Evolving three-dimensional cellular automata to perform a quasiperiod-3 collective behavior task

We present results from experiments in which a genetic algorithm (GA) is used to develop three-dimensional cellular automata (CA) to perform a nontrivial collective behavior task. Under a fitness function that is defined as an averaged area in the iterative map, the GA detects a CA rule with quasiperiod-3 (QP3) collective behavior and another with period-3. For rules with QP3 the time autocorrelation function decays as a power law with an exponent of -1/2, according to the predictions of the Kardar-Parisi-Zhang equation, and a space-time diagram reveals the existence of propagating structures inside the system. [S1063-651X(99)14910-9].