Cellular automata (CA) are very interesting computational models that have become quite well known in recent years. Mathematical and computational scientists have at least heard of Conway’s Game of Life. Quite a few researchers and aficionados pursue their interests in this area with varying degrees of seriousness. Correspondingly, of course, there has been a large body of recent literature, popular as well as scientific, describing CA and their use as models in various application domains.

This book thus takes its place within the field, joining a host of similar works. Even so, it is a useful addition to the literature, as it presents a survey that is generally broad without being too superficial, while also offering in-depth coverage that is not too hard to understand for an interested beginner.

The book contains a preface and six chapters, which in certain contexts may be read independently of one another. The first chapter, “Preliminaries,” introduces some basic concepts from automata and computation theory, such as Turing machines and logic gates, before touching on some of the basics of fractals, information theory, and entropy. The second chapter, “Dynamical Systems,” starts with recurrence relations, before moving on to chaos and strange attractors. The third chapter, “One-Dimensional Cellular Automata,” is, in a sense, where the book really begins; it presents the basic notion of a cellular automaton, related concepts such as the transition function, the neighborhood, and the radius, and then some features of some of Wolfram’s 256 elementary CA. The chapter also discusses such properties as additivity, reversibility, universal computation, and classification of CA.

The fourth chapter, “Two-Dimensional Automata,” is devoted mostly to the Game of Life, a sufficiently profound topic, and the many interesting concepts therein, such as oscillators, gliders, and Garden of Eden configurations. The fifth chapter, “Applications,” briefly touches on some of the applications of CA in areas such as biology, physics, and game theory. The final chapter, “Complexity,” contains some discussions of advanced topics, such as the origins of consciousness, starting from the classic McCulloch-Pitts neural network model and the theories of Minsky and Penrose; random Boolean networks; and multiagent systems consisting of autonomous agents, exemplified by honeybees and ant colonies.

The book is well produced and a good introduction to its subject, but it would have benefited from some more care in proofreading, for there are a number of typographical errors throughout. Likewise, though the quality of the illustrations is generally good, and the color plates (Figures C.1 to C.19) between pages 144 and 145 are quite pleasing, some of the graphics (for example, Figures 2.5 and 2.6) appear a bit fuzzy, and are not of publication quality.