On beta-skeleton automata with memory

A β-skeleton is a proximity undirected graph whose connectivity is determined by the parameter β. We study β-skeleton automata where every node is a finite state machine taking two states, and updating its states depending on the states of adjacent automata-nodes. We allow automata-nodes to remember their previous states. In computational experiments we study how memory affects the global space–time dynamics on β-skeleton automata.

Research highlights▶ We study the effect of endowing nodes in beta-skeleton parity automata with majority memory. ▶ The effect of memory in the rate of changing nodes and in the damage spreading is examined. ▶ Memory induces a notable moderation in both parameters. ▶ Memory turns out ineffective in the control of the damage with low memory charge and in networks with high connectivity. ▶ The maximum memory effectiveness is achiev ed with half the maximum feasible memory charge.