LSysteme

L-Systeme (L-systems) are a class of formal grammars developed by Aristid Lindenmayer in 1968 to model growth processes in biological systems, especially plants. They describe how complex structures can arise from simple, parallel rewriting rules applied to strings of symbols over successive generations.

A standard L-Systeme consists of an alphabet of symbols, an initial string called the axiom, and a set of production rules that replace each symbol with a new string. In parallel L-systems, every symbol is rewritten simultaneously at each generation, producing a new string. Variants include deterministic context-free L-systems (D0L), where each symbol has at most one replacement; 0L and 1L systems; stochastic L-systems that assign probabilities to rules; and parametric or extended L-systems that attach numerical parameters to symbols and rules to model varying growth conditions. Context-sensitive L-systems allow the replacement of a symbol to depend on neighboring symbols.

Interpretation plays a central role: the generated strings are typically fed to a turtle-like graphics interpreter. Commands commonly include F for moving forward with drawing, f for moving forward without drawing, + and - to rotate by a fixed angle, and [ and ] to save and restore the current state, enabling branching. By iterating the rewriting rules and interpreting the result, one can generate plant‑like architectures, trees, fractal curves, and other natural forms.

Applications of L-Systeme are widespread in computer graphics and procedural modeling. They provide a compact, rule‑based framework for simulating botanical growth, producing realistic plant morphologies, and enabling algorithmic art and the generation of complex, self-similar structures.