Estimating topological entropy of multidimensional nonlinear cellular automata

Cellular automata are discrete dynamical systems whose config-urations are determined by local rules acting on each cell in syn-chronous. Topological entoropy is a tool for measuring the complex-ity of these dynamical systems. In this paper we estimate topologi-cal entropy of a two-dimensional nonlinear cellular automaton. The method we use is that a one-dimensional cellular automaton with positive topological entoropy is “naturally ” embedded into the two-dimensional cellular automaton. Hence we obtain a multidimensional cellular automaton with infinite topological entoropy. 1