Self-organized superlattice patterns with two slightly differing wave numbers

We report on the observation of superlattices that occur spontaneously in a nonlinear optical system with O(2) symmetry. A secondary bifurcation from hexagons yields patterns formed by twelve wave vectors. Besides irregular patterns these may either be quasiperiodic patterns or superlattices built from two classes of wave vectors differing slightly in their length. Both classes of wave vectors stem from only one pattern-forming instability. The wave vectors fit on a hexagonal or a square grid. In the former case the set of wave vectors can be decomposed into two hexagonal triads, whereas in the case of the square grid squeezed triads occur