Determinism in cellular automata - Investigation of transition rules

Cellular automata are discrete dynamic systems whose behavior is specified in terms of local interactions. Even simple local interactions may eventually manifest themselves in terms of complex and unexpected global patterns. A number of investigations have been reported on a two-dimensional lattices demonstrating exciting outcomes starting with simple initial configurations and simple rules of interactions, giving rise to the speculative possibilities of artificial life. There is a growing interest in a variety of automata including three dimensional automata and variations of transition rules, but common to all their formations are certain hard questions relating to the global determinism of the behavior of the cellular automata manifest in the local interactions. There are a number of other theoretical issues remain unresolved. A considerable theoretical work and simulation have been reported around the one-dimensional lattices, primarily because of possible visualization of the processes. In this paper we investigate the issue of density of an automata configuration and its determinism.