Geodesic
Minimal self-similar Peano curve of genus 5$\times$5
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 68-72.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/

[1] Schepin E.V., “O fraktalnykh krivykh Peano”, Geometricheskaya topologiya i teoriya mnozhestv, Sb. statei. K 100-letiyu so dnya rozhdeniya professora Lyudmily Vsevolodovny Keldysh, Tr. MIAN, 247, Nauka, M., 2004, 294–303 | Zbl

[2] Bader M., Space-Filling Curves. An Introduction with Applications in Scientific Computing, Springer-Verlag, B.–Heidelberg, 2013 | MR | Zbl

[3] Haverkort H., van Walderveen F., “Locality and bounding-box quality of two dimensional space-filling curves”, Computational Geometry, Theory and Applications, 43:2 (2010), 131–147 ; (2008), arXiv: 0806.4787v2 [cs.CG] | DOI | MR | Zbl | MR

[4] Bauman K.E., “Koeffitsient rastyazheniya krivoi Peano-Gilberta”, Matem. zametki, 80:5 (2006), 643–656 | DOI | MR | Zbl

[5] Bauman K.E., Schepin E.V., “Minimalnaya krivaya Peano”, Geometriya, topologiya i matematicheskaya fizika. I, Sb. statei. K 70-letiyu so dnya rozhdeniya akademika Sergeya Petrovicha Novikova, Tr. MIAN, 263, MAIK, M., 2008, 251–271 | MR

[6] Bauman K.E., “Odnostoronnie krivye Peano fraktalnogo roda 9”, Tr. MIAN, 275, 2011, 55–67 | Zbl

[7] Bauman K.E., “Otsenka snizu kvadratno-lineinogo otnosheniya dlya pravilnykh krivykh Peano”, Diskretnaya matematika, 80:3 (2013), 135–142

[8] \href{https://github.com/jura05/peano}f{https://github.com/jura05/peano}

[9] Biere A., Heule M., van Maaren H., Handbook of Satisfiability, IOS Press, 2009 | Zbl

[10] Audemard G., Lagniez J.-M., Simon L., “Improving Glucose for Incremental SAT Solving with Assumption: Application to MUS Extraction”, Proc. SAT, 2013 https://www.labri.fr/perso/lsimon/glucose/ | MR | Zbl

[11] https://pysathq.github.io/

[12] Shalyga D.K., “O tochnom vychislenii kubo-lineinogo otnosheniya krivykh Peano”, Prepr. IPM im. M.V. Keldysha, 2014, 088, 13 pp.

[13] Haverkort H., How many three-dimensional Hilbert curves are there?, 2017, arXiv: 1610.00155v2 [cs.CG] | MR

[14] Korneev A.A., Schepin E.V., “$L_\infty$-lokalnost trekhmernykh krivykh Peano”, Tr. MIAN, 302, MAIK, M., 2018, 1–34