The self-affine property of ( U , r ) -Carlitz sequences of polynomials deciphered in terms of graph directed IFS

By defining the m th graphical representation of a ( U , r ) -Carlitz sequence of polynomials, we visualize the nonzero elements in a number table of coefficients of the first m polynomials. When appropriately scaled, these graphical representations are compact sets contained in a fixed closed recta...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2009-11, Vol.157 (18), p.3728-3742
Main Authors: Ni, Tian-Jia, Wen, Zhi-Ying
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Beta-expansion
Cellular automata
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Exact sciences and technology
Fractal
Graph theory
IFS
Mathematical analysis
Mathematics
Measure and integration
Numeration system
Regular language
Sciences and techniques of general use
Self-affine
Theoretical computing
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Summary:By defining the m th graphical representation of a ( U , r ) -Carlitz sequence of polynomials, we visualize the nonzero elements in a number table of coefficients of the first m polynomials. When appropriately scaled, these graphical representations are compact sets contained in a fixed closed rectangle. We established the condition under which a subsequence of these scaled graphical representations converges to a compact set with respect to the Hausdorff metric. Furthermore, under the same condition, the limit set is shown to have self-affine property which can be deciphered in terms of graph directed self-affine iterated function system (GAIFS).
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2009.07.011