It has long been predicted that 2D electrons subjected simultanesously to both a magnetic field and a superlattice periodic potential will exhibit a complex self-simlar fractal energy spectrum. Termed Hofstadter’s Butterfly, after the theorist who first discovered the recursive energy structure, this phenomenon has intrigued physicists for nearly 40 years, and represents a fundamental framework for understanding the generalized behaviour of electrons in electro and magnetic fields. A complete understanding of the Butterfly spectrum, however, has remained elusive owing to the stringent experimental conditions required. Recently we demonstrated that moire superlattices, arising in bilayer graphene coupled to hexagonal boron nitride provide a nearly ideal-sized periodic modulation, enabling unprecedented experimental access to the fractal spectrum. Several intriguing questions can now be explored experimentally such as the possibility of anomalous emergent behaviour within the fractal energy landscape.