Hilbert curve
Hilbert curve
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Jump to: navigation, searchA Hilbert curve (also known as a Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891,[1] as a variant of the space-filling curves discovered by Giuseppe Peano in 1890.[2]
Because it is space-filling, its Hausdorff dimension is 2 (precisely, its image is the unit square, whose dimension is of course 2 in any definition of dimension; its graph is a compact set homeomorphic to the closed unit interval, with Hausdorff dimension 2).
Hn is the nth approximation to the limiting curve. The Euclidean length of Hn is
, i.e., it grows exponentially with n, while at the same time always being bounded by a square with a finite area.
For multidimensional databases, Hilbert order has been proposed to be used instead of Z order because it has better locality-preserving behavior.
