L-System

An L-system is a formal grammar introduced by the biologist Aristid Lindenmayer to model plant growth. It consists of an alphabet, an initial string, and a set of rewriting rules applied to every symbol simultaneously at each iteration. Interpreting the resulting string as drawing instructions produces a structure.

Parallel rewriting is what distinguishes it from an ordinary grammar and what makes it a good model for growth: every part of the organism develops at once. A handful of rules and half a dozen iterations produce ferns, trees, and shells with remarkable fidelity.

Extensions broaden the range considerably. Stochastic rules choose among alternatives probabilistically, so no two instances are identical. Context-sensitive rules depend on neighbouring symbols, allowing signals to propagate through the structure. Parametric systems attach values to symbols, so lengths and angles evolve rather than being fixed.

Beyond botany, L-systems generate road networks and street grids — the recursive branching of a main road into secondaries into local streets is naturally expressed as rewriting. Making that usable for a simulated city usually means quantising the output to a grid and generating incrementally, so that the layout is stable and extendable rather than regenerated whole.