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Abstract

Self-enhancement coupled with one or more antagonistic reactions is the crucial element in pattern forming reactions. Depending on the parameter, this can lead to patterns in space and/or in time which can be either extremely robust and reproducible or highly variable. Complex patterns result from a linkage of many pattern forming reactions, one pattern generates the prerequisites for the next. The support these models have obtained recently by molecular-genetic observations give rise to the hope that in the future an interplay between theory and experiment will lead to a still better understanding of this central issue.
Free from functional constraints, the diversity of patterns on the shells of mollusks provide a rich source to study the properties of dynamic systems in general. Everyday, we are confronted by systems that have an inherent tendency to change. The weather, the stock market, or the economic situation are examples in which self-enhancing and antagonistic processes also play a decisive role. The shell patterns are sufficiently complex to be a challenge but also sufficiently simple to be accessible to modeling. Their one-dimensional character and the preservation of the history of their formation provide unusual help for deciphering these patterns. They illustrate the range of behavior that can be generated by modifications of a basic mechanism. They can be regarded as a natural exercise book to study dynamic systems.