Pattern formation is analyzed and simulated in a nonlinear optical sys
tem involving all three space dimensions as well as time in an essenti
al way. This system, counterpropagation in a Kerr medium, is shown to
lose stability, for sufficient pump intensity, to a nonuniform spatial
pattern. We observe hexagonal patterns in a self-focusing medium, and
squares in a self-defocusing one, in good agreement with analysis bas
ed on symmetry and asymptotic expansions.