Nicholas Roberts
Triply Periodic Biogenesis is a series of studies into minimal surfaces and their relationship to the ontogeny of anatomical structures in humans. The 3D surfaces are generated from a parameterization of the gyroid, a triply periodic surface, and 3D printed using PLA. The surfaces of trabecular networks in bones display a tendency towards negative Gaussian curvature, a mean curvature of 0 and a preferred 3 way connectivity at junctions. This lends itself to modelling by gyroid derived surfaces as seen in the white model on the bottom left. On the top right is a pair of entangled but disjoint triply periodic surfaces, with opposite chirality modelling the source and drain aspects of the circulatory system.
The work comes from a study of historic fetal skeletal specimens. After much analysis of the vertebrae & their trabecular structure, a number of geometric & graphical invariants were noted. Namely that, the surfaces of the structures tended towards being minimal surfaces & when the structures where represented as graphs the majority of the nodes had 3 degrees. This inspired a search for triply periodic surfaces that could be derived from minimal surfaces. The pieces are both derived from the same parameterization of the gyroid. Whilst the white model is based on an actual scientific study of bone development, the blue & red model is an artistic conjecture about the nature of blood vessel ontogeny.