The final demo for the Barkley model shows a state that is disordered in space, but if you run it long enough you can convince yourself that the time dynamics is periodic. In the slightly modified version of the model due to Bar and Eiswirth Phys. Rev. E48 1365 (1993) simulated here the disordered state appears to be more chaotic (see however Strain and Greenside, Phys. Rev. Lett. 80 2306 (1998)).
The system size in this demonstration is 64 along each edge. The mesh size h for the finite difference code is 0.5 and the time step dt=0.05.Demonstrations-1-2-3-4-5