We report observations of transverse optical structures (traveling bright light spots) that appear in a novel type of ring resonator. In this arrangement an optically addressable liquid-crystal spatial light modulator is combined with a BaTiO(3) crystal that provides strong photorefractive beam fanning. The information traveling around is carried either by the phase or by the intensity of the light waves in different parts of the resonator. The movement of the transverse structures is related to the alignment of the resonator, which is controlled by an interferometer. It is demonstrated that such a resonator is able to store weak optical signals.