Geodesic
Chaos game in an extended hyperbolic plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 3, pp. 388-400 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain formulas for the midpoint and quasimidpoint of parabolic and nonparabolic segments in the canonical frame of the second type on the extended hyperbolic plane $H^2$ whose components in the projective Cayley–Klein model are the Lobachevsky plane $\Lambda^2$ and a positive-curvature hyperbolic plane $\widehat{H}$. We propose an algorithm for the Chaos game in the $H^2$ plane and present the results of this game played with the prepared software package pyv on triangles in the $\Lambda^2$ plane and trihedrals in the $\widehat{H}$ plane.
Keywords: extended hyperbolic plane, Lobachevsky plane, hyperbolic plane of positive curvature, Chaos game, Sierpinski triangle.
Mots-clés : fractal 
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L. N. Romakina; I. V. Ushakov. Chaos game in an extended hyperbolic plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 3, pp. 388-400. http://geodesic.mathdoc.fr/item/TMF_2023_215_3_a3/

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