Geodesic
Koch fractal in non-Euclidean geometries
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 99-103

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We propose a spherical and a hyperbolic (on the Lobachevskii plane) analogues for the Koch curve and the Koch snowflake. The formulae describing metric characteristics of these fractals are given. We also suggest the method of construction for these curves with the help of the groups of rigid motions of the spaces in question.
Keywords: Koch curve, Koch snowflake, Koch island, spherical geometry, hyperbolic geometry, Lobachevskii geometry, $L$-system.
Mots-clés : fractal 
@article{IVM_2020_6_a12,
     author = {P. I. Troshin},
     title = {Koch fractal in {non-Euclidean} geometries},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {99--103},
     publisher = {mathdoc},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_6_a12/}
}
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P. I. Troshin. Koch fractal in non-Euclidean geometries. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2020), pp. 99-103. http://geodesic.mathdoc.fr/item/IVM_2020_6_a12/