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This paper defines the Arrwwid number of a recursive tiling (or space-fillingcurve) as the smallest number w such that any ball Q can be covered by w tiles(or curve sections) with total volume O(vol(Q)). Recursive tilings andspace-filling curves with low Arrwwid numbers can be applied to optimise disk,memory or server access patterns when processing sets of points ind-dimensional space. This paper presents recursive tilings and space-fillingcurves with optimal Arrwwid numbers. For d >= 3, we see that regular cubetilings and space-filling curves cannot have optimal Arrwwid number, and we seehow to construct alternatives with better Arrwwid numbers.

Recursive tilings and space-filling curves with little fragmentation