Physicists Net Fractal Butterfly: Scientific American

Physicists Net Fractal Butterfly: Scientific American: ...the pattern describes the behavior of electrons in extreme magnetic fields...

...It was known at the time that electrons under the influence of a magnetic field would race around in circles. But Hofstadter found that in theory, if the electrons were confined inside a crystalline atomic lattice, their motion would become complicated. As the magnetic field was cranked up, the energy levels that define the motion of electrons would split again and again. When represented on a graph, those energy levels revealed a pattern that looked like a butterfly — and continued to do so, even when zoomed in to infinitely small scales...

 In May, researchers reported that they had stacked a single sheet of graphene, in which carbon atoms are arranged like a honeycomb, on top of a sheet of honeycombed boron nitride. The layers create a repeating pattern that provides a larger target for magnetic fields than the hexagons in each material — effectively magnifying the field.