reaction-diffusion equations

Reaction-diffusion equations describe how substances (like chemicals) spread out over space and change over time. The "diffusion" part represents how substances naturally move from areas of high concentration to low, like ink dispersing in water. The "reaction" part accounts for chemical transformations or interactions that create or remove substances. Together, these equations model complex patterns, such as animal coat markings, chemical waves, or biological processes, by mathematically capturing how substances interact and diffuse simultaneously to produce dynamic, often intricate, patterns in space and time.