I will review recent progress towards establishing a holographic duality for discrete spaces involving a regular tiling of hyperbolic space. In particular, I will present a recent example where an aperiodic XXZ spin chain is obtained naturally by extrapolating the bulk tiling to its boundary. The properties of this model are studied using RG techniques, which provide a tensor network construction for its ground state. We calculate and compare the entanglement entropy both at the boundary and in the bulk. I will comment on the next steps towards obtaining a full dynamical duality of discrete systems. In particular, this may be useful for going beyond the large N limit on the gravity side