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

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):

Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane


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

Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane


See the animation:

Iterations in the complex plane: the computation of the Mandelbrot set


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

Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane  
Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane Iterations in the complex plane


(CMAP28 WWW site: this page was created on 03/15/2019 and last updated on 06/04/2026 22:38:38 -CEST-)



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