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

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:

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


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