Local Structure Theory in More Than One Dimension

The local structure theory (G utowitz et al. ISJ) is an analyt ica l method for the determination of the statistical properties of cellular automaton evolution. In this paper we develop the local structure theory for mult i-dimens ional Euclidean lattices. The local st ructure theory for the Game of Life [1] is st udied in detail. Some statistica l properties of this cellular automaton are well approximated by a low orde r th eory.