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Attainment of maximum cube-to-linear ratio for three-dimensional Peano curves

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Abstract

The class of so-called q-adic Peano curves is defined, which is large enough to include the polyfractal curves. The cube-to-linear ratio for this class attains its maximum value, which can be effectively determined by an exhaustive search implementable on modern computers.

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References

  1. M. Bader, Space-Filling Curves. An Introduction with Applications in Scientific Computing, in Texts Comput. Sci. Eng. (Springer-Verlag, Berlin, 2013), Vol. 9.

  2. E. V. Shchepin, “On fractal Peano curves,” in Trudy Mat. Inst. Steklov, Vol. 247: Geometric Topology and Set Theory (2004), pp. 294–303 [Proc. Steklov Inst.Math. 242 (4), 272–280 (2004)].

    Google Scholar 

  3. H. Haverkort, An Inventory of Three-Dimensional Hilbert Space-Filling Curves, arXiv: 1109.2323v1 (2011).

    Google Scholar 

  4. D. K. Shalyga, “On exact calculation of the cube-to-linear ratio for Peano curves,” Preprint no. 88 IPM im. M. V. Keldysha RAN (Keldysh Inst. Appl.Math., Russian Academy of Sciences, 2014).

    Google Scholar 

  5. E. V. Shchepin and K. E. Bauman, “Minimal Peano curve,” in TrudyMat. Inst. Steklov, Vol. 263: Geometry, Topology, and Mathematical Physics. I (2008), pp. 251–271 [Proc. Steklov Inst. Math. 263 (1), 236–256 (2008).

    Google Scholar 

  6. E. V. Shchepin, “On Hölder maps of cubes,” Math. Notes 87 (5-6), 757–767 (2010).

    Article  MATH  Google Scholar 

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Correspondence to E. V. Shchepin.

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Original Russian Text © E. V. Shchepin, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 6, pp. 923–929.

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Shchepin, E.V. Attainment of maximum cube-to-linear ratio for three-dimensional Peano curves. Math Notes 98, 971–976 (2015). https://doi.org/10.1134/S0001434615110292

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  • DOI: https://doi.org/10.1134/S0001434615110292

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