  Diagonal or chevron patterns are known to spontaneously emerge at the
intersection of two perpendicular flows of self-propelled particles, e.g.
pedestrians. The instability responsible for this pattern formation has been
studied in previous work in the context of a mean-field approach. Here we
investigate the microscopic mechanism yielding to this pattern. We present a
lattice model study of the wake created by a particle crossing a perpendicular
flow and show how this wake can localize other particles traveling in the same
direction as a result of an effective interaction mediated by the perpendicular
flow. The use of a semi-deterministic model allows us to characterize
analytically the effective interaction between two particles.
