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 idea of generalizing the dynamic properties of the Fibonacci morphism. That fractal set can be generalized to other maps on a 3 letter alphabet, generating other fractal sets with interesting properties, such as periodic tiling of the plane and self-similarity in three homothetic parts.

The infinite tribonacci word is a word constructed by applying iteratively the Tribonacci or Rauzy map : ${\displaystyle s(1)=12}$, ${\displaystyle s(2)=13}$, ${\displaystyle s(3)=1}$. Starting from 1, the Tribonacci words are:

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