Principles and mathematical modeling of biological pattern formation
An overview of principles and mathematical models of biological pattern formation is presented. One can distinguish preformation, optimization, topological and self-organization principles. Combinations of such principles are responsible for shape and tissue formation, differentiation, regeneration, morphogenetic motion, cell division and even malignant patterns, e.g. in tumor growth. Mathematical modeling allows for a systematic analysis of the pattern-formation potential of morphogenetic principles....