Hilbert curve (nonfiction): Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
[[File:Hilbert_curve.gif|thumb|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. | [[File:Hilbert_curve.gif|thumb|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. | ||
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). | |||
== In the News == | |||
<gallery> | |||
</gallery> | |||
== Fiction cross-reference == | == Fiction cross-reference == | ||
| Line 16: | Line 19: | ||
* [[Peano curve (nonfiction)]] | * [[Peano curve (nonfiction)]] | ||
External links: | |||
* [https://en.wikipedia.org/wiki/Hilbert_curve Hilbert curve] @ Wikipedia.org | * [https://en.wikipedia.org/wiki/Hilbert_curve Hilbert curve] @ Wikipedia.org | ||
[[Category:Mathematics]] | [[Category:Nonfiction (nonfiction)]] | ||
[[Category:Mathematics (nonfiction)]] | |||
Latest revision as of 09:13, 24 June 2017
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.
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).
In the News
Fiction cross-reference
Nonfiction cross-reference
External links:
- Hilbert curve @ Wikipedia.org