Previous generations knew two ways of doing science: theory and experiment. On the one hand, theoreticians constructed symbolic representations of their domain, and manipulated them with rules of inference to derive consequences that were logically compelling (at least, within their own research community). Pride of place in theoretical studies went to those fields where “symbolic” meant “mathematical,” and where the rules of inference constituted mathematical proofs. Other forms of representation and reasoning also supported theoretical research, for example structural models in sociology. On the other hand, experimentalists queried nature directly, by manipulating the realia of their domain, and observing the consequences. Their sophistication lay, not in proving theorems, but in designing experiments that would force nature to answer the question posed to her, and in statistical analysis that could distinguish real effects from random variation.

One of the most powerful contributions of computers has been to introduce a third form of science, simulation. This is the common thread throughout the books discussed in this review.

Like theory, simulation manipulates a representation of nature, rather than nature itself. Like experiment, simulation obtains its results by observation, rather than derivation, and its discipline lies in experimental design and statistical analysis, rather than in formal inferences. Within the simulation community, two basic approaches dominate. Each is pulled toward one or the other of the older forms of science, depending on the representations that they manipulate.

Equation-based modeling begins with equations, often the same equations that a theoretician would like to manipulate. Typically, these are differential or difference equations, which describe the evolution of the system through time. A frustration of theoreticians has long been that differential equations simple enough to solve analytically omit many details of the real world that one would like to study. Equation-based modeling handles these complexities by integrating the equations numerically, to observe their evolution through time.

Entity-based modeling begins with individual software entities (agents, in the most sophisticated approaches) that correspond to entities in the physical world. These entities are endowed with behaviors that reflect the behavior of the real entities, and are then turned loose to interact with one another (and, sometimes, with a shared environment).

Simplistically, one might say that an equation-based modeler is a theoretician who uses the computer to overcome difficulties in analytic derivations, while an entity-based modeler is an experimentalist who uses the computer to perform experiments on entities whose manipulation would otherwise be difficult or unethical. Equation-based modeling is sometimes called “top-down,” because researchers find it natural to explore the evolution of aggregate, system-level characteristics (such as population l evels, or average weight), while entity-based models focus on individual members, and are naturally applied “bottom-up,” to understand the behavior of the system as a whole.

Three of the volumes reviewed here describe scientific results obtained largely through both varieties of simulation and modeling, while the fourth (Colella et al.) focuses on entity-based modeling technology, independent of the domain.

The three volumes of results span a wide range of domains. Ball focuses mostly on non-biological systems, such as fluid motion, crack formation, river branching, and granular separation. Camazine et al. deal mostly with insect societies, while Lomi and Larsen study human social structures. In spite of this broad coverage, all three use very much the same kinds of modeling and simulation tools, and expound on similar processes at work in all three domains. Camazine et al. hint at this universality by including chapters on organisms both simpler (slime molds and bacteria) and more complex (fish) than insects. Ball devotes two chapters to reaching beyond non-biological systems. One chapter discusses the development of a differentiated living body from a single fertilized cell, while another studies community structures and city formation. All three volumes use both equation-based and entity-based modeling.

Ball

Each chapter in Ball’s book discusses a single kind of phenomenon, and studies its appearance in a variety of different systems. He offers chapters on bubbles (which range from honeycombs to beer foam and soap bubbles), waves, branches, breakdowns, fluid motion, and granular dynamics, in addition to excursions into embryogenesis and city growth. The opening chapter highlights an ongoing debate regarding whether evolutionary dynamics or natural law is the source of patterns (does the spiral of a mountain goat’s horn result from survival of the fittest, or from physical and chemical constraints?), while the concluding chapter summarizes common principles of pattern formation (including symmetry breaking, dissipative structures, power laws and scaling phenomena, and competing forces). Each of the chapters that is focused on a single type of pattern explores a variety of explanations that have been offered, and reports results from all three types of science. Ball is the least technical of the three volumes, and gives few details on the models, but appendices do describe simple experiments (with real-world items!) that readers can use to explore the phenomena.

