Geodesic
Attainment of Maximum Cube-to-Linear Ratio for Three-Dimensional Peano Curves
Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 923-929.

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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, cube-to-linear ratio, square-to-linear ratio.
Mots-clés : polyfractal Peano curve, fractal genus 
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E. V. Shchepin. Attainment of Maximum Cube-to-Linear Ratio for Three-Dimensional Peano Curves. Matematičeskie zametki, Tome 98 (2015) no. 6, pp. 923-929. http://geodesic.mathdoc.fr/item/MZM_2015_98_6_a11/

[1] M. Bader, Space-Filling Curves. An Introduction with Applications in Scientific Computing, Texts Comput. Sci. Eng., 9, Springer-Verlag, Berlin, 2013 | MR | Zbl

[2] E. V. Schepin, “O fraktalnykh krivykh Peano”, Geometricheskaya topologiya i teoriya mnozhestv, Tr. MIAN, 247, Nauka, M., 2004, 294–303 | MR | Zbl

[3] H. Haverkort, An Inventory of Three-Dimensional Hilbert Space-Filling Curves, 2011, arXiv: 1109.2323v1

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

[5] E. V. Schepin, K. E. Bauman, “Minimalnaya krivaya Peano”, Geometriya, topologiya i matematicheskaya fizika. I, Tr. MIAN, 263, MAIK, M., 2008, 251–271 | MR | Zbl

[6] E. V. Shchepin, “On Hölder maps of cubes”, Math. Notes, 87:5-6 (2010), 757–767 | DOI