Editing Space-filling curve (section)

{{Short description|Curve whose range contains the unit square}}
[[Image:Peanocurve.svg|400px|thumb|Three iterations of the [[Peano curve]] construction, whose limit is a space-filling curve.]]
In [[mathematical analysis]], a '''space-filling curve''' is a [[curve]] whose [[Range of a function|range]] reaches every point in a higher dimensional region, typically the [[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 [[plane (mathematics)|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.

The closely related '''FASS curves''' (approximately space-Filling, self-Avoiding, Simple, and Self-similar curves)
can be thought of as finite approximations of a certain type of space-filling curves.<ref>
Przemyslaw Prusinkiewicz and Aristid Lindenmayer.
[https://books.google.com/books?id=4F7lBwAAQBAJ "The Algorithmic Beauty of Plants"].
2012.
p. 12
</ref><ref>
Jeffrey Ventrella.
[https://books.google.com/books?id=Qj-zAwAAQBAJ "Brainfilling Curves - A Fractal Bestiary"].
2011.
p. 43
</ref><ref>
Marcia Ascher.
[https://books.google.com/books?id=FQBaDwAAQBAJ "Mathematics Elsewhere: An Exploration of Ideas Across Cultures"].
2018.
p. 179.
</ref><ref>
[https://books.google.com/books?id=lPdQAAAAMAAJ "Fractals in the Fundamental and Applied Sciences"].
1991.
p. 341-343.
</ref><ref>
Przemyslaw Prusinkiewicz; Aristid Lindenmayer; F. David Fracchia.
[http://algorithmicbotany.org/papers/fass.html "Synthesis of Space-Filling Curves on the Square Grid"].
1989.
</ref><ref>
[https://tilings.math.uni-bielefeld.de/glossary/FASS-curve/ "FASS-curve"].
D. Frettlöh, E. Harriss, F. Gähler: Tilings encyclopedia, https://tilings.math.uni-bielefeld.de/
</ref>