TOPICS
Search

Space-Filling Function

A space-filling function is a "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

Ivanov (2026) constructs finite approximants on a sphere by ordering the triangular faces of a geodesic polyhedron along a Hamiltonian cycle in its dual graph and joining compatible paths within successive faces.

See also

Hilbert Curve, Moore Curve, Osgood Curve, Peano Curve, Peano-Gosper Curve, Plane-Filling Function, Sierpiński Curve, Space-Filling Polyhedron, Terdragon

Explore with Wolfram|Alpha

References

Ivanov, D. "Sphere-Filling Curve 1: Generating Continuous Self-Avoiding Paths on Geodesic Polyhedra via Dual Graph Hamiltonian Cycles." Wolfram Community, Sep. 29, 2026. https://community.wolfram.com/t/28210.Pappas, T. "Paradoxical Curve-Space-Filling Curve." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 208, 1989. Pegg, E. Jr. Mathematical Games. Episode 16: "Space-Filling Curves." Apr. 18, 2024. https://www.youtube.com/watch?v=3qbZadltTCI. Companion notebook: https://community.wolfram.com/t/23888.Platzman, L. K. and Bartholdi, J. J. "Spacefilling Curves and the Planar Travelling Salesman Problem." J. Assoc. Comput. Mach. 46, 719-737, 1989.Wagon, S. "A Spacefilling Curve." §6.3 in Mathematica in Action. New York: W. H. Freeman, pp. 196-209, 1991.

Referenced on Wolfram|Alpha

Space-Filling Function

Cite this as:

Weisstein, Eric W. "Space-Filling Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Space-FillingFunction.html

Subject classifications