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
*/
/**
* Represents a composition of poly functions
*
* Written by: Bryant Lee
* Date: 11/22/04
**/
#ifndef COMP_H
#define COMP_H
#include "Func.h"
#include <map>
#include <vector>
#include <string>
#include <fstream> //used in printDefinitions()
class Comp {
private:
int shiftSize; //#symbols in shift
map<string, Func *> funcStore; //available functions for composition
vector<Func *> composition; //the functions in the order to apply them
vector<string> compNames; //the composition as a list of names
//delete Func objects whose ptrs are in the funcStore map
void clearFuncStore();
public:
//constructor
Comp(int iShiftSize);
//destructor
~Comp();
//returnName
string returnName();
//printDefinitions
void printDefinitions(ofstream & fout);
//print
void print();
//set the composition
bool setComposition(const string & inStr);
//add a function available for composing
void addFunc(const string & inStr, string name, bool opt);
//return image of word x
void image(byte *word, int wordLength, byte *output);
//return image of word x
void image(unsigned int *word, int wordLength, unsigned int *output,
unsigned int blocks);
};
#endif