Shell Space: The 'Snugness' Condition

flare, W

2

spire, T

0

David Raup (among others, including Stephen Wolfram) proposes that all naturally occurring shells conform to the same basic design, varying only in a limited number of quantifiable ways. In Raup's simple model, you can specify a shell by setting the flare,

W

(the rate of growth of the spiral), the verm,

D

(the "tightness" of the shell cavity), and the spire,

T

(the rate of creep parallel to the spiral axis). If we insist that shells are snug (that is, the shell cavity is just loose enough so that each wind touches the previous and the next exactly), then the space of shells can be parametrized by flare and spire alone.