This paper presents a design approach for a fuzzy cellular automaton based on an inverse entropy optimization principle. The cells of the automaton are characterized by two state variables computed by dynamic TSK fuzzy systems. The state variables of the cells are understood as spatial information sources so that the entropy of the binary sequences produced by the cells is maximized in a given instant. An evolutionary mechanism like the Differential Evolution Algorithm has been used to solve the optimization problem effectively since entropy reveals a convex landscape. Results show different regimes of operation for the fuzzy automata can be obtained. Among these regimes, there is one in which the cell entropy fluctuates over the maximum limit and the automata exhibit interesting behaviors so that it can be used as a model of several complex phenomena.