Geodesic
Chaos game in an~extended hyperbolic plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 3, pp. 388-400

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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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     author = {L. N. Romakina and I. V. Ushakov},
     title = {Chaos game in an~extended hyperbolic plane},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {388--400},
     publisher = {mathdoc},
     volume = {215},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_215_3_a3/}
}
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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/