Sequences defined by iterated morphisms

Let A be a finite alphabet and t a morphism from A*(the set of words with letters in A) into itself, that is to say, a map such that for every words A and B of A*: $$t\left( {AB} \right) = t\left( A \right)t\left( B \right)$$ (so that t is entirely defined by its values on the letters of A).