  We combine percolation theory and Monte Carlo simulation to study in two
dimensions the connectivity of an equilibrium lattice model of interacting
Janus disks which self-assemble into an orientationally ordered stripe phase at
low temperature. As the patch size is increased or the temperature is lowered,
clusters of patch-connected disks grow, and a percolating cluster emerges at a
threshold. In the stripe phase, the critical clusters extend longer in the
direction parallel to the stripes than in the perpendicular direction, and
percolation is thus anisotropic. It is found that the critical behavior of
percolation in the Janus system is consistent with that of standard isotropic
percolation, when an appropriate spatial rescaling is made. The rescaling
procedure can be applied to understand other anisotropic systems, such as the
percolation of aligned rigid rods and of the $q$-state Potts model with
anisotropic interactions.
