Cartoon illustrating atoms (red) trapped in self-organized optical lattice. The nodal lines of the cavity mode, where the electric field intensity is zero, are shown in blue. (Top) Configuration where only one cavity mode is available. (Bottom) One of several possible (nearly degenerate) cavity modes considered by Gopalakrishnan et al. In the top panel, the pattern of atoms breaks only a discrete twofold symmetry by choosing which sublattice to occupy, but in the bottom panel, there is also the choice of which of the large number of degenerate lattice structures to adopt.