The Algorithmic Beauty of Sea Shells / Edition 3

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Overview

The patterns on the shells of tropical sea snails are not only compellingly beautiful but also tell a tale of biological development. The decorative patterns are records of their own genesis, which follows laws like those of dune formation. Hans Meinhardt has analyzed the dynamical processes that form these patterns and retraced them faithfully in computer simulations. An accompanying diskette with the corresponding algorithms offers wide scope to those with a PC to try their hand at simulating and varying the patterns. The enlarged edition includes a new chapter showing that the models proposed for shell patterning can also account for other important processes in development. The formation of organizing regions and embryonic axes and the initiation of leaves serve as examples.

Mathematical models and advanced computer-generated images are used to explain and illustrate structural growth patterns of seashells in nature. This fascinating and beautifully illustrated book conveys the intuitive appeal and the "touch of magic" that accompany the current research. A diskette, packaged with the book, contains the algorithms and simulations necessary to replicate the results. 150 illustrations.

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Editorial Reviews

From the Publisher
Review of the 4th edition: It is a strikingly beautiful book, with more than a hundred color illustrations of patterns on mollusk shells, side by side with the computer simulations that reproduce them. This bestiary of pattern formation includes stripes (straight or produced by traveling waves), dots, drops, triangles, and meshwork combined in any imaginable way. It is truly remarkable that this diversity of patterns seems to have arisen in the absence of any selective pressure, as the animals that express them spend their lives buried in mud or sand. Thus, these patterns are in essence a manifestation of Nature at play. Meinhardt has a great knack for explaining pattern-forming mechanisms in a non-technical way. In the first few chapters of his book he introduces us to the basic elements of his model in accessible and vivid terms. He shows how local non-linear self-activation combined with a rapidly diffusible repressor (or limiting substrate) leads to the formation of dots and stripes from homogeneous initial conditions, a phenomenon first described by Turing in 1952 as diffusion-driven instability. He then goes on to explain how oscillating patterns and traveling waves can be produced by the same basic model with different decay and diffusion rates. Here, the author and the book are at their best. Johannes Jaeger in: Bioessays 32: 638–640, 2010 WILEY Periodicals, Inc., DOI 10.1002/bies.201000031 From the reviews of the third edition:

This is a serious volume on the mathematical modeling of sea shell patterns. … This volume takes a rigorous approach, progressing systematically … . It would make a great text for either a course at the upper undergraduate or graduate level in mathematics or biology designed around it. It would also be a good supplemental text for a course in dynamical systems, differential equations … . It has left me with a new appreciation, wonder and curiosity about the myriad patterns on shells … ." (Amy Shell-Gellasch, MAA online, January, 2005)

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Product Details

  • ISBN-13: 9783540440109
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 2/28/2003
  • Series: Virtual Laboratory Series
  • Edition description: 3rd ed.
  • Edition number: 3
  • Pages: 236
  • Product dimensions: 8.50 (w) x 10.34 (h) x 0.74 (d)

Table of Contents

1 Shell patterns as dynamic systems 1
2 Pattern formation 19
3 Oscillations and travelling waves 41
4 Superposition of stable and periodic patterns 53
5 Meshwork of oblique lines and staggered dots 71
6 Branch initiation by global control 91
7 The big problem: two or more time-dependent patterns 103
8 Triangles 127
9 Parallel lines with tongues 143
10 Shell models in three dimensions 163
11 The computer program 183
12 Pattern formation in the development of higher organisms 197
References 227
Index 233
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