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 or the spread of a flu epidemic. Hans Meinhardt has analyzed the dynamical processes that form these patterns and retraced them faithfully in computer simulations. His book is exciting not only for the astonishing scientific knowledge it reveals but also for its fascinating pictures.
Many of the simulations are supplied on the accompanying CD-ROM in HTML format. Thus, the highly dynamic behavior of the interactions on which shell patterning is based can be inspected like conventional websites with any browser, also on a Macintosh or Linux system. The animations are given as separate files that also can be integrated, e.g., into a PowerPoint presentation if desired. Also included are animated simulations of models that describe more general problems in the development of higher organisms, e.g., formation of organizing regions, pattern formation in hydra, gene activation, formation of net-like structures, and chemotactic orientation.
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.
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.
Hans Meinhardt
algorithms artificial life biology computer graphics computer simulation dynamic processes growth processes natural phenomena simulation visualization
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)