Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter- (Visualisation tridimensionnelle haute resolution de la dynamique de Verhulst -'Les Vaisseaux du Temps', un hommage a Stephen Baxter-) {a chapter of 'Mathematics - A Virtual Instrument For Exploring Space Time And Beyond'}

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

The Time Ships

I saw that the fleet of Time Ships had gathered more closely together; they were rafts of green wire, silhouetted against the dazzling emptiness, and clustering as if for comfort. Tentacles -ropes of Plattnerite- snaked out across the glowing void between the Ships, and were connected, their terminations assimililated into the Ships' complex structures. Soon the whole armada about me was connected by a sort of web of cilia filament.

The Time Ships, book 6/chapter 3/page 465, Copyright © 1995 by Stephen Baxter

Les Vaisseaux du Temps

Je constatai que les Vaisseaux avaient resserré leurs rangs; treillis verts découpés sur le néant éblouissant, ils se rassemblaient comme pour se rassurer. Des tentacules -des câbles de plattnérite- serpentèrent dans le vide lumineux entre les unités de la flotte transtemporelle puis se rejoignirent, intégrant leurs extrémités aux structures complexes des Vaisseaux. Toute l'armada qui m'entourait fut bientôt interconnectée par un réseau de filaments ciliés.

Les Vaisseaux du Temps, livre 6/chapitre 3/page 571, Copyright © 1995 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

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 (possibly including this one):