The Hypergraphs project explores rules that generate spatial objects analogous to a sphere using graph theory. This project is inspired by Stephen Wolfram's 2020 paper positing that space may be generated as the consequence of the repeated application of pattern-matching rules to a graph structure. We explore rules where a set of ordered nodes (tuples) are transformed to other configurations where the rules apply when the rule graph pattern matches any subgraph. Rules exist where the graph becomes a linear chain, trees, and some graphs where the local neighbourhood area increases like a two-dimensional surface. We enumerate all canonical rules for the 23->33 signature class. Candidate rules go through a process that includes multi-level analysis, short runs with estimated dimensions, and long runs which score generated structures based on their curvatures, compactness, and topological consistency. The passing rules when embedded in 3-space produce closed structures, such as spheres, tori, and intermediate structures. Structures that score highly are run, meshed, and 3D printed. This research is ongoing.
Photography: Phillip C. Reiner
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