From n-grams to trees in Lindenmayer systems

TL;DR

This paper explores two approaches to Lindenmayer systems—rule-based and constraint-based—and demonstrates how string conditions can be mapped to local tree conditions for certain L-systems, enabling new structural modeling.

Contribution

It introduces a method to translate string admissibility conditions into local tree conditions for a subset of L-systems, bridging generative and model-theoretic approaches.

Findings

Mapping string conditions to tree conditions is feasible for some L-systems.

Both approaches satisfy the same structural model.

Superficial constraints can define well-formed expressions.

Abstract

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.