  An ensemble of inelastically colliding grains driven by a vibrating wall in
2D exhibits density clustering. Working in the limit of nearly elastic
collisions and employing granular hydrodynamics, we predict, by a marginal
stability analysis, a spontaneous symmetry breaking of the extended clustering
state (ECS). 2D steady-state solutions found numerically describe localized
clustering state (LCSs). Time-dependent granular hydrodynamic simulations show
that LCSs can develop from natural initial conditions. The predicted
instability should be observable in experiment.
