Turing Patterns

A Mathematical Analysis of Hydra

Abstract Hydrae present interesting physical properties, chemical properties and finally, mathematical properties. This organism may not be able to consciously make any computations, but that does not mean that mathematics cannot be used to model behaviors of this organism and gain a greater understanding of how it functions. The goal

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A Geometrical Analysis of Different Animals’ Carapace

This article explores the applications of geometry to the carapace of different organisms. The initial focus is on the three-dimensional shape of the turtle carapace to introduce the Gomboc shape which provides the self-righting feature to the turtle based on its unique property of equilibrium points. Then, the patterns of…

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Reaction Diffusion Patterns in Jaws of the Animal Kingdom

The endless number of patterns in nature is fascinating; they vary from spots on tigers, to lines on wood, to even teeth patterns in alligators. A mystery lies beneath all of this variety: how do these complex patterns arise and form such differing patterns? The origin of these patterns in…

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Mathematical Models of Molluscan Shell Patterns and Morphology

Mollusk shells’ mesmerizing diversity of forms stems from their variations in shape, features and patterns. While these forms are highly complex and diverse, research has aimed to establish an overarching model that explains the formation of these shell characteristics. This essay explores the mathematical models that capture these natural forms…

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