Geodesic
Generalized Chaos game in an extended hyperbolic plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 2, pp. 350-376 Cet article a éte moissonné depuis la source Math-Net.Ru

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We propose and theoretically substantiate an algorithm for conducting a generalized Chaos game with an arbitrary jump on finite convex polygons of the extended hyperbolic plane $H^2$ whose components in the Cayley–Klein projective model are the Lobachevsky plane and its ideal domain. In particular, the defining identities for a point dividing an elliptic, hyperbolic, or parabolic segment in a given ratio are proved, and formulas for calculating the coordinates of such a point at a canonical frame of the first type are obtained. The results of a generalized Chaos game conducted using the advanced software package pyv are presented.
Keywords: extended hyperbolic plane, Lobachevsky plane, hyperbolic plane of positive curvature, Chaos game.
Mots-clés : fractal 
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L. N. Romakina; I. V. Ushakov. Generalized Chaos game in an extended hyperbolic plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 220 (2024) no. 2, pp. 350-376. http://geodesic.mathdoc.fr/item/TMF_2024_220_2_a8/

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