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A (one dimensional) cellular automaton is a function1 F : Σ → Σ with the property that there is a K > 0 such that F (x)i depends only on the 2K + 1 coordinates xi−K , xi−K+1, . . . , xi−1, xi, xi+1, . . . , xi+K . A periodic point of σ is any x such that σ^p (x) = x for some p ∈ N, and a periodic point of F is any x such that F^q (x) = x for some q ∈ N. Given a cellular automaton F, a point x ∈ Σ is jointly periodic if there are p, q ∈ N such that σ^p (x) = F^q (x) = x, that is, it is a periodic point under both functions.

This project aims to explore the nature of one-dimensional Cellular Automata, in the hope of finding the structure of cellular automata through its periodic points.

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License: MIT
ubuntu2004
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1
import cellpylib as cpl

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import sys

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def gen_auto(init_size: int = 100, rule_number: int = 30, random: bool = True):

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    # Initialize the CA

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    auto = cpl.init_random(init_size) if random else cpl.init_simple(init_size)

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    # Evolve the CA according to the intended rule

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    return cpl.evolve(auto, timesteps=(init_size//2)+1, memoize="recursive",

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                     apply_rule=lambda n, c, t: cpl.nks_rule(n, rule_number))

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def main():

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    if (len(sys.argv) < 2):

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        raise Exception ("Need to provide rule(s) as arguments")

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    args = list(map(int, sys.argv[1:]))

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    autos = []

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    titles = []

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    for i in args:

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        titles.append("Rule {}".format(i))

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    for i in args:

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        autos.append(gen_auto(rule_number=i))

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    cpl.plot_multiple(autos, titles)

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if __name__ == "__main__":

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    main()

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