  We show how measuring real space properties such as the charge density in a
quasiperiodic system can be used to gain insight into their topological
properties. In particular, for the Fibonacci chain, we show that the total
onsite charge oscillates when plotted in the appropriate coordinates, and the
number of oscillations is given by the Chern number of the gap in which the
Fermi level lies. We show that these oscillations have two distinct
interpretations, obtained by extrapolating results from the two extreme limits
of the Fibonacci chain -- the valence bond picture in the strong modulation
limit, and perturbation around the periodic chain in the weak modulation limit.
This effect is found to remain robust at moderate interactions, as well as in
the presence of disorder. We conclude that experimental measurement of the real
space charge distribution can yield information on topological properties in a
straightforward way.
