The Shape of Shells: She Sells Self-Similar Spiral Seashells on the Seashore

It is impossible not to marvel at the beauty and regularity of seashells. These intricate forms are crafted by a humble architect—the living mollusc—building them layer by layer. Despite their remarkable diversity, the fundamental geometry of most seashells is governed by simple mathematical rules, resulting in elegant three-dimensional self-similar structures. Beyond this basic framework, molluscs embellish their shells with fascinating features such as wrinkles, spines, and spikes. In this lecture, I will demonstrate how a mathematical theory of seashell growth explains the origins of these features and resolves many enduring questions in biology.