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1-Dimensional Cellular Automata
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| #!/usr/bin/env python3 | |
| """Generate 1-dimensional automata based on various rules""" | |
| def ngrams(iterable, n=1): | |
| """Generate ngrams from an iterable""" | |
| return zip(*(iterable[i:] for i in range(n))) | |
| def states(state, rule, left_pad='0', right_pad='0'): | |
| """Generate a stream of states from an initial state and a rule""" | |
| next_state = ''.join(rule[''.join(window)] for window in ngrams(state, 3)) | |
| padding = '{}{}{}' | |
| yield state, states(padding.format(left_pad, next_state, right_pad), rule) | |
| def automata(state, rule, n): | |
| """Generate n generations given an initial state and a rule""" | |
| tail = states(state, rule) | |
| for _ in range(n): | |
| head, tail = next(tail) | |
| yield head | |
| if __name__ == '__main__': | |
| SYMBOLS = '01' | |
| WIDTH = 80 | |
| LEFT, RIGHT = (SYMBOLS[0] * (WIDTH // 2),) * 2 | |
| GENERATIONS = 30 | |
| # generate all possible 3 bit windows/keys | |
| keys = ['{:0>3b}'.format(i) for i in range(8)] | |
| # generate all possible bytes | |
| bytes_ = ['{:0>8b}'.format(i) for i in range(256)] | |
| # construct all 256 possible rule mappings of 3-bit keys to 1-bit values | |
| rules = [dict(zip(keys, byte)) for byte in bytes_] | |
| # define the seed state with a single bit activated in the middle | |
| initial_state = LEFT + SYMBOLS[1] + RIGHT | |
| # show the first 30 generations for each of the 256 rules | |
| label = 'rule #{}: {}' | |
| for i, rule in enumerate(rules, 1): | |
| print(label.format(i, rule)) | |
| for state in automata(initial_state, rule, GENERATIONS): | |
| print(state) |
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| $ ./automata.py | |
| rule #1: {'000': '0', '001': '0', '010': '0', '011': '0', '100': '0', '101': '0', '110': '0', '111': '0'} | |
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