Tridimensional display of the rounding-off errors when computing the Verhulst dynamics [Visualisation tridimensionnelle des erreurs d'arrondi dans le calcul de la dynamique de Verhulst]
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Tridimensional display of the rounding-off errors when computing the Verhulst dynamics [Visualisation tridimensionnelle des erreurs d'arrondi dans le calcul de la dynamique de Verhulst]
. X = [[R+1]X ] - [R[X X ]]
n n-1 n-1 n-1
Y = [[R+1]Y ] - [[RY ]Y ]
n n-1 n-1 n-1
Z = Z + [R[Z - [Z Z ]]]
n n-1 n-1 n-1 n-1
computed with the same initial conditions:
X = 0.5
0
Y = 0.5
0
Z = 0.5
0
They are strictly equivalent mathematically speaking and thus the
point set {Xn,Yn,Zn} should be on a straight line with equation:
Z = Y = Xin the tridimensional 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 three different numerical Verhulst dynamics. Then, the {Xn,Yn,Zn} points appear "anywhere" inside a cube.