Hilbert Curve

The Hilbert curve is a continuous fractal space-filling curve first described by David Hilbert in 1891, refining a construction Giuseppe Peano had published the year before. Despite being a one-dimensional curve, successive iterations of its construction pass arbitrarily close to every point of a two-dimensional square, so that in the limit the curve fills the square completely. Points that are close together along the curve's own length tend to stay close together once mapped onto the square, a locality-preserving property that makes the Hilbert curve useful well beyond pure mathematics, including in database indexing, image processing and computer graphics.