L-System Grammar

From Wikipedia:

"An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures. L-systems were introduced and developed in 1968 by Aristid Lindenmayer, a Hungarian theoretical biologist and botanist at the University of Utrecht. Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development. L-systems have also been used to model the morphology of a variety of organisms[1] and can be used to generate self-similar fractals."

Examples

* The following examples are explained thoroughly in the Wikipedia article above

1) Algae Growth Example

alphabet=['A', 'B']
constants=[]
rules={'A':'AB', 'B':'A'}

grammar=LSystemGrammar(alphabet, constants, rules)

axiom='A'
steps=7

string=grammar.generate(axiom, steps)

OUTPUT: 'ABAABABAABAABABAABABAABAABABAABAAB'

2) Fractal Tree Example

alphabet=['0', '1']
constants=['[', ']']
rules={'1':'11', '0':'1[0]0'}

grammar=LSystemGrammar(alphabet, constants, rules)

axiom='0'
steps=3

string=grammar.generate(axiom, steps)

OUTPUT: '1111[11[1[0]0]1[0]0]11[1[0]0]1[0]0'