The Geometry and Pigmentation of Seashells

Seashells are beautiful objects that are admired for both their intricate shapes and the patterns on their surfaces. Despite their complexity these shapes are easily described using only elementary tools from geometry. Indeed a wide variety of natural shell shapes can be composed as surfaces in a 3-space and rendered using computer graphic imagery. Moreover, the pigmentation motifs that decorate many shells in the form of wavy stripes and checks as well as chaotic and tent designs can be generated by cellular automaton models, and in particular by the famous “Rule 30”. The photograph in Fig. 1 shows some typical ∗Department of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK. email: