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 Istvan Kolossvary, and with Karoly Simon, Boris Solomyak
and Adam Ĺpiewak.
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The Chaos Game: stationary measure and convergence rate
28.01.2022 15:15 - 16:15
Organiser:
H. Bruin, R. Zweimüller
Location:
zoom-meeting