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Matematicheskie Zametki, 2015, Volume 98, Issue 6, Pages 923–929
DOI: https://doi.org/10.4213/mzm10909 (Mi mzm10909) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

E. V. Shchepin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (447 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm10909
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.
Received: 17.06.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 6, Pages 971–976
DOI: https://doi.org/10.1134/S0001434615110292
Bibliographic databases:
Document Type: Article
UDC: 519
Language: Russian
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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  • https://doi.org/10.4213/mzm10909
  • https://www.mathnet.ru/eng/mzm/v98/i6/p923
    • This publication is cited in the following 2 articles:
    1. Yuri Malykhin, Evgeny Shchepin, “Search of fractal space-filling curves with minimal dilation”, Discrete Comput. Geom., 70 (2023), 189–213  mathnet  crossref
    2. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    References:42
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