Geodesic
The dilation factor of the Peano–Hilbert curve
Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 643-656 
K. E. Bauman. The dilation factor of the Peano–Hilbert curve. Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 643-656. http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the maximum value of the ratio $|p(x)-p(y)|^2/|x-y|$ for the Peano–Hilbert curve $p\colon[0,1]=I\to I^2$ is equal to 6.

[1] E. V. Schepin, “Povyshayuschie razmernost otobrazheniya i nepreryvnaya peredacha informatsii”, Voprosy chistoi i prikladnoi matematiki, 1, Priokskoe knizhnoe izd-vo, Tula, 1987, 148–155

[2] E. V. Schepin, K. E. Bauman, “O krivykh Peano fraktalnogo roda 9”, Modelirovanie i analiz dannykh, Trudy fakulteta informatsionnykh tekhnologii MGPPU, vyp. 1, Rusavia, M., 2004, 78–89

[3] E. V. Schepin, “O fraktalnykh krivykh Peano”, Tr. MIAN, 247, 2004, 294–303 | MR | Zbl