If you haven't heard of Philip Ball before, it's about time you did. Ball (who majored in chemistry at Oxford University and received his Ph.D. in physics from Bristol University) is emerging as one of the best of the science writers specializing in presenting scientific material to the general, as well as the scientifically literate, public. His first book, Designing the Molecular World: Chemistry at the Frontier (1994), and his second book, Made to Measure: New Materials for the 21st Century (1997), are wonderful presentations of the exciting new developments in our field of chemistry. They are written in a lucid style by an author who is not afraid to (successfully) tackle the task of explaining difficult concepts. Topics such as molecular and crystal structures, chemical reactions, laser chemistry, organic conductors, biochemistry, atmospheric chemistry, and the rapidly progressing field of materials science (e.g., photonics, information storage, biomaterials, polymers) are discussed from first principles to current developments, with many references to both the primary and secondary literature. For the readers of this Journal, who have strong chemistry backgrounds, each of the chapters in these two books can be read independently.

However, in spite of the excellent writing, profuse and illustrative diagrams and photographs, and intelligent selection of timely topics, these books do not compare with the tour de force presented by Philip Ball in his latest book, The Self-Made Tapestry: Pattern Formation in Nature. This book, an expanded version of Chapter 9 of Designing the Molecular World, is best read as a coherent unit from beginning to end. It describes the formation of the many naturally occurring patterns, from the spots on a leopard to the ripples on sand dunes to the spirals found in oscillating chemical reactions. Pattern formation in chemistry, biology, physics, mathematics, geology, cosmology, urban planning, atmospheric dynamics, and mineralogy are but some of the areas covered by the author, who shows us how similar patterns arising in different circumstances are interrelated.

We can ask "Where does the pattern come from? Is it built into the system? How can the symmetry of the effect differ from that of the cause? Why are some patterns universal?" The main thesis of this book is that the formation of patterns is due to the operation of basic scientific principles, but the answers to these questions arise only partly from the derivation of the mathematical equations that describe the interaction of the variables in the system. Of equal importance is the ability to solve these equations. Since many of them are intractable, it is only recently, with the availability of supercomputers, that reasonable solutions have been produced. In many cases involving complex systems, the older theoretical work is best understood in light of modern computational analyses. The results reported by a phalanx of scientists covering an amazing range of subjects have been mastered by Ball and formed into a coherent whole. His elucidation of these generalizations from the myriad of individual units of research is quite spectacular, even if one wishes to quibble over some aspect or other.

In his efforts to demonstrate the universality of pattern formation, Ball has organized the book by the type of pattern that is formed. The general principles governing the development of a particular pattern are described and followed by many examples, often presented in great detail, from a wide range of disciplines. In this way we are shown that the same underlying physical principles are responsible for similar patterns in apparently disparate fields.

The introductory chapter, Patterns, discusses two main topics. First, D'Arcy Thompson's 1917 thesis that biology cannot afford to neglect physics, so that much of Darwinian natural selection can be explained in terms of applied basic physics (e.g., the effect of mechanical forces). Second, symmetry breaking--a uniform, fully symmetrical gaseous system consists of randomly disordered individual molecules whose average features are symmetrical; that is, they show no patterns. The most highly symmetrical systems are also the most featureless, and patterns form when the high symmetry engendered by randomness is reduced. Symmetry breaking is responsible for the formation of patterns!

The chapter on Bubbles explains how three-dimensional soap bubbles, froths, honeycombs, geodesic domes, cell-packing, and space-filling models, as well as two-dimensional surfactant films and layered silicas, all form under the same set of rules: the need to form a minimal surface.

In the next chapter we find that the crucial characteristic of a Wave is that the elements of the pattern--its symmetry, its length scale, its rhythms--are set "not by an external agency but by the internal dynamics of the system." Oscillating chemical reactions of many types are described in terms of the autocatalysis that occurs. The BZ reaction, reactions in catalytic converters, Liesegang bands, patterns in rocks, heart rhythms, and microbial chemoattractant reactions are all described.

In one of the most fascinating chapters in the book, Bodies, we learn that Alan Turing (of computer fame) published a paper in 1952 describing a hypothetical chemical reaction that could generate spontaneous symmetry breaking, leading to stable spatial patterns (Turing patterns), in an initially uniform mixture of compounds. The paper, entitled "The Chemical Basis of Morphogenesis", is one of the more influential papers in theoretical biology. This phenomenon, which is no longer hypothetical, is currently explained as being due to a competition between activation by compound A and inhibition by compound B, where B diffuses more rapidly than A, thus differentiating between global and local reactions. These activator-inhibitor systems are responsible for the formation of patterns on animal pelts, seashells, and butterfly wings and in various chemical reactions.

