We say that a finite factor f of a word w is imaged if there exists a non-erasing morphism m, distinct from the identity, such that w contains m (f). We show that every infinite word contains an imaged factor of length at least 6 and that 6 is best possible. We show that every infinite binary word contains at least 36 distinct imaged factors and that 36 is best possible.
Ochem et al. (Tue,) studied this question.