Evolution of natural patterns from random fields

TL;DR

This paper explores how reaction-diffusion pattern evolution can be approximated by cellular automata, demonstrating pattern formation on different lattices with potential applications in textile manufacturing and animal skin modeling.

Contribution

It introduces a method to transition from reaction-diffusion equations to cellular automata for pattern generation on various lattices.

Findings

Cellular automata can replicate complex natural patterns.

A simple majority rule effectively models pattern evolution.

Generated patterns resemble natural textures like lizard skin.

Abstract

In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal and quadratic lattice. With this aim a random initial field is transformed by a sequence of CA actions into a new pattern. On the hexagonal lattice this pattern resembles a lizard skin. The properties of CA are specified by the most simple majority rule that adapts selected cell state to the most frequent state of cells in its surrounding. The method could be of interest for manufacturing of textiles as well as for modeling of patterns on skin of various animals.