Cellular automata became popular about twenty years ago, although the ideas go back at least as far as J. von Neumann [Theory of self-reproducing automata, University of Illinois Press (1966), Russ. translation 1971; Zbl 0247.94029)]. One of the later pioneers was S. Wolfram [Theory and applications of cellular automata, World Scientific (1986; Zbl 0609.68043)] who as we all know was very interested in symbolic computation. Thus LISP led to Mathematica. One of the big questions in my mind when I heard a lot of talk about cellular automata in the 1980s was: what problems can it actually solve? In that decade I was actively involved in computing actual fluid motions [e.g. see K. Gustafson (ed.) and J. Sethian (ed.), Vortex methods and vortex motion, SIAM (1991; Zbl 0748.76010), or K. Gustafson, Lectures on computational fluid dynamics, mathematical physics, and linear algebra, World-Scientific (1997; Zbl 0985.00008)]. I have been involved in computing for over forty years [e.g. see K. Gustafson, Parallel computing forty years ago, Math. and Computers in Simulation 51, 47–62 (1999)]. Suffice it to say, as far as cellular automata were concerned: I was waiting to be convinced.
The present book is a partial answer to my question. In my opinion, it may serve as a useful review of the attempts in the last fifteen years, 1986 to present, to apply cellular automata to simulate fluid dynamics. In the words of the authors: “The principal goal of this book is to carry two messages. The first is to show how an automaton universe with simple microscopic dynamics can exhibit macroscopic behavior in accordance with the phenomological description of classical physics. The second is to establish that the correlations of the lattice gas intrinsic fluctuations capture the essentials of actual fluctuations in real fluids.”
Of particular value could be the last chapter, Chapter 11: Guide to further reading, where the authors went to some effort to provide a considerable number of references and discussion of the relevant literature of the last fifteen years.