Summary: Over Two Decades of Pattern Formation, a
From 25 Years of Nonequilibrium Statistical Mechanics,
edited by J.J. Brey, J. Marro, J.M. Rub´i, and M. San Miguel,
Lecture Notes in Physics (Springer, 1995), p. 91 - 124.
Department of Physics and Center for Nonlinear Studies, University of
California, Santa Barbara, CA 93106
Abstract: Patterns are ubiquitous in the world that surrounds us. They can form via
bifurcations, for instance from the spatially uniform state, as a control parameter is
varied. Their nature generally is determined by nonlinear terms in the relevant equa-
tions of motion, and thus their elucidation is a non-trivial goal in nonlinear physics.
In the early 1970's, there was a revival of interest in the condensed-matter physics
community in chaos and pattern formation in nonlinear dissipative systems. Experi-
mentalists and theorists brought the tools of their field to bear on these challenging
problems. Mostly in terms of his own experiences, the author of this paper reviews
some of the issues that have been addressed, some of the techniques that have been
applied, and some of the progress that has been made by experimentalists during the
two-and-a-half decades since then, and the relationship which these results have to our
present-day understanding of nonlinear systems.