  In this paper we will attempt to classify Lindenmayer systems based on
properties of sets of rules and the kind of strings those rules generate. This
classification will be referred to as a parametrization of the L-space: the
L-space is the phase space in which all possible L-developments are
represented. This space is infinite, because there is no halting algorithm for
L-grammars; but it is also subjected to hard conditions, because there are
grammars and developments which are not possible states of an L-system: a very
well-known example is the space of normal grammars. Just as the space of normal
grammars is parametrized into Regular, Context-Free, Context-Sensitive, and
Unrestricted (with proper containment relations holding among them; see
Chomsky, 1959: Theorem 1), we contend here that the L-space is a very rich
landscape of grammars which cluster into kinds that are not mutually
translatable.

Formal Languages and Automata Theory;Computation and Language