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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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Wolfram Codes (Wikipedia)

https://towardsdatascience.com/algorithmic-beauty-an-introduction-to-cellular-automata-f53179b3cf8f

https://playgameoflife.com/ (Conway's Game of Life)

https://pypi.org/project/tomato-engine/

https://codeberg.org/CSL.dev/tomato-rules

https://github.com/lantunes/cellpylib

https://datarepository.wolframcloud.com/search?i=NKS

https://www.wolframscience.com/nks/chap-6--starting-from-randomness/

https://mathworld.wolfram.com/ElementaryCellularAutomaton.html

https://www.wolfram.com/language/11/core-language/periodicity-in-cellular-automata.html?product=mathematica

https://content.wolfram.com/uploads/sites/13/2018/02/03-2-1.pdf

https://academic.oup.com/ptp/article/89/2/325/1847821\

https://wpmedia.wolfram.com/uploads/sites/13/2018/02/15-1-1.pdf

http://atlas.wolfram.com/01/01/

https://www.researchgate.net/publication/3043410_Theory_and_Applications_of_Cellular_Automata

https://www.stephenwolfram.com/publications/academic/cellular-automata/

https://content.wolfram.com/uploads/sites/34/2020/07/computation-theory-cellular-automata.pdf

https://arxiv.org/pdf/0802.3626.pdf

https://www.sciencedirect.com/science/article/pii/S0022000072800138 Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures

https://www.gabrielnivasch.org/fun/cycle-detection

https://drive.google.com/file/d/16H_lrjeaBJqWvcn07C_w-6VNHldJ-ZZl/view

https://resources.wolframcloud.com/PacletRepository/resources/KlausSutner/Automata/ Automata theory package in mathmatica.

https://arxiv.org/pdf/math/0607178.pdf

cs.cmu.edu/~sutner/cdm.html

http://www.math.umd.edu/~mboyle/papers/18nov2006.pdf

https://www.fi.muni.cz/reports/files/2010/FIMU-RS-2010-10.pdf [Computing Strongly Connected Components in Parallel on CUDA]