Hilbert curve [wikipedia]

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Hilbert curve [wikipedia]

Summary

The Hilbert curve is a famous continuous fractal space-filling curve introduced by the German mathematician David Hilbert in 1891 as a variation of earlier work by Giuseppe Peano. It is created through a recursive process where a simple line pattern is repeatedly divided and transformed, producing an increasingly complex curve that eventually passes through every point of a square. Although it comes from a one-dimensional interval, its limit fills a two-dimensional area, giving it a Hausdorff dimension of 2. 
The Hilbert curve is important not only in fractal geometry but also in computer science, where its locality-preserving properties are used for data indexing, image processing, spatial databases, and organizing multidimensional information efficiently. 

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