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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 FPeriod.

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 *

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 * FPeriod 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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 * FPeriod 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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/* FuncNode

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 * Node used to represent a single piece of a function (term, operator,

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 * or constant)

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 *

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 * Written by: Bryant Lee

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 * Date: 10/29/04

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 */

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#ifndef FUNC_NODE_H

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#define FUNC_NODE_H

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#define byte unsigned char

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#include <fstream> //for printing

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#include <map> //for termValue_by_inputs only

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class FuncNode {

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 public:

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  int type; // 1 = term, 2 = operator, 3 = constant

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  int val; // term index, specific operator, or constant's value

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  //Operator: 1 = +, 2 = -, 3 = *, 4 = ^;

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  //No argument constructor

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  FuncNode();

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  //primary constructor

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  FuncNode(int iType, int iVal);

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  //copy constructor

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  FuncNode(const FuncNode &m);

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  //copy assignment

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  const FuncNode& operator=(const FuncNode &right);

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  //deepCopy

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  FuncNode* deepCopy();

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  //If holding a constant, returns the constant

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  //If holding a term, returns the term value based on

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  // the array x

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  int termValue(byte *x, int wLength, int i);

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  //If holding a constant, returns the constant

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  //If holding a term, returns the term value based on

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  // the array x

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  int termValue(unsigned int *x, int wLength, int i);

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  //like above except used by inputs, rather than by actual word

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  int termValue_by_inputs(byte *itTerms, int numTerms,

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			  const map<int,int> &optFindTerm);

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  //print

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  void print(ofstream & fout);

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  //relational operators

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  bool operator==(const FuncNode &right) const;

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  bool operator!=(const FuncNode &right) const;

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  bool operator<(const FuncNode &right) const;

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  bool operator>(const FuncNode &right) const;

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  bool operator<=(const FuncNode &right) const;

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  bool operator>=(const FuncNode &right) const;

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};

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#endif

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