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Peano Curve
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Construction of the Hilbert curve
Space Filling Curves
Peano curve construct
Peano's curve
Peano Curve Explorer
UST Peano Curve
curve di peano-hilbert-munari
Peano Curve in 3D
Peano curve laser engraved into anodised aluminium
Peano Curve
Creating Hilbert and Peano curves in PyMOL
IFS Peano zoom
Peano - Gosper curve -- alternate version
Negative Shelling - Using Hilbert Curve as Detailing
Peano-Gosper Curve (Rough footage)
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Polya's Space-Filling Curve
Space filling curve
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Polya's Space-Filling Curve
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Orthographic Depth Maps of Stanford Dragon Using a Zigzag 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 hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are commonly called Peano curves.
Intuitively, a continuous curve in 2 or 3 (or higher) dimensions can be thought of as the path of a continuously moving point. To eliminate the inherent vagueness of this notion Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the precise description of the notion of a continuous curve:
In the most general form, the range of such a function may lie in an arbitrary topological space, but in the most commonly studied cases, the range will lie in a Euclidean space such as the 2-dimensional plane (a planar curve) or the 3-dimensional space (space curve).
Sometimes, the curve is identified with the range or image of the function (the set of all possible values of the function), instead of the function itself. It is also possible to define curves without endpoints to be a continuous function on the real line (or on the open unit interval (0, 1)).