Chapter 11 - Cellular Automata Investigations and Emerging Complex System Principles

Abstract

This chapter is primarily about Stephen Wolfram's innovative cellular automata investigations and his associated ideas on emerging complex system principles. The chapter begins with some cellular automata history and background, and then provides a description of Wolfram's cellular automata “explicit experimentation” work. The experimentation work shows that simple programs with simple rules, repeated over and over, can yield highly complex behavior. Wolfram has identified four classes of cellular automata. Those classes and their characteristics are discussed. The correspondence between cellular automata classes and the attractors of nonlinear dynamics theory is also discussed. Another of Wolfram's important insights is that the behavior of cellular automata is indicative of the behavior of systems in general. That idea is addressed in some detail. The latter part of the chapter addresses Wolfram's computational view of systems. The topics covered include computation as a framework for system principles, the concept of computational universality, and the identification of computationally universal cellular automata. Wolfram's Principle of Computational Equivalence is then described and discussed. The chapter concludes with a summary of my perspectives on the emerging complex system principles.