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

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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$5},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {68--72},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a13/}
}
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Yu. V. Malykhin; E. V. Shchepin. Minimal self-similar Peano curve of genus 5$\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/