The Rauzy Gasket

  • Pierre ArnouxEmail author
  • Štěpán Starosta
Part of the Trends in Mathematics book series (TM)


We define the Rauzy gasket as a subset of the standard two-dimensional simplex associated with letter frequencies of ternary episturmian words. We prove that the Rauzy gasket is homeomorphic to the usual Sierpiński gasket (by a two-dimensional generalization of the Minkowski ? function) and to the Apollonian gasket (by a map which is smooth on the boundary of the simplex). We prove that it is also homothetic to the invariant set of the fully subtractive algorithm, hence of measure 0.


Hausdorff Dimension Continue Fraction Iterate Function System Subtractive Algorithm Infinite Word 
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The second author acknowledges financial support by the Czech Science Foundation grant GAČR 201/09/0584, by the grants MSM6840770039 and LC06002 of the Ministry of Education, Youth, and Sports of the Czech Republic, and by the grant of the Grant Agency of the Czech Technical University in Prague grant No. SGS11/162/OHK4/3T/14.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.IML - Institut de Mathématiques de Luminy, UPR-Cnrs 9016Marseille Cedex 9France
  2. 2.Department of MathematicsFNSPE, Czech Technical University in PraguePrague 2Czech Republic
  3. 3.Department of Theoretical Computer ScienceFIT, Czech Technical University in PraguePrague 6Czech Republic

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