  In this paper we present two approaches to Lindenmayer systems: the
rule-based (or generative) approach, which focuses on L-systems as Thue
rewriting systems and a constraint-based (or model-theoretic) approach, in
which rules are abandoned in favour of conditions over allowable expressions in
the language (Pullum, 2019). We will argue that it is possible, for at least a
subset of L-systems and the languages they generate, to map string
admissibility conditions (the 'Three Laws') to local tree admissibility
conditions (cf. Rogers, 1997). This is equivalent to defining a model for those
languages. We will work out how to construct structure assuming only
superficial constraints on expressions, and define a set of constraints that
well-formed expressions of specific L-languages must satisfy. We will see that
L-systems that other methods distinguish turn out to satisfy the same model.
