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Abstract:
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 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.
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