space-filling curve

The fourth stage of construction of a Gosper curve, a kind of space-filling curve.

space-filling curve (plural space-filling curves)

1. (mathematical analysis) a curve whose range contains the entire 2-dimensional unit square (or the 3-dimensional unit cube)

   From space-filling curves it can be deduced that ${\displaystyle \mathbb {R} ^{2}}$ and ${\displaystyle \mathbb {R} ^{3}}$ have the same cardinality as ${\displaystyle \mathbb {R} }$.

• Peano curve