Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter- [Visualisation tridimensionnelle de la dynamique de Verhulst -'Les Vaisseaux du Temps', un hommage à Stephen Baxter-].




The Verhulst dynamics is defined using the following iteration:
                    X  = 0.5
                     0
                    X  = RX   (1 - X   )
                     n     n-1      n-1
Here, in this computation, the growing rate 'R' is no longer constant but changes its value periodically using the following arbitrary cycle:
R3 ==> R3 ==> R3 ==> R3 ==> R2 ==> R2 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R2 ==> R2 ==> R3 ==> R3 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R2 ==> R2 ==> R3 ==> R3 ==> R2 ==> R2 ==> R1 ==> R1 ==> R1 ==> R1 ==> R1 ==> R1
(based on the sine function on [0,8.pi]) where {R1,R2,R3} are respectively the three coordinates of the current point inside the following domain [2.936,3.413]x[3.500,3.850]x[3.000,4.000]. Only the points corresponding to a dynamical system with a negative Lyapunov exponent are displayed.


See some related pictures:


 



See a bidimensionnal dynamics:




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