The energy spectrum of a two-dimensional electron system in a perpendicular homogeneous magnetic field and a weak lateral superlattice potential with square symmetry is composed of Landau bands with recursive internal subband structure. The Hall conductance in the minigaps is anticipated to be quantized in integer multiples of e2/h that vary erratically from minigap to minigap in accordance with a Diophantine equation. Hall measurements on samples with the requisite properties uncover this long searched for evidence of Hofstadters butterflylike energy spectrum.