Cellular automaton

def cellular_automaton(string, pattern_number, generations):
    patterns = {}
    pattern_list = ['...', '..x', '.x.','.xx','x..', 'x.x', 'xx.','xxx']
    n = len(string)

    for i in range(7,-1, -1):
        if pattern_number/(2**i) == 1:
            patterns[pattern_list[i]] = 'x'
            pattern_number = pattern_number - 2**i
        else:
            patterns[pattern_list[i]] = '.'

    for j in range(0, generations):
        new_string = ''
        for i in range(0, n):
            pattern = string[i-1] + string[i] + string[(i+1)%n]
            new_string = new_string + patterns[pattern]
        string = new_string
    return new_string