  We study a lattice model of two perpendicular intersecting flows of
pedestrians represented by hard core particles of two types, eastbound
(`$\pE$') and northbound (`$\pN$'). Each flow takes place on a strip of width
$M$ so that the intersection is an $M\times M$ square lattice. In experiment
and simulation there occurs on this square spontaneous formation of a diagonal
pattern of alternating $\pE$ and $\pN$ particles. We show that this pattern
formation may be understood in terms of a linear instability of the
corresponding mean field equations. A refined investigation reveals that the
pattern actually consists of chevrons rather than straight diagonals. We
explain this effect as the consequence of the existence of a nonlinear mode
sustained by the interaction between the two types of particles.
