Iterations in the complex plane [Itérations dans le plan complexe].




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 -red trajectory- (then C belongs to the Mandelbrot set) or Z(n+1) goes to the infinity -green trajectory- (then C does not belong to the Mandelbrot set). On this picture, the white point is the origin of the coordinates.


See the iteration process used in order to define the Mandelbrot set:




(CMAP28 WWW site: this page was created on 03/14/2019 and last updated on 03/18/2019 10:58:43 -CET-)



[See all related pictures (including this one) [Voir toutes les images associées (incluant celle-ci)]]

[Please visit the related ImagesDidactiques picture gallery [Visitez la galerie d'images ImagesDidactiques associée]]
[Go back to AVirtualMachineForExploringSpaceTimeAndBeyond [Retour à AVirtualMachineForExploringSpaceTimeAndBeyond]]
[The Y2K bug [Le bug de l'an 2000]]

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]


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