# Roger Antonsen

In order to understand something, one should look at it from different perspectives. This is one attempt to do so with the Hilbert curve, a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891. I am deeply fascinated with how code can be used to visualize, and make tangible, mathematical concepts, and especially with how complexity and beauty can arise from very simple assumptions. I find the process of experimenting with mathematical structures through computer code thoroughly rewarding and exciting. This work was partly done while I was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Illustrating Mathematics program.

This is a 52-mirror labyrinth, with a “laser beam” that traces out the Hilbert curve. The top layer of the base has slits precisely cut to hold the 52 mirrors so that their reflective back faces are on the appropriate diagonals. The symbolic “laser beam” consists of a red piece of paper resting on a wooden platform of the same shape. This illustrates an internal point of view, as the “laser beam” has no knowledge of absolute direction, and the mirrors (or their absence) serve as local directional commands. Originally I wanted to use an actual laser beam to trace out the curve, but the mirrors absorbed too much light, and the beam was invisible after a dozen bounces.

(Photo: Edmund Harriss)