Mathematical Modelling of Seashells

Jacob Usinowicz

Recognition and examination of some of the fundamental mathematical properties present in the familiar structure of the molluscan shell can be traced as far back as Aristotle. In recent decades, thanks largely to the development of computers, a much more thorough understanding of the "algorhithmic beauty" of both shell shape and color has been obtained. This project will demonstrate how differential equations can be utilized to translate a two dimensional representation of mollusc shell shape (i.e. the equiangular or logarhithmic spiral) into realistic 3-D models with the help of a computer program. This project will also provide a relatively brief discussion of how differential equations are used to describe the chemical interactions thought to produce certain characteristic molluscan pigmentation patterns.

[Odes Final Projects]

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