This paper reports two phenomena in an event driven simulation of a dilute vibrofluidized granular material in two dimensions. Both phenomena show inhomogeneity in the horizontal direction. They are convection rolls similar to the Rayleigh-Bénard thermal convection in fluids, and a clustering instability, where the bed spontaneously phase separates into coexisting dense and dilute regions. Detailed investigations show that these are different from the known instabilities in a vibrated granular medium. Characterization of these instabilities is carried out with a phase diagram using suitable parameters from the kinetic theory of vibrofluidized beds.

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