Space-Filling Curves

Volume 9 of the series Texts in Computational Science and Engineering pp 77-91


Sierpinski Curves

  • Michael BaderAffiliated withDepartment of Informatics, Technische Universität München

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All space-filling curves discussed so far were based on a recursive substructuring into squares. The Sierpinski curve, in contrast, may be geometrically constructed using a recursive substructuring based on triangles. The curve is named after Waclaw Sierpinski, who – in 1912 – presented the respective mapping as the solution of certain functional equations. Similar to the Hilbert and Peano curve, the Sierpinski curve maps the unit interval onto a square.