To most computer scientists, the term cellular automata (CA) is associated with John Conway’s Game of Life. While this association is understandable, over the past ten to 15 years, CA have been used to study a variety of real-world systems, including some relatively obvious applications in computer science, mathematics, and physics, as well as unexpected areas such as epidemiology, immunology, sociology, and finance. For example, CA have been used in the study of the immune response to HIV infection and in the study of crowd behavior.

This impressive volume, part of the well-respected Springer “Complexity” series, contains a number of chapters written by different researchers and gives an indication of just how widespread the application of CA to the study of complex systems really is. The preface states that the book is designed to give an overview of the field for practitioners, as well as a starting point for more detailed study at the graduate level or beyond. In addition, the wide variety of application areas should inspire scientists in other fields to consider how CA can also be applied to their own disciplines.

A cellular automaton is a discrete system, usually visualized as a grid with any number of dimensions, in which the behavior of each cell in the grid, at each unit of time, is determined by the cell’s neighbors. The inherent parallelism of the model is, of course, well matched to the increasing use of parallelism in today’s computers, both in terms of algorithms and hardware. The introductory material in the book emphasizes that CA will provide a model for some behavior of a complex system, but not a complete description. As noted in the foreword, “CA are primarily a conceptual tool for understanding and taming a complex system and not running an industrial version of it.”

The book is divided into three parts. After the foreword, preface, and an introductory chapter written by the editors, there is a set of eight theoretical chapters that talk about how to apply CA of various types. The next five chapters are more practical, providing specific examples of what happens when we apply CA to a number of different disciplines. There is a final chapter on some of the software available to help in the implementation of CA simulations.

Most of the chapters are roughly 20 to 30 pages long. Each is essentially self-contained, starting with an introduction and ending with a summary or concluding section. As expected, the various chapters are an interesting mix of styles. Some are quite formal, with a series of equations and complex diagrams; some are informal, with much simpler pictures of the growth of CA; and some seem almost philosophical, especially when talking about self-reproduction (a la von Neumann). Despite this variety, the editors do an excellent job of making the chapters come together to form a whole. Each chapter has an extensive set of references, making it easy for the reader to pursue a particular topic in more depth.

One minor quibble: there is no overall bibliography for the book. It would have been interesting to see what papers were referenced in more than one chapter and which of the papers were cited most.

Most of the chapters are written by European researchers, and it is obvious that English is not their native language. Nonetheless, the sections are all quite readable, with only a few minor grammatical errors here and there. The editors have succeeded in presenting an overview of this fascinating field.