We studied the mechanism of alternating pattern competition between alpha and beta modes at the surface of a fluid layer that is forced vertically. We found that when chaos is realized, the beta pattern develops the degeneracy beta(R), beta(L) such that the choice between beta(R) and beta(L), after each excitation of the alpha mode, becomes undeterministic. We found, however, well defined time variability for such a chaotic pattern selection, which appears generic.