  Turing's theory of pattern formation has been used to describe the formation
of self-organised periodic patterns in many biological, chemical and physical
systems. However, the use of such models is hindered by our inability to
predict, in general, which pattern is obtained from a given set of model
parameters. While much is known near the onset of the spatial instability, the
mechanisms underlying pattern selection and dynamics away from onset are much
less understood. Here, we provide new physical insight into the dynamics of
these systems. We find that peaks in a Turing pattern behave as point sinks,
the dynamics of which are determined by the diffusive fluxes into them. As a
result, peaks move towards a periodic steady-state configuration that minimizes
the mass of the diffusive species. We also show that the preferred number of
peaks at the final steady-state is such that this mass is minimised. Our work
presents mass minimization as a simple, generalisable, physical principle for
understanding pattern formation in reaction diffusion systems far from onset.
