Richard J. Gaylord

The following review appeared in SIGSAM Bull. 30/3 (1996) 24

Modeling Nature with Cellular Automata using Mathematica
by Richard Gaylord and Kazume Nishidate

publisher: Springer-Verlag (TELOS)
ISBN 0-387-94620-9
Reviewed by: Chris Adami (California Institute of Technology)

This new book by Gaylord and Nishidate is the third by Gaylord on Mathematica applications, and the second on applications in the physical sciences. In this one, the authors focus exclusively on the Cellular Automata (CA) approach for modeling complex physical phenomena. For those not immediately familiar with the approach, CA's approximate the interaction of agents (which could be anything, from molecules to bacteria, ants, and cars) by assigning a
finite number of states to each agent, and specifying rules which dictate the next state of the agent as a function of its own state and the states of its immediate nearest neighbors. Then, the time evolution of the system is deterministic after specifying the initial state of each agent. As such, the approach is extremely general, and can in general approximate any macroscopic behavior of a collection of agents that is otherwise described by differential equations. The advantage of the approach becomes apparent when modeling phenomena that become laborious to describe via the differential equation approach, especially when very many agents are concerned, and the interactions are not simple. The most famous example of a CA is the celebrated "Game of Life", which
displays complex emerging behavior that would be extremely hard to describe analytically, even though this must of course be possible in principle. This example fittingly constitutes the first application of the book. In general, the authors concede, Mathematica may not be the best medium to code CA's, simply because of the speed and memory limitations. However, the ease with which very specific problems can be addressed with a minimum of coding and a maximum return in results, shows that the authors had the right intuition. The routines presented here, and the general philosophy displayed by the authors in their attack on problems, could spark a minor revolution in the way scientists tackle the physics of complex phenomena. Most of the examples presented would generally fall into the area of computational physics, with a few applications in what may be termed "Simulation Science", e.g. the simulation of traffic flow or the (social or non-social) interactions of agents in an abstract economy. Whether it is
Simulation Science or Computational Physics, these branches are result-driven, and as a consequence require the writing of code that is robust, testable, and reliable. In the past and present, this requires a considerable amount of work. What struck me most going over the examples of phase ordering, solidification of crystals, interaction of random walkers, percolation, and many more, was the ease with which the specifics of these two-dimensional physical problems could be translated into rules which
allow for a qualitative analysis of the emergent phenomena, with only minimal programming on top of the CA structures which have been programmed in a general manner already. Note that this does not mean that progress is for free when using the tools of this book. In order to understand the macroscopic aspects of a physical phenomenon, the microscopic interactions of the agents have to be understood as well as possible. This requires a good understand-
ing of the physics that goes on at this level. Scientific thinking, intuition, and the proper planning of experiments including controls, the replication of known results, cross-checking, etc., are still required in order to produce convincing evidence for a hypothesis. It is not these elements that are cut-short by the tools of this book. It is the time between the idea and the implementation of it that is cut drastically. It does not replace ideas. Having said this, I must point out a few caveats associated with the authors approach. One is immediately obvious, and is not denied by the authors. Due to the overhead associated with Mathematica, one cannot hope to use these tools to treat large, or even medium-large problems, with the size always given by the number of agents. While the routines are written for arbitrary lattice sizes, the authors rarely use lattices larger than 100xl00. The other caveat must be issued over the philosophical slant of the authors, who imply that simulation, or computation, is at least equivalent to the formulation of physical laws in terms of equations, and argue for a change in paradigm in the computational sciences. I am not particularly overwhelmed by these thoughts. I personally believe that computation and measurement are, conceptually, one and the same, and therefore it does not appear as a miracle that everything that can be measured can be computed. However, it is entirely possible (as suggested by the laws of quantum mechanics, for example) that not everything that can be described by equations can in fact be measured, or computed. Thus, I think the demise of the rule of equations is not to be expected anytime. Let me now veer to what I believe is the expected audience for this book. Those that will benefit most from it will be people actively involved in research concerned with complex phenomena, whether in academia or industry. Similarly, it could be used with much value as a teaching tool, even though this book is not a textbook, as it does not go in-depth into the physical foundations of the processes being modeled. This is, by the authors' own admission, due to their lack of expertise, which is understandable as the book covers a wide variety of subjects. It would be interesting to see textbooks on specific complex phenomena, such as percolation or diffusion-limited accretion etc., solely relying on these methods as far as the computational aspect is concerned. But such a book would require an equal amount of theory to counterbalance the computations. Unlike the authors, I believe that the computational experiments outlined here are worthless without equations that ought to describe them. This of course does not mean that this book is worthless, as the authors mostly describe experiments for which there is well-established theory. I have very little doubt that the tools introduced here will seep into the research community, even though the speed is not predictable. Researchers change their habits only slowly, but the gain inherent in using the methods of this book may overcome this after all. In the end, however, it will be the younger generation of physicist, biologists, and maybe even chemists and engineers, that will use this approach most. In the end, what surprised me the most about this book is how many things can be done, with so little investment of time. In fact, I am somewhat surprised (jaded by the amount of secrecy that is prevalent in many areas of research) how freely the authors give away tools that even undergraduates can use to obtain publishable answers to modern questions rather rapidly. Usually, such tools are made available only after the easy things have been done and published. This is the case for some of the applications, but some others are simply left for grabs. And for anyone doubting the seriousness of the research that can be done, a paper with results from Chapter 7 (Random Walkers) by the authors recently appeared in Physical Review Letters, the premier journal of the physics community. My advice to people interested in the simulation and characterization of emergent phenomena in complex systems, especially those that can be described by the interaction of agents in two, and even three dimensions, is to take a look at this book, go through the ample examples and exercises provided, then
code their ideas and start writing their paper!… (mehr)