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The Algorithmic Beauty of Sea Shells

  • Book
  • © 2003

Overview

Authors:
  1. Hans Meinhardt

    1. Max-Planck-Institut for Developmental Biology, Tübingen, Germany

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  • A fascinating reconstruction of the processes forming the patterns on the shells of tropical sea snails.
  • The corresponding algorithms are described in detail.
  • An accompanying CD-ROM gives all the algorithms for simulating the natural pattern formation and growth processes on a PC.

Part of the book series: The Virtual Laboratory (VIRTUAL LAB.)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. Shell patterns — a natural picture book to study dynamic systems and biological pattern formation

    • Hans Meinhardt
    Pages 1-18

  3. Pattern formation by local self-enhancement and long range inhibition

    • Hans Meinhardt
    Pages 19-40

  4. Oscillations and travelling waves

    • Hans Meinhardt
    Pages 41-52

  5. Superposition of stable and periodic patterns

    • Hans Meinhardt
    Pages 53-70

  6. Crossings, meshwork of oblique lines and staggered dots: the combined action of two antagonists

    • Hans Meinhardt
    Pages 71-90

  7. Branch initiation by global control

    • Hans Meinhardt
    Pages 91-102

  8. The big problem: two or more time-dependent patterns that cause interference

    • Hans Meinhardt
    Pages 103-126

  9. Triangles

    • Hans Meinhardt
    Pages 127-142

  10. Parallel lines with tongues

    • Hans Meinhardt
    Pages 143-162

  11. Shell models in three dimensions

    • Przemyslaw Prusinkiewicz, Deborah R. Fowler
    Pages 163-182

  12. The computer program

    • Hans Meinhardt
    Pages 183-196

  13. Appendix: Pattern formation in the development of higher organisms

    • Hans Meinhardt
    Pages 197-225

  14. Back Matter

    Pages 227-236
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Keywords

About this book

As mentioned repetitively in the book, the models describing shell patterning are only special applications of a mechanism developed to account for biological pattern formation in general. To illustrate the dose connection) a new chapter ­ originally written for the first German edition - has been added that provides a survey of these general models. Discussed is, for instance, how an embryo can obtain its primary axes, how gene activation can proceed under the influence of such signals in a position-dependent manner, how complex netlike structures such as the vein of leaves can be generated and how legs and wings are initiated during development at precise positions. Other sections of this chapter deal with phenomena at which the intimate connection to the mechanisms worked out for shell patterning are especially obvious. The utilization of travelling waves in blood coagulation, in the conduction of nerve pulses and in the chemotactic orientation of cells are examples. Closeparallels between a shell pattern and phyllotaxis suggest an alternative view of how the helical arrangement of leaves is achieved. Using the shell patterns as a natural exercise book, the computer program supplied with the first edition has been used in the meantime at several universities to teach students in basic properties of dynamic systems. I have been frequently asked to make the programs for general pattern formation available. The programs for the above mentioned models have been added to the accompanying diskette.

Reviews

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)

Authors and Affiliations

  • Max-Planck-Institut for Developmental Biology, Tübingen, Germany

    Hans Meinhardt

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