AVirtualSpaceTimeTravelMachine : Iterations in the complex plane : the computation of the Mandelbrot set (Iterations 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):