View source for Morphic word

A infinite [[word]] over an alphabet $A$ which is invariant under a non-erasing endomorphism $\phi$ of the [[free monoid]] $A^*$: that is, a map $\phi : A \rightarrow A^*$ which does not map any letter of $A$ to the empty word.

Examples: the [[Thue–Morse sequence]] on $A = \{a,b\}$ is invariant under $a \mapsto ab$, $b \mapsto ba$; the [[Fibonacci word]] on $A = \{a,b\}$ is invariant under $a \mapsto ab$, $b \mapsto a$.

See also: [[D0L-sequence]].

====References====
* Allouche, Jean-Paul; Shallit, Jeffrey ''Automatic Sequences: Theory, Applications, Generalizations'' Cambridge University Press (2003) ISBN 978-0-521-82332-6 {{ZBL|1086.11015}}
* Lothaire, M. ''Combinatorics on Words'' (2nd ed.) Encyclopedia of Mathematics and Its Applications '''17''''  Cambridge University Press (1997) ISBN 0-521-59924-5 {{ZBL|0874.20040}}
* Lothaire, M. ''Algebraic Combinatorics on Words'' Encyclopedia of Mathematics and Its Applications '''90''' Cambridge University Press (2011 [2002]) ISBN 978-0-521-18071-9 {{ZBL|1221.68183}}
* Pytheas Fogg, N. (ed.) ''Substitutions in dynamics, arithmetics and combinatorics'' Lecture Notes in Mathematics '''1794''' Springer (2002) ISBN 978-3-540-44141-0 {{ZBL|1014.11015}}

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