Numerical simulations and laboratory experiments are conducted for thin layers of particles in a vertically oscillated container as a function of the frequency f, amplitude A, and depth H. The same standing wave patterns (stripes, squares, or hexagons oscillating at f/2 or f/4) and wavelengths are obtained in the simulations and experiments for a wide range of (f,A) and two layer depths. Two model parameters are determined by fits at just two points (f,A,H). Simulation results lead to heuristic arguments for the onset of patterns and the crossover from squares to stripes.
