Homogeneous dynamics for square boolean automata with null boundary conditions

Abstract

This paper is concerned with the study of square Boolean four-neighbor peripheral cellular automata with boundary conditions xed as zero. It is rst shown that, due to plane re ection symmetry transformations, the number of dynamically nonequivalent such automata is equal to 9 616. The dynamics of the two homogeneous con gurations are studied and it is shown that, in contrast with what happens in the case of periodic boundary conditions, the homogeneous con guration consisting only of ones can have various interesting dynamics, including the one typically observed for automata in Wolfram's Class III. Finally, an example of a rule where there is coexistence between a homogeneous nal state and other dynamics is presented.