Curvature

“The lesson of curvature is quite general and has nothing to do with what tissues or material is involved. Forms curls so that the faster growing or longer surface lies outside and the slower growing or shorter surface lies inside, there being more room outside than inside. . . If the rate of growth or expansion of two surfaces are equal, the material lies straight. If the rates are unequal, the material curls so that the slower growing surface is inside the faster growing surface.”

“That difference in growth automatically causes the coiling to take place.
Again, no gene need remember or plan the final shape of the shell; it need only facilitate a difference in growth between the inner and outer parts.”
Peter S. Stevens
Patterns in Nature

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Spiral Shells

Seashells illustrate the concept of growth without intent: organisms do not plan their structures. Seashells grow in many different shapes, each the result of simple instructions. The wide variety of spiral shells shows how nature adopts a common theme and exploits it to suit a multiplicity of different micro-environments.

Four Million Years of spiral shell growth
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More pictures of Spiral Shells

Diagram of Curvature