Spatial patterns of a transient photon condensate inside a microcavity

We show that a photon condensate inside a dye-filled microcavity forms long-lived spatial patterns when incoherently excited by a focused pump orbiting around the cavity axis. The discrete rotational symmetry of the patterns is controlled by the orbital frequency of the pump spot and despite the absence of any effective photon-photon interactions the condensate is phase-coherent over its full spatial extent.