Two-mode rhomboidal states in driven surface waves

Two-mode rhomboid patterns are generated experimentally via two-frequency p arametric forcing of - kz = kl where surface waves. These patterns are form ed by the simple nonlinear resonance: (k) over right arrow(2)(')- and (k) o ver right arrow(2) = (k) over right arrow(1) where k(1) and k(2)(= k(2)(')) are concurrently excited eigenmodes. The state possesses a direction-depen dent time dependence described by a superposition of the two modes, and a d imensionless sealing delineating the state's region of existence is present ed. We also show that 2n-fold quasipatterns naturally arise from these stat es when the coupling angle between (k) over right arrow(2) and (k) over rig ht arrow(2)(') is 2 pi/n.