ABSTRACT
This chapter introduces algebraic techniques for the analysis of additive cellular automata in the context of a specific simple example. It derives general results for all additive cellular automata. The chapter allows cellular automata in which the sites are arranged in a square or cubic lattice in two, three or more dimensions, rather than just on a line. It discusses generalizations in which the cellular automaton time evolution rule involves several preceding time steps. The chapter considers alternative boundary conditions. It also discusses non-additive cellular automata. The chapter gives a discussion of the results obtained, comparing them with those for other systems. It generalizes the formalism to several dimensions and more neighbours. The chapter develops algebraic techniques for the analysis of cellular automata in the context of the simple cellular automaton. It illustrates some methods which may be applied to the analysis of non-additive cellular automata, and some of the results which may be obtained.
