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Computing the language of an $S$-adic shift

I have been looking online for how or if one can compute the language of an $S$-adic subshift generated by finitely many substitutions. I know that one can compute the language of a substitution ...
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Computing admissible patches of a substitution

I have been recently trying to look at substitution tilings with finite local complexity by examining their admissible patch\pattern atlas, which is sometimes called their language. I have also seen ...