  Pattern formation is ubiquitous in nature from morphogenesis and cloud
formation to galaxy filamentation. More often than not, patterns arise in a
medium driven far from equilibrium due to the interplay of dynamical
instability and nonlinear wave mixing. We report, based on momentum and real
space pattern recognition, formation of density patterns with two- (D$_2$),
four- (D$_4$) and six-fold (D$_6$) symmetries in Bose-Einstein condensates
(BECs) with atomic interactions driven at two frequencies. The symmetry of the
pattern is controlled by the ratio of the frequencies. The D$_6$ density waves,
in particular, arise from a resonant wave mixing process that coherently
correlates and enhances the excitations that respect the symmetry.
