We investigated spatio-temporal pattern formation in a reaction-diffusion system assuming a periodic cellular space. The reaction space is an array of cells, where diffusion is assumed to be fast inside the cells and relatively slow in the walls separating them. The simulation results showed that the spatio-temporal development of the concentration pattern on the array depends on some specific parameters such as the diffusion coefficients in the cell walls and the size of cells. In a certain parameter region, the concentration inside each cell takes either a high or low value, and moreover, these locally discretized cells generate an alternating pattern spreading into the entire space. Whole of this process can be regarded as discretization of state, time, and space of a chemical reaction system which is intrinsically continuous. This kind of discretization mechanism is expected to provide a new way of the implementation of cellular automata based on molecular reactions.