Cellular automaton obtained by the tropical discretization from the competitive diffusion equation

Abstract

We proposed a method for generating cellular automata from reaction-diffusion equations automatically. Tropical discretization is a method that uses positive discretization and ultradiscretization. The tropical discretization is used to create a cellular automaton from the competitive diffusion equation in this paper. It has been demonstrated that constructed difference equations, ultradiscrete equations, and cellular automata have a similar property to competitive diffusion equations in that the order of the solutions is conserved.