Brief communications

Koch fractal in non-Euclidean geometries

P. I. Troshin

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

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.

UDC: 514.135:514.132

Received: 12.03.2020
Revised: 12.03.2020
Accepted: 25.03.2020

DOI: 10.26907/0021-3446-2020-6-99-103

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:6, 86–90

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