In 1952, A. M. Turing proposed the notion of “diffusion-driven instability” in his attempt of modeling biological pattern formation. Following his ingenious idea, many reaction-diffusion systems have been proposed later on. On the other hand, Turing patterns can be explained by some cellular automata. Cellular automata are theoretical models which consist of a regular grid of cells, and they exhibit the complex behavior from quite simple rules. In this paper, we describe the mathematical properties of reaction-diffusion systems modeling pattern formation, in particular, Turing patterns. Moreover, we explain ideas which connect differential equations with cellular automata.