One dimension cellular automation in Python

• Instead of

  binrule = bin(rule)[2:]
  binrule = (8-len(binrule))*'0' + binrule
  

  you can use string formatting:

  binrule = '{:08b}'.format(rule)
  

• Let the caller compute binrule so this only gets done once.

• Better yet, precompute a transition table: a dictionary that maps cell triplets directly to the new values.

  transitions = dict(zip(ncells, binrule))
  

• Slightly more convenient than this

  for i in range(len(state)):
      cells = state[i-1] + state[i] + state[(i+1)%len(state)]
  

  is this:

  padded_state = state[-1] + state + state[0]
  for i in range(len(state)):
      cells = padded_state[i:i+3]
  

Putting it all together:

NCELLS = ['111','110','101','100','011','010','001','000']

def next_state(state, transition_table):
    padded_state = state[-1] + state + state[0]
    triplets = [padded_state[i:i+3] for i in range(len(state))]
    newstate = ''.join(transition_table[cells] for cells in triplets)
    return newstate

def wolfram(init_state, generations, rule):
    state = init_state
    binrule = '{:08b}'.format(rule)
    transitions = dict(zip(NCELLS, binrule))
    for i in range(generations):
        yield state 
        state = next_state(state, transitions)

for i in wolfram('000000000010000000000', 30, 30):
    print i