[physonaught]

Some very cool physics involved-- a lot of basic quantum mechanics (electrons hopping on a lattice), but it has a lot of really broad implications about symmetries. There is a lot of recent interest in the butterfly [1,2].

It turns out that it is a very important state to study the Quantum Hall effect[3], and the fractional Quantum Hall effect[4], which seem to be in vogue in Condensed Matter physics these days.

Sorry to bog you down with details, I just wanted to mention how neat it is that Hofstadter's butterfly is still being studied today!

[1] http://www.nature.com/nature/journal/v497/n7451/full/nature1... [2] http://physics.aps.org/articles/v6/118