Every coiled shell is one tube that grows as it turns. Three numbers decide how it looks.
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One tube
A shell is a single tube that grows as it turns. The amber ring is the opening, sweeping around an axis and getting bigger at a steady rate. Every whorl is a scaled copy of the one before: a logarithmic spiral. This one is a nautilus.
Cephalopod Deep slopes of Indo-Pacific coral reefs, usually several hundred metres down.
What the shell is for
It lives in the last chamber. The older chambers hold gas and liquid, and a tube through them, the siphuncle, slowly changes the liquid to adjust its buoyancy.
It was long called a living fossil; it is now known to be only a distant relative of the ammonites.
It has about 90 tentacles, and none of them have suckers.
Its eye has no lens: it works like a pinhole camera, open to the sea.
Cephalopod Early Jurassic seas, about 180 million years ago; fine fossils come from England and Germany.
What the shell is for
A chambered float, like every ammonite. Its whorls barely overlap, so every turn stays on show.
Ammonites were once sold as "snakestones", sometimes with a snake’s head carved on, and legend credited St Hilda of Whitby with turning snakes to stone.
It spread fast and widely, so geologists use it to date Early Jurassic rocks.
Its ribbed whorls are almost perfectly round in cross-section.
Where whorls overlap, the animal reuses the old whorl as its inner wall. The render shows the buried part too.
Morphospace
The cube
Each point is a shell. Drag across the map to set W and D, and the strip on the right for T. Below the amber line, whorls touch.
Regions are approximate, after Raup (1966). The model assumes a circular tube and steady growth, so real shells only sit near their points.
About the model
In the 1960s the paleontologist David Raup asked a computer to draw shells. He found that one rule covers nautiluses, ammonites, snails, clams and brachiopods: a tube that keeps its shape while it grows and turns around an axis. Three numbers set its form, so all possible shells fit in one cube, and real animals use only a small part of it.
Raup, D. M. (1962). Computer as aid in describing form in gastropod shells. Science 138.
Raup, D. M. (1966). Geometric analysis of shell coiling: general problems. Journal of Paleontology 40.
McGhee, G. R. (1999). Theoretical Morphology: The Concept and Its Applications. Columbia University Press.
