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No. 101: Sep-Oct 1995

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The algorithmic beauty of seashells

Most will admit that many seashells are pretty, but how did all those colors and geometrical markings arise? Perhaps a more profound question is: Why do sea-shells need to be pretty in the first place? After all, most (but not all) of the shell owners do not have eyes with which to appreciate their handiwork! However, mathematicians and computer modellers do have eyes. They have also had a lot of fun and some success in devising algorithms (mathematical methods) for the generation of seashell markings. In fact, our title above is also the title of a new book by H. Meinhardt, which suggests how a suite of simple biochemical processes can create those shells coveted by collectors.

Meinhardt has devised equations that describe chemical factors that turn pigment-generating cells on and off. In its simplest form, a mathematically modelled seashell is a two-dimensional sheet that grows along only one edge. Cells on this edge may or may not secrete pigment depending upon chemical "influences." B. Hayes describes how this sort of model operates:
Triangular pattern on Cymbiola innexa
The triangular pattern on Cymbiola innexa suggests the presence of a "global control element" that turns the pigment-secreting cells on and off in the correct order -- something like a computer-controlled loom!

"Given this generating mechanism, some shell patterns are easy to understand. A series of vertical stripes -- that is, stripes running perpendicular to the growing edge -- implies a static distribution of pigment secreting cells in the mantle margin. Where a cell or group of cells is permanently turned on, there is a dark stripe of pigment, and where the cells are dormant, there is an unpigmented space. The complementary pattern -- horizontal stripes, parallel to the growing edge -- results from a temporal rather than a spatial oscillation. All the secretory cells turn off and on in synchrony, so that light and dark bands are left behind on the surface of the shell as the growing edge moves on."

All well and good, but some seashells have intricate patterns that require modellers to imagine traveling waves of excitation, oscillating chemical systems, signals that travel faster than chemical diffusion, and longrange synchrony employing a "global control element." These patterngenerating schemes are clever and rather successful on the theoretical level. Indeed, the seashell modellers are rather smug about their accomplishments. (Hayes, Brian; "SpaceTime on a Seashell," American Scientist, 83:214, 1995.)

Comment. The seashell modellers, of course, do not have to explain how or why "global control elements" evolved. The biological rendering of "long-range synchrony" is left unexplained. Although humans will pay large sums for intricately patterned seashells, the anomalist must ask why these patterns exist at all? Why are they beautiful? Of what use are the patterns to the sea-shell inhabitants who cannot appreciate them?

From Science Frontiers #101 Sep-Oct 1995. 1995-2000 William R. Corliss

Science Frontiers Sourcebook Project Reviewed in:

Quotes

  • "A sourcebook of unexplained phenomena is therefore a valuable addition to a collection of scientific literature. William R. Corliss has provided this in the past with his source books of scientific anomalies in several subjects, and now he has provided it for astronomy. He has done an excellent job of collecting and editing a large amount of material, taken in part from scientific journals and in part from scientific reporting in the popular or semi-scientific press." -- "The Mysterious Universe: A Handbook of Astronomical Anomalies", reviwed by Thomas Gold, Cornell University, in Icarus, vol.41, 1980

  • "An interesting, systematic presentation of unusual weather [..] This book is recommended for a general audience" --"Corliss, William R., Tornados, Dark Days, Anomalous Precipitation, and Related Weather Phenomena, Sourcebook Project, 1983.", revieweed in Choice, September 1983
  • "..the science is necessarily somewhat speculative, but Corliss's symthesis is based on reputable sources." -- "Corliss, William R. (Compiler). Lightning, Auroras, Nocturnal Lights, and Related Luminous Phenomena" reviwed by Joseph M. Moran, Univ. of Wisconsin in Science Books and Films, Sep/Oct 1983

  • "Before opening the book, I set certain standards that a volume which treads into dangerous grounds grounds like this must meet. The author scrupulously met, or even exceeded those standards. Each phenomenon is exhaustively documented, with references to scientific journals [..] and extensive quotations" -- "Book Review: The moon and planets: a catalog of astronomical anomalies", The Sourcebook Project, 1985., Corliss, W. R., Journal of the Royal Astronomical Society of Canada, Vol. 81, no. 1 (1987), p. 24., 02/1987