Complex Systems

Changing the States of Abstract Discrete Systems Download PDF

James Hay
Department of Chemical and Biochemical Engineering
University of Western Ontario
London, ON, Canada

David Flynn
King's University College
London, ON, Canada

Abstract

The four classes or states of discrete systems—chaos, complexity, and two types of order—have been established by S. Wolfram in [1]. We describe how the ratio d/c of two parameters, differentiation and centrality, explains changes among these states. Both parameters were developed in the social sciences and have been used to explain changes of state in social systems, which are also discrete systems [2]. Differentiation is the variety within the structure of a discrete system. Centrality measures the variety of outside information presented to a discrete system. Although these ideas can be applied to cellular automata (CAs), the range of these two variables is very limited for a given CA. In this paper we use the idea of a global cellular automaton (GCA), as developed by Wolfram in [3], and a GCA network (GCAN), as developed by S. Chandler in [4], to show how changes in the state of abstract discrete systems are related to changes in the ratio d/c.