Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of...

One of the most fascinating and intriguing aspects of natural phenomena is that complex systems may undergo symme try-breaking instabilities leading to pattern formation or coherent temporal behavior over macroscopic space and time scales. Therefore the understanding of why order may appear spontananeously in open systems far from equilibrium and which planforms are selected among a large manifold of possi bilities has become a major theme of research both theore- cally and experimentally. These studies, first related to fundamental questions, appear now to be of technological importance,...

Understanding the origin of spatio-temporal order in open systems far from thermal equilibrium and the selection mechanisms of spatial struc tures and their symmetries is a major theme of present day research into the structures of continuous matter. The development of methods for pro ducing spatially ordered microstructures in solids by non-equilibrium methods opens the door to many technological applications. It is also be lieved that the key to laminar/turbulence transitions in fluids lies in the achievement of spatio-temporal order. Let us also emphasize the fact that the idea of...

One of the most fascinating and intriguing aspects of natural phenomena is that complex systems may undergo symme try-breaking instabilities leading to pattern formation or coherent temporal behavior over macroscopic space and time scales. Therefore the understanding of why order may appear spontananeously in open systems far from equilibrium and which planforms are selected among a large manifold of possi bilities has become a major theme of research both theore- cally and experimentally. These studies, first related to fundamental questions, appear now to be of technological importance,...