Various Methods of Pattern Formation

  • Alexander E. Filippov
  • Stanislav N. Gorb
Part of the Biologically-Inspired Systems book series (BISY, volume 16)


Evolution of different systems can be described in terms of their relaxation to the minimums of some effective potential relief. This observation faces us with a question how to generate corresponding potential patterns which describe adequately various physical and biological systems. In this chapter, we present a number of different ways to generate 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 evolution, they form majority of meta-stable structures which we observe in real world. Counting on mentioned above universality of naturally-generated fractal structures and their further utilization in next chapters of this book, we reproduce also formal algorithms of generation of such structures based on random deposition technique and Fourier-transform approaches.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alexander E. Filippov
    • 1
  • Stanislav N. Gorb
    • 2
  1. 1.Donetsk Institute for Physics and EngineeringDonetskUkraine
  2. 2.Zoological InstituteKiel UniversityKielGermany

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