Wall text · the map of all shells
Why a shell must be a spiral
A shell grows only at its edge. The animal adds material at the aperture and cannot go back to remodel what it has already built. To stay the same shape while getting larger, the edge has to enlarge by the same ratio with every turn, and that single constraint forces a logarithmic spiral.
r (θ) = r0 · W θ / 2π W, how fast the tube widens · D, how far it stands from the axis · T, how fast it slides along the axis · S, the shape of its mouth
In the 1960s the palaeontologist David Raup used early computers to draw the shells this rule allows, and mapped the space of possible forms. He noticed that real animals occupy only part of it. Large regions that are perfectly easy to compute are empty in the sea.
The chart is a slice through that space. Each small figure is computed at its own coordinates; the crosshair marks the shell on the plinth. Touch anywhere to send it there.