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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
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from tomato.classes import cell

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import tomato as tt

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from tomato.functions import utils

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from tomato_rules import game_of_life as rule

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def main():

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    cell_size = 4

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    dimensions = 200

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    state_matrix = utils.random_matrix(dimensions, 2)

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    board = tt.Board(rule, cell_size=cell_size)

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    board.start(state_matrix)

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if __name__ == '__main__':

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    main()

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