for help with the experiments. Reviewer information Nature thanks Hua Zhang and the other anonymous reviewer(s) for their contribution to the peer review of this work.

The unique correspondence between mathematical operators and photonic elements in wave optics enables quantitative analysis of light manipulation with individual optical devices. Phase-transition materials are able to provide real-time reconfigurability of these devices, which would create new optical functionalities via (re)compilation of photonic operators, as those achieved in other fields such as field-programmable gate arrays (FPGA). Here, by exploiting the hysteretic phase transition of vanadium dioxide, an all-solid, rewritable metacanvas on which nearly arbitrary photonic devices can be rapidly and repeatedly written and erased is presented. The writing is performed with a low-power laser and the entire process stays below 90 °C. Using the metacanvas, dynamic manipulation of optical waves is demonstrated for light propagation, polarization, and reconstruction. The metacanvas supports physical (re)compilation of photonic operators akin to that of FPGA, opening up possibilities where photonic elements can be field programmed to deliver complex, system-level functionalities.