Lsystemsare

L-systems are a formalism used to model growth processes of plants and other organisms. They were introduced by Aristid Lindenmayer in 1968 as a parallel rewriting system and formal grammar. An L-system 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 each generation, the production rules are applied simultaneously to all symbols in the current string, producing the next string. This parallel application allows complex structures to emerge from simple rules.

Variants of L-systems include deterministic context-free L-systems (where each symbol has a single replacement), 0L- and 1L-systems (with increasing constraints), stochastic L-systems (SL-systems) where symbols replace according to probabilities, and parametric L-systems in which symbols carry parameters. Context-sensitive L-systems extend the rules to depend on neighboring symbols.

Interpretation often uses turtle graphics: a symbol like F draws a line, + and - rotate, and [ and ] save and restore the current position and state to model branching. By adjusting parameters such as angle, length, and production rules, a wide variety of plant-like forms can be generated, from simple ferns to complex trees and fractal structures.

Applications include modeling biological growth, generating realistic vegetation for computer graphics and games, and exploring mathematical properties of parallel rewriting systems. L-systems provide a compact, rule-based framework for simulating morphogenesis and growth.