Geodesic
The dilation factor of the Peano--Hilbert curve
Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 643-656.

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. 
@article{MZM_2006_80_5_a0,
     author = {K. E. Bauman},
     title = {The dilation factor of the {Peano--Hilbert} curve},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--656},
     publisher = {mathdoc},
     volume = {80},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a0/}
}
TY  - JOUR
AU  - K. E. Bauman
TI  - The dilation factor of the Peano--Hilbert curve
JO  - Matematičeskie zametki
PY  - 2006
SP  - 643
EP  - 656
VL  - 80
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a0/
LA  - ru
ID  - MZM_2006_80_5_a0
ER  - 
%0 Journal Article
%A K. E. Bauman
%T The dilation factor of the Peano--Hilbert curve
%J Matematičeskie zametki
%D 2006
%P 643-656
%V 80
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a0/
%G ru
%F MZM_2006_80_5_a0
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/

[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