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 complexity, and in
which initial concepts of dissipative structures or synergetics are
deeply rooted. In pioneering domains related to hydrodynamics or
chemical instabilities, the interactions between experimentalists and
theoreticians, sometimes on a daily basis, have been a key to progress.
Everyone in the field praises the role played by the interactions and
permanent feedbacks between ex- perimental, numerical, and analytical
studies in the achievements obtained during these years. Many aspects of
convective patterns in normal fluids, binary mixtures or liquid crystals
are now understood and described in this framework. The generic pres-
ence of defects in extended systems is now well established and has
induced new developments in the physics of laser with large Fresnel
numbers. Last but not least, almost 40 years after his celebrated paper,
Turing structures have finally been ob- tained in real-life chemical
reactors, triggering anew intense activity in the field of
reaction-diffusion systems.