In the chapter on Branches we find detailed descriptions of dendritic growth of crystals, formation of snowflakes, tree-branch growth, and bacterial colony formation presented in terms of diffusion-limited aggregation (DLA) and fractal geometry. DLA describes systems in which the "rate of growth is governed by the rate of diffusion of particles. It differs from the way regular, faceted crystals grow, in that there is no opportunity for the impinging particles to rearrange themselves so that they pack together most efficiently. Since this takes place at the surface of the growing crystal, it soon becomes jagged and disorderly."

The details of the final shape are a function of the kinetics of crystal growth, where the branched clusters are nonequilibrium structures. The fractal dimension is a measure of how densely packed the branches are and is a property that is precise, reproducible, and characteristic of the apparently irregular, branched objects. We also learn that the algorithms used to describe the shape of a tree are much more complex than one would imagine; several examples are described.

In Breakdowns, which in some ways is a continuation of the previous chapter, glass fracture, electrical discharges, earthquake-induced crustal fractures, and landscape evolution are analyzed in terms of fractal geometry. The pattern developed as a river forms from its converging streams is described best by a fractal scaling law that is characteristic of most branched networks including cracks and DLA clusters.

In the discussion of Fluids we find that smooth flow, patterned flow, and turbulence are described by several basic theories covering flow through a pipe, convection in Earth's mantle, shapes of clouds, and interactions of fluids of various viscosities and compositions. We learn that even chaotically turbulent flows have some general discernible patterns.

The section on Grains teaches us that sand dunes, grain elevators, landslides, and avalanches all have something in common with the gas-liquid critical point. Specifically, density fluctuations lead into the phenomenon of self-organized criticality (SOC). "The addition of even a single grain to a sand pile can induce a landslide of any magnitude. This scale-invariant behavior is characteristic of turbulent flows as well and indicates that the sand pile is constantly seeking the least stable state. States like these, which are susceptible to fluctuations on all scales at the slightest provocation, are called critical states. Every liquid achieves a critical state at a well-defined temperature and pressure, called the critical point. A fluid, at its critical point, undergoes density fluctuations on all length scales and is unstable to even the slightest disturbance. Sand piles, unlike fluids, seem to seek a return to the critical state." This phenomenon has been termed SOC, reflecting the fact that the critical state seems to organize itself into this unstable configuration. This concept of SOC has been applied in many fields.

In Communities the patterns of ecocycles, population growth, game theory, and urban spread are modeled using the principles described above--oscillations, autocatalysis, self-organization, activation-inhibitor interactions, fractal dendritic growth, and computer modeling.

As mentioned earlier, the author has assembled and assimilated an amazing amount of information from an astonishingly large number of research areas. He presents these in a carefully planned sequence of chapters, in such a way that maximum benefit will be obtained if the book is read from beginning to end. Then when you think you have learned all there is to know about pattern formation in nature, the last chapter, Principles, recasts everything in terms of a beautiful discussion of irreversible thermodynamics. Pattern formation, which is the point at which a nonequilibrium system is driven across a particular threshold, is the result of competing forces, symmetry breaking, formation of dissipative structures, phase-space attractors, instabilities, scale invariance, bifurcations, and higher-order phase transitions. The experimental and computational results of these analyses all contribute to our understanding of how patterns form in nature, even if we have not yet reached the level of understanding why a particular pattern develops. It is worth reading the whole book just to be able to understand and appreciate this final chapter. (If you find, when you are finished reading it, that you are motivated to study the subject in more detail, you might start with An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos, by I. R. Epstein and J. A. Pojman, 1998, also published by Oxford University Press and reviewed by Field in this issue of J. Chem. Educ. Or, you can look at the use of Mathematica in studying oscillations, complexity, and chaos in chemical kinetics in this Journal : J. Chem. Educ. 1999, 76, 861, and references cited therein.)

After his presentation of the principles guiding the natural formation of patterns, Ball concludes "I believe it is one of the principal messages of this book that we can map many of nature's tapestries onto some universal blueprint, in which specifics cease to matter."

As in his other books, there are many and excellent photographs and diagrams, a section of beautiful color plates, and references to the primary and secondary literature. Finally, there are detailed instructions in the appendix for preparing and studying seven different experiments that demonstrate the material described in the text.

This book, with its many broad generalizations accompanied by detailed examples, is well worth the time and effort it takes to read it. It should be available to everyone teaching in the sciences. The author, who was a senior editor for Nature for 11 years, is now a consulting editor for them and devotes his time to free-lance writing.

His next book, due out in the spring of 2000, is titled H₂O: A Biography of Water.