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Recent experiments by Kudrolli, Pier and Gollub on surface waves,parametrically excited by two-frequency forcing, show a transition from a smallhexagonal standing wave pattern to a triangular ``superlattice'' pattern. Weshow that generically the hexagons and the superlattice wave patterns bifurcatesimultaneously from the flat surface state as the forcing amplitude isincreased, and that the experimentally-observed transition can be described byconsidering a low-dimensional bifurcation problem. A number of predictions comeout of this general analysis.Comment: 4 pages, RevTex, revised, to appear in Phys. Rev. Let

Nonlinear Competition between Small and Large Hexagonal Patterns