How nature keeps in shape

Since reading this book I have looked with renewed interest at the patterns around me. It has brought new life to the froth of my beer, the waves on the rough seas of Dorset's coast over the Christmas holiday, or even the patterns as I stir a cup of coffee at different speeds. In fact, my family have become quite tired of my constant recognising of the numerous natural patterns that surround our everyday life.

We tend to regard a pattern as a regular array of identical units, such as in a carpet or mosaic tiling. But this masterful analysis of pattern covers a much broader spectrum of units that are similar, but not necessarily identical, such as the pattern of dots on the pelt of a jaguar or the ripples in the sand on a beach. Because of the irregularity in these patterns, they are harder to quantify or define mathematically, but they are still patterns that our brains immediately recognise.

Philip Ball focuses on the most common, everyday patterns, from the way bees build hexagonal honeycombs with exact precision to the physics of bubble formation through the effect of surfactants. His two main heroes, who have contributed greatly to the theory behind patterns, feature prominently. The first is the well-known zoologist of the early part of this century, D'Arcy Wentworth Thompson, who introduced an engineer's approach to biology. The second is the code-breaking mathematician Alan Turing, whose work underpins much of the present-day research into artificial intelligence. Turing's 1952 paper, "The chemical basis of morphogenesis", is repeatedly referred to by Ball. Its central question concerns symmetry breaking in cell division leading to the development of particular organs: what breaks the symmetry of the embryo?

The chapter on waves is not about the ocean, but about Russian biochemist Boris Pavlovitch Belousov's oscillating chemical reactions, in which a chemical mixture keeps changing colour from clear to yellow and back again at regular intervals instead of reaching equilibrium; the chemistry of bands now fossilised in rocks; the pulses of the human heartbeat; and the migration of progressive waves spreading out in a bacterial colony. In the chapter on bodies, where Turing and morphogenesis are introduced, we read about the zebra's stripes and the remarkably few factors that control an infinite variety of patterns on the wings of butterflies. We are also introduced to the Fibonacci sequence, illustrated by photographs of a pine cone and a sunflower.

The next chapter, on "Breakdowns" - the way in which objects break - brought back childhood memories of the results of cricket balls hitting the windows of my mother's house. In addition to shattered glass, the cracks in mud as a lake-bottom dries up or even the larger fractures in the earth's crust along the San Andreas fault are covered. I was fascinated by the section on river channels and how the flow creates a mosaic of islands.

The author is equally interesting in showing how liquids that flow slowly can take a smooth featureless course, but as velocity increases, a progressive series of patterns emerges until this breaks down into the chaos of turbulence. Jupiter's great red spot is analysed in terms of its flow and what maintains its stability. A chapter on grains shows how they are part-time solids and part-time fluids. The homes built on sand in Santa Cruz, California were destroyed in an earthquake because of the liquefaction of the sand, which flowed like treacle. Avalanches are explained in simple terms, such as tipping up a sugar bowl. The "Brazil nut effect" is the way in which larger grains, say nuts in a packet of muesli, progressively rise to the top when the packet is shaken. I could not help wondering if a similar effect is in operation in my garden where, however many stones I remove, more always seem to come to the surface!

The penultimate chapter is on communities. This ranges from the oscillation of populations of animals in nature to the patterns of development in man-made cities. The oscillation between predators and prey is illustrated by examples from lynxes and hares and from host-parasitoid interactions. The Lotka-Volterra equations show that the mathematics of predator-prey interactions, which either reach a steady state or more commonly, vary periodically with the predator cycles lagging behind those of the prey. The clustering and patchy distribution of organisms are discussed and then applied to conservation theory. Some ecosystems need space to spread out so that they can organise themselves into patchy communities that can coexist with predators or pathogens.

Throughout, there is a splendid mixture of biological and physical patterns, natural and man-made. The chapter on branches, for instance, ranges from the bronchial/arterial structure of lumps to the branching of trees. Perhaps the most fascinating of all branching patterns is found in the infinite variety of snowflakes with, nevertheless, their symmetrical, hexagonal branching pattern. But I was surprised to find no reference to tree architecture and the work of Francis Halle and Rolf Oldeman or the classification of leaf vein types by Leo Hicky. Still, with such a broad range of topics from so many disciplines, the author can hardly be faulted for missing a few references.

The Self-Made Tapestry is a scholarly interdisciplinary mixture of biology, chemistry, physics and mathematics that seeks to explain patterns, where possible in equations. The complex topics are conveyed in a relatively simple manner and I found myself able to understand many parts that are far from my field of botany.

But at times the book does become hard to understand - not because of any failure by the author, but because of the sheer complexity and magnitude of the subject that he is covering. I guarantee that anyone who reads this book will be constantly looking for patterns and will possess a better knowledge of their causes.

In addition, there is an abundance of excellent photographs and drawings (including 24 fine colour plates) that are a pleasure to study. And for the experimenter and teacher, there are seven appendices that give instructions on how to create various chemical and physical patterns, varying from experiments with soap bubbles to observations of the stratification of different-sized grains in a Makse cell.

In my view, the author has achieved the goal stated in his preface: to create "the kind of excitement that I now feel when I observe the lace-work of the sky or the outrageous designs of a butterfly's wings". Nature is, indeed, a most wonderful self-made tapestry.

Sir Ghillean Prance is director, Royal Botanic Gardens, Kew.