Space-filling curve

Curve whose range contains the unit square

In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square. 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.

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