Emergence of Cellular Automata Rules through Fluctuation Enhancement
Burton Voorhees, Carey Luxford and Rhyan Arthur
A process of random selection acting on pairs of binary strings is coupled with a scheme that reinforces the probability of specific pairs related by sets of cellular automata rules. The result is the apparent operation of a deterministic dynamical rule subject to fluctuations. The evolution of the probability distribution governing the selection process is determined. Branching ratios for competitions between rules are computed and two entropy measures, one decreasing and one increasing, are defined. The combination of random selection subject to reinforcement bias gives an example of apparently deterministic global dynamical laws emerging from a stochastic process.
Keywords: cellular automata, fluctuation enhancement, Hebbian reinforcement