Theory & application of space-filling curves
Richard Crandall · Apple Distinguished Scientist, Advanced Computation Group
Space-filling curves (or "space-fills") provide an elegant way to transform an N-dimensional problem into an M-dimensional one, for M <> N. 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 the 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 information theory to hard science.