Henry Segerman
Artists
Henry Segerman
Associate Professor of Mathematics
Oklahoma State University
Stillwater, Oklahoma, USA
Statement
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.
Artworks
![Image for entry 'Cuboctahedral fractal graph'](/_next/image?url=https%3A%2F%2Fsubmit.bridgesmathart.org%2Frails%2Factive_storage%2Fblobs%2Fproxy%2FeyJfcmFpbHMiOnsiZGF0YSI6ODk0MSwicHVyIjoiYmxvYl9pZCJ9fQ%3D%3D--2d4bf0c75c189b15d419f3074c1eb649b461e637%2Fcuboctahedron_1800.jpg&w=1536&q=75)
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.
![Image for entry 'Octahedron fractal graph'](/_next/image?url=https%3A%2F%2Fsubmit.bridgesmathart.org%2Frails%2Factive_storage%2Fblobs%2Fproxy%2FeyJfcmFpbHMiOnsiZGF0YSI6ODk0MiwicHVyIjoiYmxvYl9pZCJ9fQ%3D%3D--2d20687a357c186f33877eba5c3741b4a6dcb1c2%2Fsfg_octahedron_1800.jpg&w=1536&q=75)
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.
![Image for entry 'Space filling graph 1'](/_next/image?url=https%3A%2F%2Fsubmit.bridgesmathart.org%2Frails%2Factive_storage%2Fblobs%2Fproxy%2FeyJfcmFpbHMiOnsiZGF0YSI6ODk0MywicHVyIjoiYmxvYl9pZCJ9fQ%3D%3D--57f84a8e3838125c5f9a4603768dfce55d85a2bc%2Fsfg_cube_corner_1800.jpg&w=1536&q=75)
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.