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Mat. Zametki, 2015, Volume 98, Issue 6, Pages 923–929 (Mi mz10909)  

This article is cited in 1 scientific paper (total in 1 paper)

Attainment of Maximum Cube-to-Linear Ratio for Three-Dimensional Peano Curves

E. V. Shchepin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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.

Keywords: three-dimensional Peano curve, $q$-adic Peano curve, fractal Peano curve, polyfractal Peano curve, fractal genus, cube-to-linear ratio, square-to-linear ratio.

DOI: https://doi.org/10.4213/mzm10909

Full text: PDF file (447 kB)
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English version:
Mathematical Notes, 2015, 98:6, 971–976

Bibliographic databases:

UDC: 519
Received: 17.06.2015

Citation: E. V. Shchepin, “Attainment of Maximum Cube-to-Linear Ratio for Three-Dimensional Peano Curves”, Mat. Zametki, 98:6 (2015), 923–929; Math. Notes, 98:6 (2015), 971–976

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Korneev, E. V. Shchepin, “$L_\infty $-locality of three-dimensional Peano curves”, Proc. Steklov Inst. Math., 302 (2018), 217–249  mathnet  crossref  crossref  mathscinet  isi  elib
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