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Bidimensional display of the rounding-off errors when computing the Verhulst dynamics [Visualisation bidimensionnelle des erreurs d'arrondi dans le calcul de la dynamique de Verhulst].

This picture displays the two following Verhulst dynamics (for 1000 iterations):
                    X  = [[R+1]*X   ] - [R*[X   *X   ]]
                     n           n-1         n-1  n-1

Y = [[R+1]*Y ] - [[R*Y ]*Y ] n n-1 n-1 n-1
computed with the same initial conditions:
                    X  = 0.5

Y = 0.5 0
They are strictly equivalent mathematically speaking and thus the point set {Xn,Yn} should be on a straight line with equation:
                    Y = X
in the bidimensional space. Unfortunately, when the R parameter increases (from 2.0 -picture 01- to 3.0 -picture 16-) the rounding-off errors become huge and give birth to two different numerical Verhulst dynamics. Then, the {Xn,Yn} points appear "anywhere" inside a square.

This double precision (64 bits) computation was made on a SGI O200 under IRIX 6.5 and C compiler release 7.2.1.

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