these systems have been studied by biologists and
mathematicians to see what patterns may be formed.
Andrew Witkin and Micheal Kass considered
reaction-diffusion systems as a model for fingerprints.
Many people have used reaction-diffusion derived algorithms
to generate pretty pictures. You can get nice backgounds from
Machine by Roy Williams and Bruce Spears.
Also Andrew Witkin and Micheal Kass won the Prix Ars Electronica 1992 for
their picture 'RD Texture Buttons'.
Greg Turk looks at generating textures using a cascade of
multiple reaction-diffusion systems.
Greg Turk also introduces a method by which the texture is
generated directly over an arbitrary surface.