"Scaling, universality and natural pattern formation"

Peter Sheridan Dodds

This talk introduces the concepts of scaling and universality via elementary examples and some efforts to describe elements of the natural world. Simply put, theories of scaling apply wherever there is similarity across many scales. This similarity may be found in geometry and/or in dynamical processes. Universality arises when the qualitative character of a system is sufficient to quantitatively predict its essential features, such as the exponents that characterize scaling laws. We discuss, in particular, the KPZ equation which describes simple, nonlinear growth or erosion. An example of its use is found in sedimentology in the attempt to understand the origin of stromatolites. We also examine the use of scaling and universality more broadly in geomorphology where we consider the geometry of river networks and the statistical structure of topography.