METHODS OF THE PATTERN FORMATION IN NUMERICAL MODELING OF BIOLOGICAL PROBLEMS

Abstract

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.