Chaos game for IFSs on topological spaces

Michael F. Barnsley; Krzysztof Leśniak; Miroslav Rypka

doi:10.1016/j.jmaa.2015.11.022

Chaos game for IFSs on topological spaces

Michael F. Barnsley
, Krzysztof Leśniak
, Miroslav Rypka^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

We explore the chaos game on continuous IFSs on topological spaces. We prove that the existence of an attractor implies that the chaos game can be used to construct approximations of the attractor. The essential role of basin of attraction is discussed.

Original language	English
Pages (from-to)	1458-1466
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	435
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2015.11.022
Publication status	Published - 2016

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title = "Chaos game for IFSs on topological spaces",

abstract = "We explore the chaos game on continuous IFSs on topological spaces. We prove that the existence of an attractor implies that the chaos game can be used to construct approximations of the attractor. The essential role of basin of attraction is discussed.",

keywords = "Basin of attractor, Chaos game, Iterated function system, Pointwise basin, Strict attractor",

author = "Barnsley, \{Michael F.\} and Krzysztof Le{\'s}niak and Miroslav Rypka",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

doi = "10.1016/j.jmaa.2015.11.022",

language = "English",

volume = "435",

pages = "1458--1466",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

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TY - JOUR

T1 - Chaos game for IFSs on topological spaces

AU - Barnsley, Michael F.

AU - Leśniak, Krzysztof

AU - Rypka, Miroslav

PY - 2016

Y1 - 2016

N2 - We explore the chaos game on continuous IFSs on topological spaces. We prove that the existence of an attractor implies that the chaos game can be used to construct approximations of the attractor. The essential role of basin of attraction is discussed.

AB - We explore the chaos game on continuous IFSs on topological spaces. We prove that the existence of an attractor implies that the chaos game can be used to construct approximations of the attractor. The essential role of basin of attraction is discussed.

KW - Basin of attractor

KW - Chaos game

KW - Iterated function system

KW - Pointwise basin

KW - Strict attractor

UR - https://www.scopus.com/pages/publications/84961960503

U2 - 10.1016/j.jmaa.2015.11.022

DO - 10.1016/j.jmaa.2015.11.022

M3 - Article

SN - 0022-247X

VL - 435

SP - 1458

EP - 1466

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Chaos game for IFSs on topological spaces

Abstract

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