A `replacement sequence' method for finding the largest real root of an integer monic polynomial

To every integer monic polynomial of degree m can be associated a `replacement rule' that generates a word W* from another word W consisting of symbols belonging to a finite `alphabet' of size 2m. This rule applied iteratively on almost any initial word Wo, yields a sequence of words {Wi}. From acount of different symbols in the word Wi, one can obtain a rational approximate to the largest real root of the polynomial.