Toeplitz Words, Generalized Periodicity and Periodically Iterated Morphisms

We consider so-called Toeplitz words which can be viewed as generalizations of one-way infinite periodic words. We compute their subword complexity, and show that they can always be generated by iterating periodically a finite number of morphisms. Moreover, we define a structural classification of Toeplitz words which is reflected in the way in which they can be generated by iterated morphisms.