Lifshitz-Petrich Equation
The equation is a modified version of the Swift-Hohenberg model constructed to develop quasicrystalline patterns. You can find out more about quasicrystals on the web site of Ron Lifshitz. The simulation is in a 64x64 system.
You can run the same equation in a system size twice as large (128 x 128) here.
Demonstrations-1-2-3