New Visions on Form and Growth

Abstract

It is now nearly 90 years since the publication of D'Arcy Thompson's book On Growth and Form, a classic work that attempted a unification of pattern-forming phenomena in systems ranging from inanimate to living matter. Thompson's book came early in the development of mathematical techniques in biology. His work has had enormous influence in succeeding decades and has helped inspire the rapid growth in the application of theoretical techniques to biological phenomena. Pelce's book New Visions on Form and Growth takes its inspiration and title directly from D'Arcy Thompson. Furthermore, Pelce attempts what could not be achieved in D'Arcy Thompson's time, namely the presentation of a quantitative analysis of pattern forming phenomena. However, it should be emphasised that the vast majority of this book is concerned with inanimate matter, with rather little discussion of biology. The book begins with a presentation of the basic physics, including surface tension, first-order phase transition kinetics and a brief outline of chemical kinetics. With the essential physics established, Pelce then investigates simple growth forms, before showing how these regular geometries are destabilized into more complex forms by instabilities. The problem of velocity selection of growing patterns is then extensively discussed, before the question of (secondary) instabilities of the more complex growth forms is analysed. A chapter on stochastic patterns is also included. For the most part, the book concentrates on a few intensively studied pattern forming systems in physics, particularly viscous fingering in Hele–Shaw cells, the growth of dendrites, electrodeposition, flames, and, in the chapter on stochastic patterns, diffusion-limited aggregation. Only in a rather brief final chapter is a more speculative link made with biological pattern formation and morphogenesis. In general, I found the book to be a useful reference work on the theory of pattern forming systems. However, the presentation is quite advanced, at the level of a graduate text, and newcomers to the field may in places have difficulty following the arguments. For example, the subtle topic of the renormalization group is rather abruptly introduced in the discussion of interface structures. Furthermore, the presentation is not helped by some typographical errors in the equations. Curiously for a book on pattern formation, there is rather little discussion of reaction–diffusion systems, or of Turing-type instabilities. I also found the discussion of biological systems in the final chapter to be too brief and speculative to be really useful. This subject is vast and it would have been worthwhile to attempt a more comprehensive review of pattern formation in biology to link it more concretely with the simpler and better understood pattern-forming systems in physics. Nevertheless, Pelce's book is worthwhile and forms a useful addition to the literature on pattern formation in physics and biology.