Balázs Bárány (BME Budapest):

Title:
The Chaos Game: stationary measure and convergence rate

Abstract: 
In the 1988 textbook "Fractals Everywhere", Barnsley introduced an algorithm for generating fractals through a
random Markovian procedure which he called the chaos game. In this talk we study it from two perspectives.
We will study how long it takes the orbit of the chaos game to reach a certain density inside the attractor
of a strictly contracting iterated function system. On the other hand, we will study the Hausdorff dimension
and absolute continuity of the unique stationary measure of the process. This talk is based on two joint works
with Natalia Jurga and István Kolossváry, and with Károly Simon, Boris Solomyak and Adam Śpiewak.