# Henry Segerman

Assistant Professor of Mathematics

Oklahoma State University

Stillwater, OK, USA

Henry Segerman is an assistant professor in the Department of Mathematics at Oklahoma State University. 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.

Developing Fractal Curves

Four pieces: 140x135x115mm, 147x50x119mm, 103x98x98mm, and 158x112x71mm

PA 2200 Plastic, Selective-Laser-Sintered

2012

Many fractal curves can be produced as the limit of a sequence of polygonal curves, where the curves are generated via an iterative process, e.g. an L-system. We can make an animation by smoothly interpolating between the curves in this sequence. Each of these sculptures is the result of replacing the time dimension of such an animation with a space dimension, producing a surface. We scale the distances between the steps of the sequence exponentially, so that self-similarity of the curves is reflected in self-similarity of the surface.

The four sculptures correspond to the Sierpinski arrowhead, terdragon, Hilbert, and the Heighway dragon curves. The idea of representing these sequences of curves as surfaces is due to Geoffrey Irving.

The four sculptures correspond to the Sierpinski arrowhead, terdragon, Hilbert, and the Heighway dragon curves. The idea of representing these sequences of curves as surfaces is due to Geoffrey Irving.