Complex Chaotic Behavior of a Class of Subshift Cellular Automata

A class of parameterized boolean, one-dimensional, biinfinite cellular autom at a has been st udied and t heir behavior observed when some param eters of the local funct ion are changed. T hese aut omata are equivalent to a par t icular class of boolean neural networks and t he change in t he parameters corresponds to a change in the symmetricity of t he connect ion matrix. T he purpo se is to ana lyze t he different dynamics, beginning with a symmet ric connect ion matrix and moving toward an ant isymmet ric one. We have observed that simp le dynamics corresponds to the symmetric situation, whereas the antisymmet rical case yields more complex behavior. On the basis of these observatio ns, we have identified a new class of cellular auto mata tha t is characterized by shift like dynamics (simple and complex subshift rules); these cellular automata correspond to t he asymmet ric sit uations and they are chaotic dynamical syst ems.