Peano- Hilbers Space-filling Curve

Theoretical Physics and Astronomy, Radiative processes, Mathematics, Galactic Dynamics, Gravitational Systems, orbit theory, ...
User avatar
Posts: 313
Joined: Sun Feb 05, 2017 8:31 am

Peano- Hilbers Space-filling Curve

Postby Shahram » Sat Feb 17, 2018 11:16 am

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 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 {\displaystyle 2} 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 3D:

Space-filling curve:
In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an n-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are sometimes called Peano curves, but that phrase also refers to the Peano curve, the specific example of a space-filling curve found by Peano.
(18.69 KiB) Downloaded 5 times

Return to “Theoretical Toolbox”

Who is online

Users browsing this forum: No registered users and 1 guest