Alexander E. Filippov, Stanislav N. Gorb

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Evolution of different systems can be described in terms of their relaxation to the minimums of some effective potential relief. This observation leads us to face us with a question how to generate corresponding potential patterns which describe adequately various physical and biological systems. In this review, we present a number of different ways of generating such potentials demanded by the problems of different kinds. For example, we reproduce such a generation in the framework of a simple theory of phase transitions, automatic blocking of the growing phase nucleation and universal large scale structure. Being frozen at late stages of their evolution they form majority of meta-stable structures which we observe in real world. Counting on above-mentioned universality of naturally-generated fractal structures and their further utilization in numerical simulations of biological problems, we reproduce also formal algorithms of generation of such structures based on random deposition technique and Fourier-transform approaches.


Pattern formation, Phase transitions, Large river effect, Nucleation, Biological applications, Frozen kinetics

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