Chaos and Images (Page 5)

When two chaotic systems are in synchrony, the relation between the individual components might contain very complicated structures. The functional relation between them can be smooth or wrinkled (nondifferentiable). In the more severe case, the relation might not even be a function and it might become multivalued. Here are some of the examples. The first three animated pictures are constructed by an iterative graph transform method. The last animated picture demonstrates the development of the multivalued synchronization set as loops form with varying degree of noninvertibility.

Smooth Synchronization Set by Paul So, Ernest Barreto - animated
Wrinkled Sychronization Set by Paul So, Ernest Barreto - animated
Cusped Synchronization Set by Paul So, Ernest Barreto - animated
Looped Synchronization Set by Paul So, Ernest Barreto - animated