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Seashells
This nOde last updated December 17th, 2004 and is permanently morphing...
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seashell

seashell (sê´shèl´) noun
The calcareous shell of a marine mollusk or similar marine organism.



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THE ALGORITHMIC BEAUTY OF SEASHELLS

Pattern
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.

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  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:

"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 internal linkoscillation. 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 internal linkwaves 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.)



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Busy Signals - Pure Energy on Sugar Free (2002)



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Take seashells. One of the most esteemed documents of modern paleontology is Stephen Jay Gould's doctoral thesis on shells. According to Gould, the fact that there are thousands of potential shell shapes in the world, but only a half dozen actual shell forms, is evidence of natural selection. Not so, says Wolfram. He's discovered a mathematical error in Gould's argument, and that, in fact, there are only six possible shell shapes, and all of them exist in the world.

In other words, you don't need natural selection to pare down internal linkevolution to a few robust forms. Rather, organisms evolve outward to fill all the possible forms available to them by the rules of cellular automata. Complexity is destiny - and Darwin becomes a footnote. "I've come to believe," says Wolfram, "that natural selection is not all that important.



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Of Montreal - Coquelicot Asleep in the Poppies: A Variety of Whimsical Verse on Kindercore (2001) Atom Heart - Shellglove CD on Recent Programmings (1996)
 
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