Affiliation:
1. Department of Mathematics and Information Technology, The Education University of Hong Kong, Hong Kong
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P. R. China
Abstract
Let [Formula: see text], where [Formula: see text] are integers and [Formula: see text] be a digit set. Then the pair [Formula: see text] generates a fractal set [Formula: see text] satisfying [Formula: see text] which is a unit square. However, if we remove one digit from [Formula: see text], then the structure of [Formula: see text] will become very interesting. A well-known example is the Sierpinski carpet. In this paper, we study the resulting self-affine sets of moving a digit in [Formula: see text] to a different place. That is, we consider a digit set [Formula: see text], where [Formula: see text]. We give a complete characterization for the connectedness of self-affine carpet [Formula: see text] in terms of the domains of [Formula: see text] and [Formula: see text].
Funder
Fundamental Research Funds for the Central Universities
Venture and Innovation Support Program for Chongqing Overseas Returnees
Dean's Research Fund of The Education University of Hong Kong
Natural Science Foundation of Chongqing
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Cited by
4 articles.
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