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Rauzy fractal

Known as: Tribonacci word 
In mathematics, the Rauzy fractal is a fractal set associated to the Tribonacci substitution It has been studied in 1981 by Gérard Rauzy, with the… Expand
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2020
2020
Number the cells of a (possibly infinite) chessboard in some way with the numbers 0, 1, 2, ... Consider the cells in order… Expand
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2015
2015
  • O. Turek
  • J. Integer Seq.
  • 2015
  • Corpus ID: 5484001
According to a result of Richomme, Saari and Zamboni, the abelian complexity of the Tribonacci word satisfies $\rho^{\mathrm{ab… Expand
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2014
2014
Abstract In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry… Expand
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2014
2014
There is a long tradition, going back to Hadamard and Morse, of associating symbolic infinite words with dynamical systems coming… Expand
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2013
2013
We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with… Expand
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2013
2013
  • O. Turek
  • Theor. Comput. Sci.
  • 2013
  • Corpus ID: 36215931
We propose a technique for exploring the abelian complexity of recurrent infinite words, focusing particularly on infinite words… Expand
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2013
2013
We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles associated with beta-substitutions related… Expand
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1997
1997
Let (Nn,(+1)n) be the adic system associated to the substitution: 1 → 12,…,(n − 1) → 1n, n → 1. In Sirvent (1996) it was shown… Expand
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1996
1996
Abstract In this paper we study some relationships between the dynamical systems that arise from the family of substitutions: 1… Expand
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Highly Cited
1994
Highly Cited
1994
— We prove a conjecture of Gérard Rauzy related to the structure of billiard trajectories in the cube : let us associate to any… Expand
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