New Visions on Form and Growth: Fingering Growth, Dendrites, and Flames, P. Pelcé. Oxford University Press (2004). 387 pp., ISBN: 0 19 852701 3 (original) (raw)

The book is about growth patterns and in particular about the formation of branching growth patterns in the natural world. In the book branching patterns from the abiotic world like viscous fingering are discussed, these growth patterns are for example formed in experiments where air displaces a viscous fluid and where a ''fingering'' shape emerges. Other examples from the inanimate world are electro-chemical deposits formed at electrodes, electric discharge patterns, crystal formation and flames. The biological examples mentioned by Pelcé in the book are algae, filamentous fungi and neurons. The main idea presented in the book is that we can explain a certain class of growth patterns from physics and biology using the same mathematical laws. The idea that we can find in the abiotic world analogies of growth patterns in biology, has a remarkable history. The analogy between electric discharge patterns and biological growth patterns was also made by the Scottish anatomist J. Bell Pettigrew in the illustrated volume ''Design in Nature'' (1908) [2]. Pettigrew was an anatomist who was interested in the relationships between physical and biological growth forms. In Pettigrew's book examples are presented of branched structures, including electric discharge patterns and the branching growth form of the red coral (Corallium rubrum), to illustrate the similarities in the underlying design of physical and biological objects. Quite remarkably, Pettigrew's search for underlying physical mechanisms for explaining growth patterns in nature was driven by religious and anti-Darwinistic motivations. The idea that we can find in the abiotic world analogies of growths patterns in the living world has become famous by D'Arcy Thompson's book ''On Growth and Form'' (1917) [3]. Chapter 1 starts with the typical growth patterns from physics, which will be discussed later on in great detail in the book, like viscous fingering, crystal formation, flames and electrochemical deposition. The examples are followed by a general introduction into mass conservation, the first and the second law of thermodynamics and self-similarity of growth patterns. The role of fluctuations is discussed in pattern formation. A famous example here is the [5] model for diffusion-limited aggregation. Fluctuations, due to the irregular shape of the interface, have become so large in this example that it is no longer possible to describe the growth process by the dynamics of a continuous medium and a microscopic rule is required to model the growth of an aggregate by the attachment of particles under diffusion-limited conditions. Chapters 2-4 discuss the basic physics and chemistry of viscous fingering, formation of crys

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