In Schiff’s words, this book is “an introduction into the brave new world of cellular automata, hitting the highlights as the author sees them.” It is divided into six chapters: “Preliminaries,” “Dynamical Systems,” “One-Dimensional Cellular Automata,” “Two-Dimensional Automata,” “Applications,” and “Complexity.”

The preface gives very helpful links to several Web sites that provide commercial and public domain software for cellular automata (CA), as well as other resources. Throughout the book, Schiff gives links to other Web sites that either illustrate and expand upon his points or provide software. Moreover, the publisher has also set up a Web site associated with the book, from which further examples, Java applets, and CA computer code can be downloaded, and to which readers can contribute further material. This initiative definitely enhances the value of the book for teaching and independent study purposes.

The mathematical theory of cellular automata is purportedly concentrated primarily in the first two chapters. However, this is primarily descriptive, rather than formal. No attempt is made to give precise definitions or to formulate theorems. Moreover, many of the ideas introduced here--Kolmogorov dimension, for example--are, in fact, never used in the rest of the text, leading a reader to wonder why the author bothered with them. This is a shame, because there is an interesting formal theory of cellular automata that students and researchers should know is there, even if they do not delve into it too deeply.

In the remaining chapters, the author admits that “outbreaks of mathematics have deliberately been kept to a minimum”--meaning that the material has been dumbed down, which is definitely the case. Basically, the rest of the book is organized like a medieval bestiary: come and see all the odd and wonderful creatures out there and hear something of what we know about them. General concepts, if introduced at all, are given for the special case being discussed, and left to the reader to generalize. For example, on page 62, the author writes: “Irreversible cellular automata may exhibit a decrease in the number of possible configurations over time.” This seems to be his way of defining the notion of “irreversible,” but on page 67, he writes: “We found that in irreversible automata the number of configurations could diminish with time.” This implies that this is a property, not a definition of irreversibility. So how do we define an irreversible cellular automaton?

The lack of depth and rigor makes the book unsuitable as a textbook, but it is nonetheless an interesting read and worth browsing by somebody interested in getting a general background on CA. The examples are many and varied, and the numerous citations--both to electronic and printed media--are very helpful. There are many illustrations; they are sometimes a bit confusing, since the method of graphically representing CA is not uniform--it varies with the work being cited. If you want to find out “what these guys study” and have no time to go through Wolfram’s 1,200-page tome [1], this is probably as good a place to begin as any.