  We consider a gas of non-interacting spinless fermions in a rotating optical
lattice and calculate the density profile of the gas in an external confinement
potential. The density profile exhibits distinct plateaus, which correspond to
gaps in the single particle spectrum known as the Hofstadter butterfly. The
plateaus result from insulating behavior whenever the Fermi energy lies within
a gap. We discuss the necessary conditions to realize the Hofstadter insulator
in a cold atom setup and show how the quantized Hall conductance can be
measured from density profiles using the St\v{r}eda formula.
