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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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import math

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import random

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class InitialCondition:

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    def __init__(self, size = 64):

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        self.size = size

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class FarRightIsOne(InitialCondition):

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    def __init__(self, size):

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        self.state = self._build_state(size)

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        InitialCondition.__init__(self, size)

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    def _build_state(self, size):

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        state = [0] * size

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        state[-1] = 1

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        return state

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class MiddleStateIsOne(InitialCondition):

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    def __init__(self, size):

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        self.state = self._build_state(size)

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        InitialCondition.__init__(self, size)

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    def _build_state(self, size):

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        state = [0] * size

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        middle_index = math.floor(len(state) / 2) - 1

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        state[middle_index] = 1

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        return state

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class RandomState(InitialCondition):

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    def __init__(self, size):

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        self.state = [random.randint(0,1) for i in range(size)]

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        InitialCondition.__init__(self, size)

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