Bridges Conference Galway, 2026

'Hypergraph #16' (from Hypergraphs series) was selected to be juried into Bridges 2026 Exhibition of Mathematical Art, Craft and Design at the University of Galway, Ireland, 5-8 August 2026. It is 3D printed in resin, 14.5 x 14.5 x 14.5 cm.

Hypergraph #16 comes from a search through thousands of rewriting rules applied to small sets of connected nodes. Most rules produce linear chains or branching trees. A few grow into closed forms whose local neighbourhood scales like a two-dimensional surface. #16 was one of those. The rule itself is small: three node pairs replaced by three triples. Each match rewrites part of the graph, and repeated application grows the structure until it closes. Candidates were scored for curvature and topological consistency, then meshed and 3D printed.

Research:
The Hypergraphs project explores rules that generate spatial objects analogous to a sphere using graph theory. It is inspired by Stephen Wolfram's 2020 paper positing that space may be generated as the consequence of repeated application of pattern-matching rules to graph structures. Sets of ordered nodes (tuples) are transformed to other configurations whenever a rule graph pattern matches any subgraph. All canonical rules for the 23->33 signature class are enumerated. Candidate rules pass through a process of multi-level analysis: short runs with estimated dimensions, then long runs scored for curvature, compactness, and topological consistency. Rules that pass produce closed structures when embedded in 3-space, such as spheres, tori, and intermediate structures. Structures that score highly are run, meshed, and 3D printed. This research is ongoing.