ABSTRACT
This chapter presents an exploratory study of two-dimensional cellular automata. The extension to two dimensions is significant for comparisons with many experimental results on pattern formation in physical systems. The chapter considers primarily square lattices, with the two neighborhood structures. It describes a phenomenological study of typical two-dimensional cellular automata. Its approach is largely experimental in character: cellular automaton rules are selected and their evolution from various initial states is traced by direct simulation. The chapter reports evidence that certain global properties of two-dimensional cellular automata are very similar to those of one-dimensional cellular automata. It discusses the evolution of two-dimensional cellular automata from simple "seeds," consisting of a few nonzero initial sites. The chapter considers evolution from typical disordered initial states. It discusses some quantitative characterizations of the global properties of two-dimensional cellular automata. The chapter discusses patterns formed by the evolution of cellular automata from simple seeds. It presents an exploratory study of two-dimensional cellular automata.
