Hilbert curve (nonfiction)

First 8 steps toward building the Hilbert curve.

A 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 (nonfiction) in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano (nonfiction) in 1890.

Description

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).

Fiction cross-reference

• Hilbert curve

Nonfiction cross-reference

• David Hilbert (nonfiction)
• Giuseppe Peano (nonfiction)
• Recursion (nonfiction)

External links

• Hilbert curve @ Wikipedia.org