Henry Segerman

Research Fellow
Department of Mathematics and Statistics, University of Melbourne
Melbourne, Australia

Henry Segerman is a postdoctoral mathematician. His mathematical research is in 3 dimensional geometry and topology, and concepts from those areas often appear in his work. Other artistic interests involve procedural generation, self reference, ambigrams and puzzles.

Cuboctahedral fractal graph
Cuboctahedral fractal graph
66 x 66 x 66 mm
PA 2200 Plastic, Selective-Laser-Sintered
2010

This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 3, and is replaced at the next step by 7 vertices which can be thought of as a subset of a 3 x 3 x 3 cube, with certain choices of edges connecting them to each other. Each edge is replaced at the next step by a single edge, joining to the vertex in the centre of each 3 x 3 face. We begin the construction with the first step being the edges of a cube, and this is the result at the fourth step.

Octahedron fractal graph
Octahedron fractal graph
103 x 103 x 103 mm
PA 2200 Plastic, Selective-Laser-Sintered
2010

This is a graph embedded in 3-dimensional space as a subset of an "octahedral lattice", which is related to the tessellation of space using octahedra and tetrahedra. The graph has a fractal structure, formed by a process of repeated substitution. Each vertex at each step of the construction is degree 4, and is replaced at the next step by 6 vertices arranged in an octahedron, with certain choices of edges connecting them to each other. Each edge is replaced at the next step by 2 parallel edges. We begin the construction with the first step being the edges of an octahedron, and this is the result at the fourth step.

Space filling graph 1
Space filling graph 1
68 x 68 x 68 mm
PA 2200 Plastic, Selective-Laser-Sintered
2010

This is a graph embedded in 3-dimensional space as a subset of the cubic lattice. The graph has a fractal structure, analogous to the fractal structure of a step in the construction of a space filling curve, but with greater connectivity. This greater connectivity makes the physical sculpture considerably more robust than the analogous sculpture of a step in the construction of a space filling curve would be. Each vertex at each step of the construction is degree 3, and is replaced at the next step by 8 vertices arranged in a 2 x 2 x 2 cube, with certain choices of edges connecting them to each other. Each edge is replaced at the next step by 4 parallel edges. We begin the construction with the first step being the edges of a cube, and this is the result at the fourth step. The spacing between the vertices varies in order to highlight the fractal structure.