Connected generalised Sierpiński carpets
type: Item
instance of: scholarly article
title: Connected generalised Sierpiński carpets
zbMATH Open document ID: 1195.28008
author: Ligia L. Cristea
author: Bertran Steinsky
published in: Topology and its Applications
publication date: 2010-05-10T00:00:00Z
review text: The Iterated Function Systems (IFS) introduced by Hutchinson in 1981 constitute an important generator of fractals. One of these fractals studied by Sierpinski are well known as Sierpinski carpets. They are self-similar sets in the plane. In this paper the authors consider some generalized forms of the Sierpinski carpets and analyze under which conditions they are connected with respect to the topology induced by the Euclidean metric. The generalized Sierpinski carpets considered in this paper need not to be self-similar. The construction of generalized Sierpinski carpets is discussed in Section 2. The main results are given in Sections 4 and 5, where it is presented necessary and sufficient conditions under which generalized Sierpinski carpets are connected. An example where the authors apply on of their results is given in Section 5.
reviewed by: Nicolae-Adrian Secelean
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 54H05
zbMATH DE Number: 5706270
zbMATH Keywords: fractal
zbMATH Keywords: Sierpinski carpet
zbMATH Keywords: connected set
zbMATH Keywords: graph
MaRDI profile type: Publication
full work available at URL: j.topol.2010.02.005
OpenAlex ID: W2056271805
cites work: On the connectedness of limit net sets
cites work: Q3995301
cites work: The pore structure of Sierpinski carpets
cites work: On the structure of self-similar sets
cites work: Q4740120
cites work: Modelling porous structures by repeated Sierpinski carpets
cites work: Q3994483
DOI: 10.1016/J.TOPOL.2010.02.005
description: scientific article; zbMATH DE number 5706270