2D elementary cellular automata with four neighbors

Abstract

This paper is concerned with the study of square boolean synchronous four-neighbor peripheral cellular automata. It is rst shown that, due to conjugation and plane re ection symmetry transformations, the number of dynamically nonequivalent such automata is equal to 4 856. The cellular automata for which the homogeneous nal states play a signi cant role are then identi ed. Finally, it is shown that, contrary to what happens in the case of one-dimensional boolean three-neighbor cellular automata, for some peripheral automata there is coexistence between a homogeneous nal state and other dynamics.