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Since we do not require that the reader is familiar with synergetics, we shall give a brief outline of this field first. Synergetics is an interdisciplinary field of research [1]–[3], which deals with complex systems. Such systems are composed of many parts that interact with each other. We shall be concerned with those systems that may form spatial, temporal, or functional structures spontaneously, i.e. these structures are developed by the systems themselves without any specific interference from the outside. Such structures are, of course, formed when plants or animals are developing, but they may be even found in the inanimate world of physics and chemistry, for instance by the formation of specific structures in fluids. Synergetics asks whether there are general principles that govern the formation of structures. To this end, it has developed a specific strategy, namely to look at those situations in which qualitative changes occur. A typical and instructive example for such a qualitative change is the freezing of water. Though water and ice are composed of the same constituents, namely water molecules, at the macroscopic level water and ice have quite different mechanical and optical properties. On the other hand, this example does not cover all important aspects of systems treated in synergetics, because ice is, so-to-speak, a dead system, whose state is not maintained by any influx of energy. Rather synergetics deals with so-called open systems whose states are maintained by a continuous influx of energy and/or matter. In physics pattern formation occurs in fluids once they are heated from below. Such a fluid may form structures in the form of rolls, hexagons, or spirals, or still more complicated patterns (Fig. 1).

DOI: 10.1007/978-94-015-9620-6_4

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