Space-filling curve

In mathematical analysis, a space-filling curve is a curve whose 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 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.^{[1][2][3][4][5][6]}