Not in any direct or formal sense. The specific geometric forms (such as the flower of life) commonly discussed in sacred geometry are overwhelmingly simpler than the forms that emerge even from extremely simple rules in our models. However, the notion (dating back to antiquity) that constructs can combine to reproduce nature has definite conceptual resonance with our approach. Read more

The relationship between the Wolfram model and ordinary category theory is actually relatively straightforward. One can think of a given hypergraph substitution system as being a morphism of the category Set, mapping the category of possible hypergraphs onto a power set construction on the category of possible hypergraphs, where the power set construction is considered to be an endofunctor on the category Set. Read more

Very intimately, at least so we believe; indeed, one of our current conjectures is that the most natural candidate for the limiting mathematical structure of the multiway causal graph is some generalization of the correspondence space that appears in twistor theory. The twistor correspondence, at least in Penrose’s original formulation, is a natural isomorphism between sheaf cohomology classes on a real hypersurface of complex projective 3-space (i.e. Read more

One can think of the Wolfram model as being a significant generalization of the concept of a spin network or spin foam in loop quantum gravity. In standard loop quantum gravity, a spin network is a combinatorial structure for representing the quantum state of a gravitational field on a three-dimensional spacelike hypersurface as a directed graph, Read more

Our formulation of branchlike hypersurfaces within multiway evolution graphs may be thought of as being a variant of the concept of a tensor network; in much the same way as the combinatorial structure of a hierarchical tensor network designates the entanglement structure of ground states in the context of entanglement renormalization methods, Read more

Very directly. Indeed, the causal graphs that one investigates in the context of Wolfram model systems, as a plausible candidate for the discrete structure of spacetime, are ultimately just concrete representations of causal sets: the graph itself may be thought of as being the Hasse diagram for a partial order relation between spacetime events that satisfies reflexivity, Read more

The precise correspondence is not yet clear, but we have several ideas. One possible point of connection lies in the evolution of what we refer to colloquially as “snake states”—sets of global states in the multiway evolution graph produced by maximally consistent sets of spacelike-separated updating events. The evolution of such a snake state corresponds to a purely relativistic evolution of the global state of the universe (since all states within the snake were produced via strictly spacelike-separated updating events, Read more