Geodesic
One-side Peano curves of fractal genus~$9$
Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 55-67

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This paper completes the analysis (begun by E. V. Shchepin and the author in 2008) of regular Peano curves of genus $9$ in search of a curve with the minimum square-to-linear ratio. One-side regular Peano curves of genus $9$ are considered, and, among these curves, a class of minimal curves with a square-to-linear ratio of $5\frac 23$ is singled out. A new language to describe curves is introduced which significantly simplifies the coding of these curves. 
@article{TRSPY_2011_275_a2,
     author = {K. E. Bauman},
     title = {One-side {Peano} curves of fractal genus~$9$},
     journal = {Informatics and Automation},
     pages = {55--67},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a2/}
}
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K. E. Bauman. One-side Peano curves of fractal genus~$9$. Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 55-67. http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a2/