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On Rauzy fractal. (English) Zbl 0734.28010
Summary: The boundary of a space tiling set, called the Rauzy fractal, can be constructed by means of the endomorphism $$\theta$$ 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 $$\frac{\log \lambda_ E}{\log (1/\zeta)}\Doteq 1.09338...$$, where $$\lambda_ E$$ is a maximal solution of $$\lambda^ 4-2\lambda -1=0,$$ and $$\zeta$$ is a positive solution of $$x^ 3+x^ 2+x-1=0.$$

##### MSC:
 28A80 Fractals 11K06 General theory of distribution modulo $$1$$ 28A78 Hausdorff and packing measures
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##### References:
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