Complex Systems

Information Flow in Cellular Automata Download PDF

Stan Palasek
Sonoran Science Academy
Tucson, Arizona

Abstract

Long-time correlations between components of stochastic physical systems have been observed to be stronger than an exponential decay model would predict. Simple programs should likewise exhibit slow information dissipation at large t if they are to underlie statistical systems as Stephen Wolfram's A New Kind of Science suggests. Here it is shown that information about the initial conditions of subsystems of many nontrivial cellular automata leaves the subsystem initially at an exponential rate until a certain threshold is reached at which the information loss slows and qualitatively changes form. This phenomenon appears among not only the elementary cellular automata (ECAs) but also more complicated rules that share features with physical systems.