Seashells: the plainness and beauty of their mathematical description

Washed from the ocean and scattered along the beach, seashells exert a pull on the imagination as strong as the tides. Intrigued, we pluck one up from the sand to trace its smooth curves, recesses, ribs, or spines, or hold it to an ear to hear the echoing sea. (...) Shells' pure geometries -- such as the elegant logarithmic spiral of the chambered Nautilus -- have inspired wonder and provoked mathematical analysis at least since Aristotle's day. Sandy Carlson (Seashells, 2007)

Below, by clicking in the pictures, you may see examples of the kind of shells that can be generated with this model and that illustrate the effects of the variation of the various parameters in the growth of the shell. They were made with the help of the software Mathematica.

4. Index of examples

Gastropods

boat ear moon	horse conch	turritella	top shells	cone	wentletrap	neptune	ancilla
olive	whelk	tun	struthiolaria	worm shell	limpets	planorbis	cap

Bivalves

glycymeris

lyonsia

Cephalopods

nautilus

argonauta

spirula

ammonite

Scaphopods

Elephant tusk

See stereoscopic images of these examples in the mathematics project ATRACTOR

Next: 5. The origins of limpets | Back to Index