Information-theoretic study of pattern formation: Rate of entropy production of random fractals

A model dynamical system is described which generates spatial patterns based only on connectivity and screening. The growth probability at sites on the pattern is determined by the extent to which the sites are ‘‘screened’’ by points on the exterior of the pattern. The scaling properties were found to depend on the strength of the imposed screening constraint. Information theory was used to measure the rate of entropy production of the different patterns. A critical point in the screening constraint was observed where the pattern geometry changed from two dimensional (compact) to one dimensional. At this critical point, random fractals are produced and the rate of entropy production is a maximum. Analogies are drawn between the patterns produced by our model system, and similar patterns generated by diffusive processes.