Hofstadter's butterfly

In GEB he writes:

Gplot: a recursive graph showing energy bands for electrons in an idealized crystal in a magnetic field. α, representing magnetic field strength, runs vertically from 0 to 1. Energy runs horizontally. The horizontal line segments are bands of allowed electron energies.

From Wiki:

The Hofstadter butterfly was the first fractal structure ever discovered in physics. In particular, Gplot (as Hofstadter called it) was described as "self-similar" in his 1976 article in Physical Review before Benoit Mandelbrot's word "fractal" was known.

Hofstadter is, of course, officially awesome.