Seashells: the plainness and beauty of their mathematical description

1.2 Growth of the horns of animals

Like nails and hair, a horn grows by the addition of material as its base. In order to get a perfectly straight structure, the rate at which material is added must be exactly the same on each side of the base:

On the other hand, if there is some difference (indicated in percentage, in the figures below), one of the edges of the horn will be longer than the other and, inevitably, the horn will coil to the side where less material is added, following a spiral curve:

See applet here [10]
[7] S. Wolfram, A New Kind of Science, Wolfram Research, Inc., 2004

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