We introduce a spin-chain model with dynamics consisting of a unitary circuit with discrete conformal symmetry. This model is holographically dual to a toy theory of quantum gravity in 2+1 dimensions, where certain tensor-network states correspond to classical discrete geometries. Unlike previous approaches, like holographic codes, these tensor networks and geometries evolve in time, reproducing some phenomena from general relativity. Also, these states satisfy the Ryu-Takayanagi correspondence between entanglement and geometry, but they provide much more, they contain a complete…