Space-Filling Curves

Volume 9 of the series Texts in Computational Science and Engineering pp 47-65


Arithmetic Representation of Space-Filling Curves

  • Michael BaderAffiliated withDepartment of Informatics, Technische Universität München

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Up to now, we have dealt with the finite iterations of the Hilbert and Peano curve, only. However, these can only offer an approximate impression of the “infinite” curves. Moreover, we are not yet able to compute the corresponding Hilbert or Peano mapping, i.e. to compute the image point for a given parameter. The grammar representations of space-filling curves are not directly suitable for this purpose, as they always generate the iterations as a whole.