Kolossváry István: Random orbits on fractals with applications

The chaos game is a simple iterative process which reconstructs the attractor of an iterated function system from a random sequence of points. The goal is to gain information about the fractal set by studying these random orbits, similarly to how properties of dynamical systems can be inferred from the statistical properties of typical orbits. I will give details about some prior joint work with Balázs Bárány and Natalia Jurga about the convergence rate of the chaos game and how it is determined by the Minkowski dimension of the measure generating the random sequence. A collection of open problems and possible applications will also be presented.