Complex chaotic behavior of a class of subshift cellular automata

A class of parameterized boolean, one-dimensional, biinfinite cellular autom at a has been studied and their behavior observed when some parameters of the local function are changed. These automata are equivalent to a particular class of boolean neural networks and the change in the parameters corresponds to a change in the symmetricity of the connection matrix. The purpose is to analyze the different dynamics, beginning with a symmetric connection matrix and moving toward an antisymmetric one. We have observed that simple dynamics corresponds to the symmetric situation, whereas the antisymmetrical case yields more complex behavior. On the basis of these observations, we have identified a new class of cellular automata that is characterized by shift like dynamics (simple and complex subshift rules); these cellular automata correspond to the asymmetric situations and they are chaotic dynamical systems.