A worldwide team of researchers (from the US and Japan) managed to observe Hofstadter’s butterfly fractal pattern for the first time. This pattern was predicted by Douglas Hofstadter back in 1976 - and it emerges when electrons are confined to a two-dimensional sheet, and subjected to both a periodic potential energy and a strong magnetic field.
To create the periodic potential energy, the researchers used an effect called a moiré pattern that arises naturally when graphene is placed on a flat boron nitride substrate. Mapping the graphene energy spectrum (by measuring the electronic conductivity of the samples at very low temperatures in extremely strong magnetic fields, up to 35 Tesla) showed the predicted fractal pattern. The actual mapping can be seen below: