Evolution proceeds by random mutations that generate varation, which, in turn is acted on by natural selection. Most of evolutionary theory has focussed on how natural selection affects variation in populations. But, in the words of Hugo de Vries: “Natrual selection can explain the survival of the fittest, but it cannot explain the arrival of the fittest.” In this talk I will ask what we can learn by study how variation arises in a number of simple biophysical models of self-assembling sytems. By applying concepts from algorithmic information theory, I will argue that variation is highly biased to produce certain outcomes over others, and that this may explain the spontaneous emergence of symmetry and modularity in biological systems.