An important part of formal language theory is concerned with the combinatorial structure of languages. One of the most basic combinatorial properties of a language is the repetition of subwords. Accordingly, a language L is called repetitive if, for each positive integer n, there exists a word w \in L that contains a subword of the form x^n for some non-empty word x. Already Axel Thue studied the repetition of subwords in (infinite) words. Actually he was interested in obtaining long words without repetitions, so-called square-free words.
For context-free languages repetition of subwords is a very natural property. Indeed a context-free language is not repetitive if and only if it is finite. This is an immediate consequence of the pumping lemma for context-free languages. Actually, an infinite context-free language L is not only repetitive, but it is even strongly repetitive, that is, there exists a non-empty word x such that x^n is a subword of L for all positive integers n. Hence, a context-free language is repetitive if and only if it is strongly repetitive. This equivalence is not true in general.
The context-free languages are generated by the context-free grammars, which form a special class of N. Chomsky's phrase-structure grammars. However, since the late 1960s also a different approach based on iterating morphisms has been employed successfully to describe and define languages. These are the so-called L-systems, which were intoduced by A. Lindenmayer in connection with biological considerations. The simplest type of L-system is the D0L-system, where a language L is generated from a given word w by iterating a given morphism f, that is, L={f^n (w) | n \ge 0}. Here we are interested in the repetitiveness of languages generated by morphisms and related concepts.