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Hilbert
The Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890.
Because it is space-filling, its Hausdorff dimension is 2 (precisely, its image is the unit square, whose dimension is 2 in any definition of dimension; its graph is a compact set homeomorphic to the closed unit interval, with Hausdorff dimension 2).
The Hilbert curve is constructed as a limit of piecewise linear curves. The length of the {\displaystyle n}nth curve is {\displaystyle \textstyle 2^{n}-{1 \over 2^{n}}}\textstyle 2^n - {1 \over 2^n} , i.e., the length grows exponentially with {\displaystyle n}n, even though each curve is contained in a square with area
https://en.wikipedia.org/wiki/Hilbert_curve
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