Sorting mesh faces after catmull-clark subdivision

Hi guys

So I've been trying to understand a bit more about how the catmull clark subdivision works, and I've gotten into sorting the mesh faces after the operation is performed.

Looking at the pointlist gives a very good description of how the mesh isreconstructed, as shown below, from 0 subdivisions through to 3.

My question is, would anyone know how to create a script to sort these into loops of faces, so that, for instance, the sequence 0,1,4,5,16,17,20,21 could be sorted into an ascending item number of 0 through to 7, and so on and so forth for the rest of the rows or columns in the mesh?