  A simple generalization of the Swift-Hohenberg equation is proposed as a
model for the pattern-forming dynamics of a two-dimensional field with two
unstable length scales. The equation is used to study the dynamics of surface
waves in a fluid driven by a linear combination of two frequencies. The model
exhibits steady-state solutions with two-, four-, six-, and twelve-fold
symmetric patterns, similar to the periodic and quasiperiodic patterns observed
in recent experiments.
