW site: this page was created on 03/15/2019 and last updated on 03/19/2019 11:11:16 -CET-)



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Copyright (c) Jean-François Colonna, 2019.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2019.