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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 491, Pages 68–72
DOI: https://doi.org/10.31857/S2686954320020150 (Mi danma5) 		 
This article is cited in 2 scientific papers (total in 3 papers)

MATHEMATICS

Minimal self-similar Peano curve of genus 5$\times$5

Yu. V. Malykhin, E. V. Shchepin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.31857/S2686954320020150
Abstract: The paper presents a plane regular fractal Peano curve with a Euclidean square-to-line ratio ($L_2$-locality) of 5$\frac{43}{73}$, which is minimal among all known curves of this class. The presented curve has a fractal genus of 25. Performed calculations allow us to state that all the other regular curves with a fractal genus not exceeding 36 have a strictly greater square-to-line ratio.
Keywords: space-filling curves, Peano curves, square-to-line ratio, regular fractal curves.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 26
The authors were partially supported by the RAS program 26 "Fundamentals of Creating Algorithms and Software for Advanced High-Performance Computing" (project "Multidimensional fractal Peano curves").
Received: 22.01.2020
Revised: 22.01.2020
Accepted: 29.01.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 2, Pages 135–138
DOI: https://doi.org/10.1134/S1064562420020155
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: Yu. V. Malykhin, E. V. Shchepin, “Minimal self-similar Peano curve of genus 5$\times$5”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 68–72; Dokl. Math., 101:2 (2020), 135–138
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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