A Study of higher order Cellular Automata with Examples

Abstract

Cellular automata are discrete dynamical systems which are practical to use for simulations. Higher order cellular automata are a natural extension of cellular automata, and are expected to be a useful way of improving already existing cellular automata models. We present here an introduction to cellular automata including background, definition and notation. We then present higher order cellular automata, motivated by the notion of hyperstructures. Two examples of how higher order cellular automata are used in modelling then follows. The first model use higher order cellular automata to improve traffic flow in a graph-traffic problem derived from a set of single lane-traffic cellular automata rules. The second model shows another way of using higher order cellular automata. It is based on the majority vote cellular automaton which does a naive emulation of a voting situation in a population. Inspired by hyperstructures in a real population, higher order layers are added, and their effects on the system are observed to be significant.