We have all heard on various occasions that the universe is expanding. We have also seen many extraordinary pictures of galaxies, and most of them have the tendency to be planar. One might ask: Why is it so?

The goal of this talk is to describe an analogous mathematical problem, where similar questions can be answered in a reasonable way. The main objects of our analysis will be iterated Fourier series. As we will see, the almost everywhere convergence of them is deeply related to the understanding of such phenomena.