l-system

#!/usr/bin/env python

from __future__ import division
from numpy import *
import sys
import pylab
import optparse

def iterate(system,start,steps):
  s = start
  for step in xrange(steps):
    print 'step %d, size %d'%(step,len(s))
    s = ''.join(system.get(c,c) for c in s) 
  return s

def draw(turns,forward,s):
  theta = 0
  thetas = []
  lengths = []
  for c in s:
    if c in forward:
      thetas.append(theta)
      lengths.append(forward[c])
    if c in turns:
      theta += turns[c]
  return cumsum(lengths*cos(thetas)),cumsum(lengths*sin(thetas))

usage = 'usage: %prog koch|triangle|hilbert|other'
parser = optparse.OptionParser(usage)
options,args = parser.parse_args()
if len(args)!=1:
  parser.error('expected exactly one "kind" argument')
kind, = args

if kind=='koch':
  # http://en.wikipedia.org/wiki/Koch_snowflake#Representation_as_Lindenmayer_system
  axiom = 'F++F++F'
  system = {'F':'F-F++F-F'}
  turns = {'+':pi/3,'-':-pi/3}
  forward = {'+':1,'-':1}
  steps = 7
elif kind=='triangle':
  # http://en.wikipedia.org/wiki/L-system#Example_6:_Sierpinski_triangle
  axiom = 'A'
  system = {'A':'B-A-B','B':'A+B+A'}
  turns = {'+':pi/3,'-':-pi/3}
  forward = {'+':1,'-':1}
  steps = 8
  steps = 11
elif kind=='hilbert':
  axiom = 'A'
  system = {'A':'-BF+AFA+FB-','B':'+AF-BFB-FA+'}
  turns = {'+':pi/2, '-':-pi/2}
  forward = {'F':1}
  steps = 4
elif kind=='other':
  axiom = 'A'
  system = {'A':'+FA-FA'}
  turns = {'+':pi/1.2, '-':-pi/1.2}
  forward = {'F':1,'B':-1}
  steps = 10
else:
  print>>sys.stderr, 'unknown kind = %s'%kind
  sys.exit(1) 

x,y = draw(turns,forward,iterate(system,axiom,steps))
pylab.plot(x,y) 
pylab.show()