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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 6, Pages 99–103
DOI: https://doi.org/10.26907/0021-3446-2020-6-99-103 (Mi ivm9588) 		 
Brief communications

Koch fractal in non-Euclidean geometries

P. I. Troshin

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2020-6-99-103
Abstract: 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, fractal, $L$-system.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00295
Received: 12.03.2020
Revised: 12.03.2020
Accepted: 25.03.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 6, Pages 86–90
DOI: https://doi.org/10.3103/S1066369X20060134
Bibliographic databases:
Document Type: Article
UDC: 514.135:514.132
Language: Russian
Citation: P. I. Troshin, “Koch fractal in non-Euclidean geometries”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 6, 99–103; Russian Math. (Iz. VUZ), 64:6 (2020), 86–90
Citation in format AMSBIB
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