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.
Space-Filling Function
See also
Hilbert Curve, Peano Curve, Peano-Gosper Curve, Plane-Filling Function, Sierpiński Curve, Space-Filling PolyhedronExplore with Wolfram|Alpha
References
Pappas, T. "Paradoxical Curve-Space-Filling Curve." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 208, 1989.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 FunctionCite this as:
Weisstein, Eric W. "Space-Filling Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Space-FillingFunction.html