Connected generalised Sierpiński carpets
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.
scientific article; zbMATH DE number 5706270