2018 Bridges Conference

Jeffrey Geiringer & Robert Voorheis


Robert Voorheis


Ann Arbor, Michigan, USA


Jeffrey Geiringer is an artist and digital manufacturer based in Brooklyn, NY. Robert Voorheis is a digital artist specializing in algorithmically-generated artwork. They combine backgrounds in mathematics and 3D-modeling to generate and print unique forms.


Image for entry 'n=17, a=7 (helios)'

n=17, a=7 (helios)

21 x 21 x 21 cm

3D-printed PLA


A visualization of a 3D graph in which each vertex lies on a three-dimensional integer lattice. The set of vertices defining the graph is precisely the set of points (x, y, z) such that x*y*z ≡ 7 modulo 17. The set of vertices has tetrahedral symmetry; that is, they can be separated into 4 distinct quadrants which can be permuted analogously to the 4 vertices of a regular tetrahedron. This visualization of modular multiplication reveals a unexpectedly pleasing geometric structure that appears simultaneously randomized and highly-structured.