The Narayana Morphism and Related Words

The Narayana morphism $\nu$ maps $0\to 01$, $1\to 2$, $2\to 0$ and has a fixed point $\mathbf{n}=n_0{n}_1{n}_2\cdots =\mathtt{0120010120120}\cdots$. In this paper we study the properties of this word and related words using automata theory.