  We present calculations of the equilibrium current density and Chern numbers
for a 2DEG in a periodic potential with infinite strip geometry and a
perpendicular magnetic field. We consider a triangular lattice of anti-dots
with large (a = 120 nm) lattice spacing. Such a system is known as artificial
graphene (AG). To compute the current density we numerically diagonalise the AG
Hamiltonian over a set of Landau level basis states, this takes into account
coupling between different Landau levels. Our calculations show that, at
magnetic fields typical for quantum Hall measurements, extended streams of
current are present in the bulk of the sample. We investigate the scaling of
these streams with potential strength. Knowledge of the AG energy levels allows
us to compute the Chern number associated with each energy gap. We demonstrate
that in tuning the height of the potential modulation the Chern number can
undergo a transition between two different values.
