Photoinduced shape morphing has implications in fields ranging from soft robotics to biomedical devices. Despite considerable effort in this area, it remains a challenge to design materials that can be both rapidly deployed and reconfigured into multiple different three-dimensional forms, particularly in aqueous environments. In this work, we present a simple method to program and rewrite spatial variations in swelling and, therefore, Gaussian curvature in thin sheets of hydrogels using photoswitchable supramolecular complexation of azobenzene pendent groups with dissolved α-cyclodextrin. We show that the extent of swelling can be programmed via the proportion of azobenzene isomers, with a 60% decrease in areal swelling from the all trans to the predominantly cis state near room temperature. The use of thin gel sheets provides fast response times in the range of a few tens of seconds, while the shape change is persistent in the absence of light thanks to the slow rate of thermal cis–trans isomerization. Finally, we demonstrate that a single gel sheet can be programmed with a first swelling pattern via spatially defined illumination with ultraviolet light, then erased with white light, and finally redeployed with a different swelling pattern.