I'm just noodling around with the Python-Omega parser (https://gitorious.org/python-omega), and I used it to implement a simple version of the Anabaena catenula "simulator" from the book "The Algorithmic Beauty of Plants" http://algorithmicbotany.org/papers/#abop One interesting thing is that the DOL-system is meant to evaluate its terms in para…

Algorithmic Beauty of Plants.py

#!/usr/bin/env python
'''
A simple demonstration of a deterministic and context-free "DOL-system"
"...used to simulate the development of a fragment of a multicellular
filament such as that found in the blue-green bacteria Anabaena catenula..."
- "The Algorithmic Beauty of Plants" http://algorithmicbotany.org/papers/#abop

Implemented by simple parsers in the Omega parser language (a variant of
Warth's OMeta language.) https://gitorious.org/python-omega
'''
from itertools import chain
from omega import BaseParser


class AnabaenaCatenulaStringParser(BaseParser):
  __grammar = '''

    Ar = "Ar" -> ('AlBr') ;
    Al = "Al" -> ('BlAr') ;
    Br = "Br" -> ('Ar') ;
    Bl = "Bl" -> ('Al') ;

    strand = ( Ar | Al | Br | Bl )+:cells -> (''.join(cells)) ;

    '''


class AnabaenaCatenulaSequenceParser(BaseParser):
  __grammar = '''

    Ar = 'Ar' -> (('Al', 'Br')) ;
    Al = 'Al' -> (('Bl', 'Ar')) ;
    Br = 'Br' -> (('Ar',)) ;
    Bl = 'Bl' -> (('Al',)) ;

    strand = ( Ar | Al | Br | Bl )+:cells -> (tuple(chain(*cells))) ;

    '''


def demo(strand, parser, iterations=5):
  for _ in range(iterations):
    print strand
    strand = parser.match(strand)
  print strand


if __name__ == '__main__':
  print __doc__
  print
  demo('Ar', AnabaenaCatenulaStringParser)
  print
  demo(('Ar',), AnabaenaCatenulaSequenceParser)
  print

Example output:

Ar
AlBr
BlArAr
AlAlBrAlBr
BlArBlArArBlArAr
AlAlBrAlAlBrAlBrAlAlBrAlBr
('Ar',)
('Al', 'Br')
('Bl', 'Ar', 'Ar')
('Al', 'Al', 'Br', 'Al', 'Br')
('Bl', 'Ar', 'Bl', 'Ar', 'Ar', 'Bl', 'Ar', 'Ar')
('Al', 'Al', 'Br', 'Al', 'Al', 'Br', 'Al', 'Br', 'Al', 'Al', 'Br', 'Al', 'Br')

Also, I confused the two kinds of possible parallelism in the description above. There are two: the cells are normally growing and reproducing each independently, and they know what they are turning into next so they don't have to perform the "strand" rule. In contrast, the parser/simulator has to walk the strand of cell/terms in order by design, and it tests the options in the "strand" rule (on each term) in order as well. The model and the living system jibe.