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 FPeriod.
*
* FPeriod 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.
*
* FPeriod 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
*/
/* FuncNode
* Node used to represent a single piece of a function (term, operator,
* or constant)
*
* Written by: Bryant Lee
* Date: 10/29/04
*/
#ifndef FUNC_NODE_H
#define FUNC_NODE_H
#define byte unsigned char
#include <fstream> //for printing
#include <map> //for termValue_by_inputs only
class FuncNode {
public:
int type; // 1 = term, 2 = operator, 3 = constant
int val; // term index, specific operator, or constant's value
//Operator: 1 = +, 2 = -, 3 = *, 4 = ^;
//No argument constructor
FuncNode();
//primary constructor
FuncNode(int iType, int iVal);
//copy constructor
FuncNode(const FuncNode &m);
//copy assignment
const FuncNode& operator=(const FuncNode &right);
//deepCopy
FuncNode* deepCopy();
//If holding a constant, returns the constant
//If holding a term, returns the term value based on
// the array x
int termValue(byte *x, int wLength, int i);
//If holding a constant, returns the constant
//If holding a term, returns the term value based on
// the array x
int termValue(unsigned int *x, int wLength, int i);
//like above except used by inputs, rather than by actual word
int termValue_by_inputs(byte *itTerms, int numTerms,
const map<int,int> &optFindTerm);
//print
void print(ofstream & fout);
//relational operators
bool operator==(const FuncNode &right) const;
bool operator!=(const FuncNode &right) const;
bool operator<(const FuncNode &right) const;
bool operator>(const FuncNode &right) const;
bool operator<=(const FuncNode &right) const;
bool operator>=(const FuncNode &right) const;
};
#endif