Power law distribution functions are everywhere, why?

Power law distribution functions of various properties are prevalent in a vast range of systems, from the smallest dust grains between stars to the largest dark matter halos. It describes the  frequency of various phenomena, and appears also in biology, economy, sociology, and linguistics. I will show simulations of a very simple system of colliding hard spheres, which explore the conditions where a power law distribution function appears, and the possible implications for various other systems