Abstract

Nonlinear feedback systems may show a principally different dynamical behavior compared with linear systems: Chaos may appear; in other words, unpredictability in any practical sense. Sometimes, however, cooperative effects can be observed. We use the term cooperative when stable patterns evolve with long-range spatial correlation. With optics, TV, and a computer we can study the dynamics of pictures running through a nonlinear feedback loop. Coupling between different pixels is introduced by convolution. The most interesting features of such pictorial feedback systems are (1) weak coupling of adjacent pixels always leads to chaos, (2) strong coupling with positive point-spread function leads to chaos, (3) strong coupling with bipolar point-spread functions leads to stable patterns with long-range spatial order, (4) stability is not destroyed by a considerable amount of noise.

© 1985 Optical Society of America