Minimal self-similar Peano curve of genus 5$\times$5
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 68-72
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The paper presents a plane regular fractal Peano curve with a Euclidean square-to-line ratio ($L_2$-locality) of 5$\frac{43}{73}$, which is minimal among all known curves of this class. The presented curve has a fractal genus of 25. Performed calculations allow us to state that all the other regular curves with a fractal genus not exceeding 36 have a strictly greater square-to-line ratio.
Keywords:
space-filling curves, Peano curves, square-to-line ratio, regular fractal curves.
@article{DANMA_2020_491_a13,
author = {Yu. V. Malykhin and E. V. Shchepin},
title = {Minimal self-similar {Peano} curve of genus 5$\times$5},
journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
pages = {68--72},
publisher = {mathdoc},
volume = {491},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a13/}
}
TY - JOUR AU - Yu. V. Malykhin AU - E. V. Shchepin TI - Minimal self-similar Peano curve of genus 5$\times$5 JO - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ PY - 2020 SP - 68 EP - 72 VL - 491 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DANMA_2020_491_a13/ LA - ru ID - DANMA_2020_491_a13 ER -
%0 Journal Article %A Yu. V. Malykhin %A E. V. Shchepin %T Minimal self-similar Peano curve of genus 5$\times$5 %J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ %D 2020 %P 68-72 %V 491 %I mathdoc %U http://geodesic.mathdoc.fr/item/DANMA_2020_491_a13/ %G ru %F DANMA_2020_491_a13
Yu. V. Malykhin; E. V. Shchepin. Minimal self-similar Peano curve of genus 5$\times$5. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 68-72. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a13/