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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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from tomato.classes import cell

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class Cell(cell.CellTemplate):

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    def update(self, state_matrix):

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        self.state_matrix = state_matrix

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        if self.value == 0:

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            if self.live_neighbors == 1:

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                self.value = 1

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    @property

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    def neighbors(self):

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        return self.moore_neighborhood

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    @property

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    def live_neighbors(self):

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        return sum(self.neighbors)

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    @staticmethod

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    def display(val):

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        return (255, 255, 255) if val else (0, 0, 0)

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    @staticmethod

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    def from_display(val):

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        return 0 if (val == (0, 0, 0)).all() else 1

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