0Lsystem

0L-system, short for deterministic 0L-system (D0L-system), is a type of Lindenmayer system used to model growth processes and generate fractal-like patterns through parallel string rewriting. In a 0L-system, production rules are applied to all symbols simultaneously and independently of context. The '0' denotes the absence of contextual information: a symbol is replaced by a fixed string every iteration, without regard to its neighbors. The system is deterministic when each symbol has a single, fixed replacement.

Formal definition: An alphabet V of symbols, an axiom ω ∈ V*, and a morphism h: V → V* that assigns to each symbol a replacement w_a ∈ V*. The stage n word is ω_n, defined by ω_0 = ω and ω_{n+1} = h(ω_n). Rewrites are applied in parallel, i.e., h is applied to every symbol in ω_n to produce ω_{n+1}.

Example: Let V = {A,B} with rules A → AB and B → A, starting from ω = A. The generated sequence begins A, AB, ABA, ABAAB, ABAABABAAB, and so on.

Applications: 0L-systems are used to model plant morphology, generate fractal curves, and, via turtle graphics interpretations, create complex graphical structures. They are the simplest class of L-systems and can be extended with variants such as stochastic rules or context-sensitive forms (1L, 2L) for more complex modeling.

History and terminology: The concept was introduced by Aristid Lindenmayer in 1968 to formalize growth processes in biology and has since become a standard tool in computer graphics and formal language theory.