The development of macroscopic forms or patterns is a charcteristic of nonequilibrium open systems, including living organisms, ecosystems, inorganic chemical reactions and fluid systems. For a certain class of these phenomena, a set of parabolic partial defferential equations called reaction-diffusion equations works well as a model or a metaphor. In this article, some basically important spatio-temporal patterns exhibited by reaction-diffusion equations are summarized. They include standing periodic structure, propagating domain, trigger waves and their modifications, phase waves, and chaotic pattern. The origins and the properties of these patterns are explained in a qualitative way, without going into mathematical details.
