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. The project enumerates the full canonical rule space in the 23→33 signature class and 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
