Pattern Formation and Pattern Recognition
The world around us is composed of rather well-defined structures. The living world abounds with them, but structures may be formed also in laboratory experiments, e.g. in fluids, or in chemical reactions, where hexagonal structures or spiral waves are observed. In the following, we shall use the word pattern instead of structures. Patterns are not only found in the spatial domain, but also in the temporal one. Consider for example the coherent oscillation of a laser, or its more complicated temporal patterns in the case of multimode operation (Haken 1970, 1981). Some twenty years ago, I coined the term ‘synergetics’ in order to characterize an interdisciplinary field of research that studies the spontaneous, i.e. self-organized, formation of patterns from a unifying point of view. The question I asked is as follows: ‘Are there general principles irrespective of the nature of the subsystems that govern the spontaneous formation of patterns?’ Over the past twenty years this question could be answered in the affirmative for large classes of systems provided we focus our attention on those situations in which the qualitative behavior of the system changes at macroscopic scales (Haken 1983, 1987). Examples for such kind of changes are provided by the laser, where the incoherent light of the lamp is replaced by the qualitatively quite different coherent laser light, by a fluid heated from below, in which the homogeneous state is replaced by hexagonal or roll pattern, by chemical reactions giving rise to formation of spirals, etc.