Article

Japan Journal of Industrial and Applied Mathematics

, Volume 8, Issue 3, pp 461-486

First online:

On Rauzy fractal

  • Shunji ItoAffiliated withDepartment of Mathematics, Tsuda College
  • , Minako KimuraAffiliated withDepartment of Mathematics, Tsuda College

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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