Self-synchronization of Cellular Automata: An Attempt to Control Patterns
Cellular automata display configurations that are constant in time. We implement a stochastic synchronization between the present configurations of the system and its precedent ones in order to search for these constant patterns. For most of the known evolution rules with complex behavior a dynamic competition among all the possible constant patterns is established and no stationary regime is reached. For the particular rule coded by the decimal number 18, a self-synchronization phenomenon can be obtained, even when strong modifications to the synchronization method are applied.
KeywordsCellular Automaton Cellular Automaton Evolution Rule Decimal Number Synchronization Transition
- 2.Morelli, L.G., Zanette, D.H.: Synchronization of stochastically coupled cellular automata. Phys. Rev. E 58, R8–R11 (1998); Synchronization of coupled extended dynamical systems: a short review. Int. J. Bifurcation and Chaos, 13, 1-16 (2003)Google Scholar
- 4.Sánchez, J.R., López-Ruiz, R.: A method to discern complexity in two-dimensional patterns generated by coupled map lattices. Physica A 355, 633–640 (2005); Detecting synchronization in spatially extended systems by complexity measurements. Discrete Dynamics in Nature and Society 9, 337-342 (2005)Google Scholar
- 5.Toffoli, T., Margolus, N.: Cellular automata machines: a new environment for modeling. MIT-Press, Cambridge (1987)Google Scholar