4 citations · 9 across the 4 of their papers we have counts for
6 papers
Chaos game for IFSs on topological spaces
Michael F. Barnsley, Krzysztof Lesniak, Miroslav Rypka
We explore the chaos game for the continuous IFSs on topological spaces. We prove that the existence of attractor allows us to use the chaos game for visualization of attractor. Th…
Basic Topological Structure of Fast Basins
Michael Fielding Barnsley, Krzysztof Lesniak
We define fractal continuations and the fast basin of the IFS and investigate which properties they inherit from the attractor. Some illustrated examples are provided.
Playing cooperatively with possibly treacherous partner
Krzysztof Leśniak
We investigate an alternative concept of Nash equilibrium, m-equilibrium, which slightly resembles Harsanyi-Selten risk dominant equilibrium although it is a different notion. M-eq…
The chaos game on a general iterated function system from a topological point of view
Michael F. Barnsley, Krzysztof Leśniak
We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the st…
On the continuity of the Hutchinson operator
Michael F. Barnsley, Krzysztof Leśniak
We investigate whether the Hutchinson operator associated with the iterated function system (IFS) is continuous. It clarifies several partial results scattered across recent litera…
The Chaos Game on a General Iterated Function System
Michael Barnsley, Andrew Vince
The main theorem of this paper establishes conditions under which the "chaos game" algorithm almost surely yields the attractor of an iterated function system. The theorem holds in…