Theory & application of space-filling curves

Richard E. Crandall
Vollum Adjunct Professor of Science, Reed College

Abstract: Space-filling curves (or "space-fills") provide an elegant way to transform an N-dimensional problem into an M-dimensional one, for MN. Examples of this expedient include: "sorting" in N-dimensions, fractal measures derived from spacefill trajectories, data compression, many-body physics, and so on. The key to such applications is the transition from theoretical (analytic) picture to the discrete (digital) picture. Indeed, discrete spacefills are demonstrably powerful software tools that apply across a wide spectrum from graphics to hard science.