First six iterations of the Hilbert curve 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,[1] as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890.[2] Because it is space-filling, its Hausdorff dimension is 2 (precisely, its image is the uni