In theories of emergent gravity and holography the classical geometry of spacetime is arising from entanglement patterns of states of a conformal quantum field theory (CFT) living on its boundary. Using the AdS/CFT correspondence in this talk we elucidate how boundary entanglement patterns of the CFT vacuum are encoded into the bulk via the dynamics of a cluster algebra.
For a subdivision of the boundary into n parts the conditional mutual informations of overlapping boundary regions are mapped to triangulations of geodesic n-gons of the bulk. Such triangulations are mapped to tilings of kinematic space with causal diamonds. In this picture cluster dynamics is just a scanning of kinematic space by a seed pattern of such diamonds. We show that the space of all such tilings forms an associahedron, an object also known form recent studies of the theory of the S-matrix. Finally we observe that the flips relating the tilings are reminiscent of errors in an error correcting code.