Emergent properties in random complex automata

Abstract

Studies of large, randomly assembled binary (Boolean) node automata have demonstrated that such systems can spontaneously exhibit enormously ordered dynamical behavior. An important approach to characterizing these behaviors has consisted of studying ensembles of automata. Ensemble specifications have been based on: 1) choice of Boolean function regulating each node in the automaton; 2) random or biased mappings of the 2^N automata states into themselves; 3) the numbers of inputs, K, per node. This article briefly reviews these approaches, reports new results on the expected behavior of threshold automata, and automata with a particular class of biased mappings. In addition, it discusses emergent, highly ordered dynamical behavior in random automata rich in a specific class of “canalizing” Boolean functions due to the crystallization of powerful subautomata called forcing structures. The ordered behaviors may be of importance in biological evolution, in physics, and in the design of adaptive automata.