Book Review: Modeling Nature with Cellular Automata using Mathenmtica by Richard Gaylord and Kazume Nishidate

Abstract

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.