When Martin Gardner published the rules of John Conway’s Game of Life four decades ago [1], the result was an explosion of interest in cellular automata among both amateur hobbyists and experienced researchers in computing, mathematics, and the sciences. Furthermore, this interest hasn’t diminished over the years.

The simple rules of the original Life are merely one set of possible sets of rules governing the evolution of patterns in a two-dimensional (2D) space. Some sets do not create any interesting features; the patterns all die, the entire space becomes filled, or the space has a few resulting uninteresting static features. Conway’s rules give rise to a two-dimensional (2D) universe of both stable and oscillating forms, as well as collections of cell patterns that move across the space. Several other sets of rules are capable of generating interesting features and have been used as model systems.

Among the significant factors in our continual fascination with Life are its accessibility to virtually anyone because of its simple rules, its amenability to experimentation and observation, and the perception of possible analogues of Life (and similar rule sets) to scientific problems and applications in the real world. Life allows for empirical research on model systems without glassware or expensive instrumentation.

With this book, Andrew Adamatzky has assembled a superb collection of papers on Life that encompass work going back more than 20 years. Several of the earlier papers are reprints of reports published in the 1980s, which provide a historical perspective. These are very useful in laying the foundation for the more contemporary papers in the remainder of the book. Adamatzky’s book maintains a good balance between interconnectedness and recognition of the papers as independent contributions.

The book is organized into eight principal parts, preceded by an introductory chapter by Carter Bays that introduces cellular automata and Conway’s Game of Life.

The first part is historical. It starts with a personal recollection by Robin Wainwright, who edited a short-lived newsletter on Life that started within a year of Gardner’s report. This newsletter crystallized the Life community. The next three chapters in this part, by Harold McIntosh, were originally published in 1988. They feature the taxonomy and behavior of the patterns found in Life. The content and style of these papers resemble those written by biologists reporting the inventory of biota in a region.

The second part is a collection of classical topics. The five chapters in this part cover the growth and decay of patterns as a function of initial conditions, including design or randomness, the generation of moving objects (gliders, glider guns, and puffer trains), oscillators, still lifes (static objects), alternative rule sets to that in Conway’s Life, and the maximum density of occupancy.

A relaxation of the rules and some of the constraints in Conway’s Life is the general theme of the six chapters in the third part. Among these constraints is asynchronous behavior (the clock does not run the same everywhere in the 2D universe), expansion of the neighborhood around a cell beyond its immediate neighbors, and the ability of the cells to have a memory of past states. Among the variations on Life are the Larger than Life model, the Real-Life model, Life with continuous (instead of discrete) states, cells that remember what they had once been, and modeling the behavior of physical systems and statistical mechanics with mean field analysis, phase transitions, and diffusion.

Conway’s Life and many other rule sets are applied to a grid of squares. The fourth part discusses lattices that are not built of squares: triangles, hexagons, and three-dimensional (3D) structures such as spheres. A single chapter by Nick Owens and Susan Stepney recasts Life on Penrose tilings, and looks for still lifes and oscillators on this space.

The theme of Part 5 is complexity and emergent behavior. The first chapter, by Nick Gotts, concentrates on how the patterns that develop illustrate complexity and emergent phenomena. The second chapter, by A.R. Hernandez-Montoya et al., emphasizes data analysis and correlation functions.

The sixth part, which contains two chapters, focuses on physics. The first chapter, by Claudio Conti, considers the interaction between light (in a 2D universe) and cells obeying Life rules. It poses questions on the recovery of systems undergoing catastrophic change and on whether genetic adaptations can be represented. The chapter by Adrian Flitney and Derek Abbott reports on their investigation of the behavior of Life where one can represent the states of the cells by a quantum indeterminacy.

When users run Life, it generates a visual pattern that is often aesthetically pleasing. In the single chapter in the seventh part, on music, Eduardo Miranda and Alexis Kirke discuss their work on representing visual patterns by sound, including using conventional music notation to capture the sound to be produced. It is unfortunate that no audio clips are available, as it would be interesting to compare them to the works of Brian Eno and other contemporary composers.

The final part of the book describes using Life as a computer. Two of the three chapters show how one can use Life to construct a register machine, including all of the necessary switches, gates, and latches, and the third chapter explains how to simulate a Turing machine.

Each of the chapters has its own set of references. A brief index at the end of the book points the reader to topics discussed in the chapters. This book is a treasure trove of history, concepts, and models. It is a good starting place for a newcomer to the study of Conway’s Game of Life, an opening of vistas for the amateur hobbyist, and a serious handbook for the professional researcher.