Self-organized biological patterns driven by growth and expansion

The reaction-diffusion (RD) model, involving the diffusion of two types of morphogens (``activator'' and ``inhibitor'') whose interaction stimulates their own synthesis, is an established paradigm to explain the autonomous generation of space-filling patterns in biology. Starting from random initial perturbations, the RD model typically generates patterns via the development of finite-wavelength dynamical instabilities in confined geometries. In this talk, I will describe examples where elements of the RD model, together with the open, expanding geometries offered by growing biological systems, give rise to novel strategies to generate well-defined patterns in space and time.