Hidden automatic sequences

An automatic sequence is a letter-to-letter coding of fixed point uniform morphism. More generally, morphic sequences are codings points arbitrary morphisms. There many examples where an, priori, with non-uniform morphism happens to be an sequence. example the Lysënok \(a \to aca\), \(b d\), \(c b\), \(d c\), which also \(2\)-automatic Such identification useful for describing dynamical systems generated by point. We give several ways uncover such hidden sequences, and present examples. focus in particular on morphisms associated Grigorchuk groups.Keywords: Morphic groups.Mathematics Subject Classifications: 11B85, 68R15, 37B10