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A ``Curve'' (i.e., a continuous map of a 1-D Interval) into a 2-D area (a Plane-Filling Function) or a 3-D volume.
See also Hilbert Curve, Peano Curve, Peano-Gosper Curve, Plane-Filling Curve, Sierpinski Curve, Space-Filling Polyhedron
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.