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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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/*

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 * Copyright (C) 2004 Bryant Lee

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 *

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 * This file is part of FDense.

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 *

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 * FDense is free software; you can redistribute it and/or modify

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 * it under the terms of the GNU General Public License as published by

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 * the Free Software Foundation; either version 2 of the License, or

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 * (at your option) any later version.

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 *

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 * FDense is distributed in the hope that it will be useful,

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 * but WITHOUT ANY WARRANTY; without even the implied warranty of

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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

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 * GNU General Public License for more details.

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 *

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 * You should have received a copy of the GNU General Public License

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 * along with FPeriod; if not, write to the Free Software

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 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA

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 */

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/*

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 * MList

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 * Has the list of m-words (lexicographic and truncated) not in any jointly

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 * periodic point at the current period.

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 *

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 * Written by: Bryant Lee

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 * Date: 9/02/05

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 */

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#ifndef M_LIST_H

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#define M_LIST_H

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#include <string>

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#include "StorageKey.h"

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#define byte unsigned char

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class MList {

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 public:

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  unsigned int currPeriod;

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  list <string> List;

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  bool pending;

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 public:

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  MList() {

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    pending = true; //see comment below

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  }

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  MList(unsigned int icPeriod) {

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    currPeriod = icPeriod;

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    //This indicates that the result for this MList element is not yet valid.

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    //The program flips pending to false when this MList element is filled in.

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    //This is used by FDense.

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    pending = true;

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  };

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};

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#endif

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