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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
# This class is to provide all utils functions that will not install with the tomato-engine via pip

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import numpy as np

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def point_matrix(size, value):

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    """

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    Creates an array of zeros with an element of specified value not medium.

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    """

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    try:

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        m, n = size

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    except TypeError:

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        m,n = size, size

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    state_matrix = np.zeros((m,n))

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    state_matrix[m // 2, n // 2] = value

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    return state_matrix

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