THE CHAOS GAME ON POLYGONS IN A HYPERBOLIC PLANE OF POSITIVE CURVATURE

Abstract

In this paper we present an example of computer simulation of the Chaos game in a hyperbolic plane H ^ of positive curvature. Unlike the fundamental group of transformations of the Euclidean plane, the fundamental group of transformations of the plane 𝐻̂ does not contain similarity transformations. Nevertheless, the results of the Chaos game are analogs of known fractal objects of the Euclidean plane. The starting point of the study was the task of construction a Sierpinski triangle in the plane 𝐻̂ , solved within the framework of educational research practice.