A Comprehensive Taxonomy of Cellular Automata

Abstract

Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and abundant computational power, the current lack of a complete survey on the 'taxonomy' of various families of CAs impedes efficient and interdisciplinary progress. This review paper mitigates that deficiency; it provides a methodical overview of five important CA 'families': asynchronous, stochastic, multi-state, extended-neighbourhood, and non-uniform CAs. These five CA families are subsequently presented from four angles. First, a rigorous mathematical definition is given. Second, we map prominent variations within each CA family, as such highlighting mathematical equivalences with types from other families. Third, we discuss the genotype and phenotype of these CA types by means of mathematical tools, indicating when established tools break down. Fourth, we conclude each section with a brief overview of applications related to information theory and mathematical modelling.