Moore Curve

The Moore curve is a closed plane-filling function obtained by joining four appropriately oriented copies of the Hilbert curve so that their endpoints join (Moore 1900). Its limiting traversal is therefore a continuous function from a circle onto a unit square, rather than a traversal with two distinguished endpoints.

Successive polygonal approximants are constructed recursively by replacing each of four constituent squares with a rotated or reflected copy of the Hilbert curve pattern. Because every constituent square is traversed at every refinement and its diameter tends to zero, the limiting curve covers the unit square (Sagan 1994).