Shells (*) Resize

The mathematical description of seashells growth

"How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?"
Albert Einstein

One might at first tend to think that the growth of plants and animals, because of their elaborate forms, are ruled by highly complex laws. However, this is surprisingly not always true: many aspects of the growth of plants and animals may be described by remarkably simple mathematical laws. An obvious example of this are the seashells and snails, as we show here: with a very simple model it is possible to describe and generate any of the many types of seashells that one may find in nature.

Some examples of seashells (in stereoscopy)

A simple model

Translated for Atractor by a CMUC team, from its original version in Portuguese. Atractor is grateful for this cooperation.

(*) This work was carried out under the guidance of Professor Jorge Picado from the Universidade of Coimbra, under a grant by the Calouste Gulbenkian Foundation to develop a project for the promotion of Mathematics in Atractor.
Since many browsers are blocking Java nowadays, it was decided to convert to Javascript the original applets of this section. This conversion was carried out within the scope of a support received from FCT - Fundação para a Ciência e a Tecnologia, through FACC (Fundo de Apoio à Comunidade Científica).

Difficulty level: Upper Secondary, University