This example attempts to demonstrate the Gray-Scott Reaction-Diffusion model. The reactions are:
U + 2V -> 3V
V -> P
where U, V, and P represent the reactants. The time evolution of the system is described by a pair of partial differential equations.
This system is modelled here as a 2D continuous Cellular Automaton with a von Neumann neighbourhood of radius 1. The state of a cell consists of the tuple (u, v), where u is the concentration of U, and v is the concentration of V. Both u and v assume continuous values between 0 and 1. (The concentration of the decomposition product, P, is not explicitly modelled.) This is an example of a system that is in a constant state of disequilibrium: it is kept in chemical non-equilibrium by virtue of the fact that the substrate is constantly being replenished.
The full source code for this example can be found here.
More information:
Pearson, John E. "Complex patterns in a simple system." Science 261.5118 (1993): 189-192.
Froese, Tom, Nathaniel Virgo, and Takashi Ikegami. "Life as a process of open-ended becoming: Analysis of a minimal model." ECAL. 2011.