Shapes of the Living

Abstract

The relationship between form and function in living systems is treated, starting from the difference between volume and surface forces, and their different scaling with size. Surface tension appears as the main player in this context, contrasting the bulk effects of gravity. Chemical gradients and synchronised oscillators are the two other protagonists. The apparent regularities of many natural patterns and forms provide the excuse to describe a range of naturally occurring shapes, also allowing to make interesting links with palaeontology and fossile remains of ancient life on Earth. This chapter owes a lot to the original works of D'Arcy Wentworth Thompson, the celebrated pioneer of mathematical biology, especially in the parts dealing with the mathematics of geometrical transformations, and their relationship with the evolution of species.