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.
License: MIT
ubuntu2004
/*
* Copyright (C) 2004 Bryant Lee
*
* This file is part of FDense.
*
* FDense is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* FDense is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with FPeriod; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*/
/*
* MList
* Has the list of m-words (lexicographic and truncated) not in any jointly
* periodic point at the current period.
*
* Written by: Bryant Lee
* Date: 9/02/05
*/
#ifndef M_LIST_H
#define M_LIST_H
#include <string>
#include "StorageKey.h"
#define byte unsigned char
class MList {
public:
unsigned int currPeriod;
list <string> List;
bool pending;
public:
MList() {
pending = true; //see comment below
}
MList(unsigned int icPeriod) {
currPeriod = icPeriod;
//This indicates that the result for this MList element is not yet valid.
//The program flips pending to false when this MList element is filled in.
//This is used by FDense.
pending = true;
};
};
#endif