Gray-Scott model: great site with codes, theory and results of a simple chemical reaction-diffusion that generates very complicated patterns. Also link to relevant paper on pattern generation by reaction-diffusion equations.
Fonseca CR, Coutinho RM, Azevedo F, Berbert JM, Corso G, Kraenkel RA (2013) Modeling Habitat Split: Landscape and Life History Traits Determine Amphibian Extinction Thresholds. PLoS ONE 8(6): e66806.