Reading this book is like going to an art gallery with a friend who is very learned. Ball presents a rich variety of patterns that exist in nature and the common principles that explain them, even when they appear in unrelated circumstances.
The Introduction sets the subject in context and shows the geometric designs in ancient architecture and in the natural world of the living and nonliving. Chapter 1 includes examples of bilateral symmetry exhibited by fish, mammals, insects, and birds. Snowflakes and honeycombs with hexagonal symmetry have long been admired, photographed, and studied. Sometimes patterns are obtained by breaking the symmetry. In chapter 2, fractals (hierarchical repetition of the same general form at decreasing scales) are illustrated with examples such as florets of broccoli, tree branches, and coastlines. Chapter 3 discusses logarithmic spirals, in which a cone rolls up, and Archimedean spirals, in which a rope rolls up. Spirals show up in chameleon tails, mollusk shells, and in swirling stars of galaxies. Flowing fluids often organize themselves into spiral vortices, with tornados being a dramatic example. Chapter 4 discusses patterns of flow and the emergence of chaotic behavior. Chapter 5 explains how wave patterns form, as in a plate sprinkled with sand and vibrated. Granules move away from vibrating places and fall onto nodal lines, where the plate is not vibrating, and form what is called a Chladni figure. Cracks due to electric discharge form a wavy pattern called Lichtenberg figures. Sand dunes show wave patterns.
Chapter 6 discusses bubbles and foams, where surface tension and pressure of the gas inside control the patterns to minimize the surface. Chapter 7 includes arrays and tilings, starting with wallpapers and flooring, and progresses to crystals and quasicrystals, which are five-sided and were once considered impossible. Chapter 8 covers how a pattern of cracks forms on dry mud, glazes, and paints on a coated surface. The top layer shrinks as it dries, while the bottom layer is still wet and swelling. As a result, there is a differential stress, released by forming a network of cracks with polygonal shapes. Chapter 9 explains the pattern of spots and stripes on animals, such as the zebra, using the reaction–diffusion model of Turing. In this model, ingredients called activators and inhibitors are present in cells. Depending on how they diffuse and react, chemical waves arise, and patterns are formed.
This book draws many examples from materials science: dendrite growth, crystallography, liquid crystals, quasicrystals, dielectrics, and naturally formed materials, which can inspire the creation of new materials and engineering designs. The book appeals to all scientists and to those who like to see art in science. There are 250 patterns in color pictures, juxtaposed thoughtfully, to bring out common themes. After you read this book, you will enjoy looking for patterns around you.
Reviewer: N. Balasubramanian is an independent research scholar and science writer working in Bangalore, India.
