# Henry Segerman

Research Fellow

University of Melbourne

Australia

I am a research fellow in the Department of Mathematics and Statistics at the University of Melbourne. My mathematical research is in 3-dimensional geometry and topology, and concepts from those areas often appear in my work. Other artistic interests involve procedural generation, self reference, ambigrams and puzzles.

Developing Fractal Curves

Three pieces: 107x71x162mm, 98x98x103mm, and 119x50x147mm

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, for example an L-system. One can visualise such a sequences of curves as an animation that steps through the sequence. A small part of the curve at one step of the iteration is close to a corresponding part of the curve at the previous step, and so it is natural to add frames to our animation that continuously interpolate between the curves of the iteration.

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

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