L-system (Lindenmayer system)

- developed by  Aristid Lindenmayer, a botanist/biologist , in1968 to simulate growth pattern.
- a recursive system written with formal grammar.
- AI, Self similarity, complexity, fractal
- tuple: G = (V, ω, P)

  where

• V (the alphabet) is a set of symbols containing elements that can be replaced (variables)
• ω (start, axiom or initiator) is a string of symbols from V defining the initial state of the system
• P is a set of production rules or productions defining the way variables can be replaced with combinations of constants and other variables. A production consists of two strings, the predecessor and the successor. For any symbol A in V which does not appear on the left hand side of a production in P, the identity production A → A is assumed; these symbols are called constants or terminals.

Lindenmayer's original L-system for modelling the growth of algae.

variables : A B

constants : none

start  : A

rules  : (A → AB), (B → A)

which produces:

n = 0 : A

n = 1 : AB

n = 2 : ABA

n = 3 : ABAAB

n = 4 : ABAABABA

n = 5 : ABAABABAABAAB

n = 6 : ABAABABAABAABABAABABA

n = 7 : ABAABABAABAABABAABABAABAABABAABAAB

source: http://en.wikipedia.org/wiki/L-system