The Hypergraphs study searches for rewriting rules that produce sphere-like spatial structures from simple graph operations. The work builds on Stephen Wolfram's 2020 paper proposing that space could emerge from repeated application of pattern-matching replacement rules on hypergraphs. Starting from a small set of ordered node tuples, each rule replaces matched subgraphs with new configurations — some produce linear chains, others branch into trees, and a few grow into structures whose local neighborhoods scale like two-dimensional surfaces. A systematic enumeration of the full canonical rule space in the 23->33 signature class filters candidates through a multi-stage pipeline: structural analysis, short simulations with dimension estimates, and extended scoring for curvature, compactness, and topological consistency. Rules that pass produce closed globular forms (spheres, tori, or intermediate surfaces) when embedded in three dimensions. Top-scoring geometries are meshed and 3D printed. The investigation remains ongoing.
Photography: Phillip C. Reiner
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