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The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules with complex behavior a dynamic competition among all the possible stable 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.
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex symmetrical pat
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial selection for
In studying the predictability of emergent phenomena in complex systems, Israeli & Goldenfeld (Phys. Rev. Lett., 2004; Phys. Rev. E, 2006) showed how to coarse-grain (elementary) cellular automata (CA). Their algorithm for finding coarse-grainings of
We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for cas to be number-conserving is proved. Using this condition, we give a linear-time algorithm to decide num
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter, and features a global symmetry. One then extends th