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On Rauzy fractal

  • Shunji Ito
  • Minako Kimura
Article

Abstract

The boundary of a space tiling set, called the Rauzy fractal, can be constructed by means of the endomorphism θ on a free group of rank 3 according to Dekking’s fractal generating method. Using this method, the Hausdorff dimension of the Rauzy fractal is calculated by\(\frac{{\log \lambda _{\rm E} }}{{log (1/\zeta )}} \mathbin{\lower.3ex\hbox{$\buildrel{\mathbin{\buildrel\scriptstyle.\hfill\over{\smash{\scriptstyle=}\vphantom{_{\scriptstyle x}}}}}\over{\hfill\smash{\scriptstyle\cdot}}$}} 1.09338 \cdots \) where λ E is a maximal solution of λ4 - 2λ - 1 = 0, and ζ is a positive solution ofx 3+x 2+x−1=0.

Key words

fractal space tiling Hausdorff dimension 

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References

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Copyright information

© JJIAM Publishing Committee 1991

Authors and Affiliations

  • Shunji Ito
    • 1
  • Minako Kimura
    • 1
  1. 1.Department of MathematicsTsuda CollegeKodaira, TokyoJapan

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