Iterated function systems: A comprehensive survey
arXiv:2211.14661v1 [math.PR] 26 Nov 2022 Page 1 Iterated Function Systems: A
Comprehensive Survey Ramen Ghosh ∗ Jakub Mareček † November 29, 2022 Abstract We …
Comprehensive Survey Ramen Ghosh ∗ Jakub Mareček † November 29, 2022 Abstract We …
Weakly contractive iterated function systems and beyond: a manual
K Leśniak, N Snigireva, F Strobin - Journal of Difference Equations …, 2020 - Taylor & Francis
We give a systematic account of iterated function systems (IFS) of weak contractions of
different types (Browder, Rakotch, topological). We show that the existence of attractors and …
different types (Browder, Rakotch, topological). We show that the existence of attractors and …
On the chaos game of iterated function systems
Every quasi-attractor of an iterated function system (IFS) of continuous functions on a first-
countable Hausdorff topological space is renderable by the probabilistic chaos game. By …
countable Hausdorff topological space is renderable by the probabilistic chaos game. By …
Contractive iterated function systems enriched with nonexpansive maps
F Strobin - Results in Mathematics, 2021 - Springer
Motivated by a recent paper of Leśniak and Snigireva Iterated function systems enriched
with symmetry, preprint, we investigate the properties of the semiattractor A_ F ∪ G^* AF∪ …
with symmetry, preprint, we investigate the properties of the semiattractor A_ F ∪ G^* AF∪ …
Iterated function systems enriched with symmetry
K Leśniak, N Snigireva - Constructive Approximation, 2022 - Springer
An iterated function system (IFS) can be enriched with an isometry in such a way that the
resulting fractal set has prescribed symmetry. If the original system is contractive, then its …
resulting fractal set has prescribed symmetry. If the original system is contractive, then its …
Small and minimal attractors of an IFS
M Fitzsimmons, H Kunze - … in Nonlinear Science and Numerical Simulation, 2020 - Elsevier
Lasota and Myjak demonstrated that one can study attractors to an iterated function system
(IFS) possibly containing discontinuous functions. We continue this line of thought by …
(IFS) possibly containing discontinuous functions. We continue this line of thought by …
On the convergence rate of the chaos game
B Bárány, N Jurga, I Kolossváry - … Mathematics Research Notices, 2023 - academic.oup.com
This paper studies how long it takes the orbit of the chaos game to reach a certain density
inside the attractor of a strictly contracting IFS of which we only assume that its lower …
inside the attractor of a strictly contracting IFS of which we only assume that its lower …
Rate of convergence in the disjunctive chaos game algorithm
K Leśniak, N Snigireva, F Strobin - Chaos: An Interdisciplinary Journal …, 2022 - pubs.aip.org
The rate of convergence of the chaos game algorithm for recovering attractors of contractive
iterated function systems (IFSs) is studied. As with successive Picard iterates in the Banach …
iterated function systems (IFSs) is studied. As with successive Picard iterates in the Banach …
Necessary/sufficient conditions for the chaos game to render quasi attractors
M Fitzsimmons, H Kunze - … in Nonlinear Science and Numerical Simulation, 2020 - Elsevier
We explore when the chaos game renders a quasi attractor of an iterated function system
(IFS); we emphasize the role of the set in which the chaos game is initialized. For IFS with …
(IFS); we emphasize the role of the set in which the chaos game is initialized. For IFS with …
The Hutchinson-Barnsley theory for generalized iterated function systems by means of infinite iterated function systems
ER Oliveira - arXiv preprint arXiv:2204.00373, 2022 - arxiv.org
The study of generalized iterated function systems (GIFS) was introduced by Mihail and
Miculescu in 2008. We provide a new approach to study those systems as the limit of the …
Miculescu in 2008. We provide a new approach to study those systems as the limit of the …