Localized Structures in Reaction-Diffusion Systems Irving R. Epstein, Brandeis University A localized structure is a well-defined area whose state differs significantly from that of the neighboring “background,” e.g., a blood clot in a vein or a blob of ball lightning. In chemical systems, these structures can arise from the coupling of nonlinear reaction kinetics with diffusion. We are exploring the conditions under which such structures can arise and whether they might have any practical importance. We have found several novel phenomena in computer simulations of reaction-diffusion systems. The picture on the left shows “jumping oscillons,” which periodically vanish and then reappear at a fixed distance. On the right, we see negative refraction of localized waves, a phenomenon found experimentally in so-called metamaterials.