Space-filling curve
（重定向自Spacefilling curve）
![Three iterations of the Peano curve construction, whose limit is a space-filling curve.](/Images/godic/202502/12/Peanocurve.svg1935.png")
![Das Standardbeispiel: die Hilbert-Kurve](/Images/godic/202502/12/Hilbert-Kurve1935.png")
![Extrait de l'article original de Hilbert](/Images/godic/202502/12/Dessins_de_Hilbert_de_sa_courbe_remplissante1935.png")
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.