A word generated by coding of irrational rotation with respect to a general decomposition of the unit interval is shown to have an inverse limit structure directed by substitutions. We also characterize primitive substitutive rotation words, as those having quadratic parameters.
Shigeki AKIYAMA. Masayuki SHIRASAKA. "Recursively renewable words and coding of irrational rotations." J. Math. Soc. Japan 59 (4) 1199 - 1234, October, 2007. https://doi.org/10.2969/jmsj/05941199