Camazine et al.

Camazine et al. organize their work into three parts. The seven chapters in Part 1 define self-organization, explain the basic principles that make it work (which overlap extensively with those in Ball’s concluding chapter), and develop a methodology for studying self-organization in biology. Camazine et al. distinguish three classes of models: differential equations, cellular automata, and Monte Carlo. By a Monte Carlo model, they mean an entity-based model, in which the behaviors of entities are selected stochastically rather than by more complicated reasoning (a form of model that other authors sometimes call microsimulation).

Each of the 13 chapters in Part 2 of Camazine et al. deals with a specific kind of organism and functionality. For example, three chapters are devoted to ants: one to trail formation, one to swarming raids, and one to wall building. A final chapter outlines common lessons. Each chapter in Part 2 also offers several different models, often of different forms, in addition to reporting experimental results. Eight chapters offer differential equation models of the phenomena they describe, two offer cellular automata models, and eight offer Monte Carlo models. Chapter 16, on comb patterns in honeybee colonies, includes all three kinds of model. This technique of studying a single phenomenon with different types of models is a crucial discipline for simulation science, since it enables the researcher to distinguish between artifacts of an individual modeling technology, and persistent characteristics of the system under study. Though the book has six editors, and some chapters are clearly focused on the interest of one or another editor, the work is well integrated, and bears only a few signs of its composite origin. The treatment is more technical than that of Ball, discussing the structure of models in sufficient detail to enable readers to reconstruct them.

Lomi and Larson

Lomi and Larson offer a more conventional collection of individually authored and attributed studies. Their lengthy introduction shows that their focus is on the contribution of computer modeling to sociological methodology, rather than to specific phenomena studied by simulation and other methods; they organize their 14 papers in terms of their contribution to sociology, namely into three parts: “Rediscovering Problems,” “Framing Arguments,” and “Taking Views.” The subtle distinctions among these aspects of research method, and their correlation with the papers grouped under each heading, will be more evident to some readers than to others). The topics analyzed include organizational culture, the relation between organizational structure and corporate learning, how status competition affects group performance, diffusion of innovation, and how products diversify in an industry, among others. All but two of these studies use entity-based modeling.

Colella et al.

The growth of computer simulation has been fueled by the increased availability of software that provides the basic framework within which models may be constructed. Colella and her colleagues provide an engaging introduction to one of the most accessible of these tools, StarLogo. StarLogo is a descendant of the Logo programming language, a simplified dialect of Lisp that was developed mainly as a tool to teach programming to pre-college students. Logo programs control a graphic “turtle,” a small shape that moves over, and interacts with, a grid of ̶ 0;places.” The main innovation of StarLogo is support for multiple concurrently executing turtles. Colella’s book is clearly aimed at the education market. Successive “Challenge” chapters introduce different features of the language, by way of programming projects of increasing complexity. At first, students are invited to modify programs that are included, along with the StarLogo software, on a CD included with the book. The book is more than a programming manual, however; it is a lucid exposition of the whole agenda of building computational models. An “Adventure” chapter, preceding each “Challenge” chapter, describes a human role-playing experiment, and the following challenge is concerned with constructing a computerized model of the behavior that students observe in the human experiment.

StarLogo, and a close dialect, NetLogo, unlike Logo, have proven useful beyond the classroom as modeling tools for serious researchers. In particular, Camazine has assembled a collection of StarLogo models that illustrate many of the mechanisms in the book. The URL advertised in the book did not seem to be active, but the models are available at http://www.scottcamazine.com.

These four volumes provide an excellent introduction to the new science of computer simulation, and along the way provide glimpses of underlying common processes that generate the high-level behavior of systems of interacting parts, whether those parts be molecules, bacteria, insects, birds and fish, or humans. The rise of simulation science, and in particular entity-based modeling, has disclosed profound similarities among these very different domains of study, and these volumes form an excellent introductory library to begin their exploration.