Parameter estimation for cellular automata

Abstract

Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and successfully apply a sound statistical method to estimate these parameters. The decisive difference to earlier applications of such approaches is that, in our case, both the CA rules and the resulting patterns are discrete. The method is based on constructing Gaussian likelihoods using characteristics of the structures, such as the mean particle size. We show that our approach is robust for the method parameters, domain size of patterns, or CA iterations.