Dynamical Behavior of Cellular Automata under the Constraint of Neighborhood Coherence

Abstract

The emergence of spatial discrete patterns has attracted little research interest among geographers, especially as far as the phenotypical aspects of the pattern are concerned. How can we understand the development of such patterns? What role is played by generative rules underlying this process? Using the cellular automata theory, a model (SISPAQ) was built to probe into the role of the neighborhood coherence principle (NCP) as a generative rule. Several remarkable properties of NCP are unveiled. A self‐organizing behavior is shown, which allows the system to counteract the maximum entropy law and build a pattern with a relatively high level of organization. Not only does NCP provide sufficient conditions for the building up of an organized pattern, but it also provides a self‐maintaining capacity. This is evidenced by the fact that under a critical value (the emancipation probability), any cell or group of cells displaying an aberrant state will be eradicated by a locally dominant state. 1989 The Ohio State University