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 polynomial function in terms x[-s,t] mod N
*
* Written by: Bryant Lee
* Date: 10/31/04
**/
#ifndef FUNC_H
#define FUNC_H
#include "FuncNode.h"
#include <fstream> //for printing
#include <string>
#include <list>
#include <vector>
#include <map> //actually used only for opt polynomials
#include "StorageKey.h" //used only for opt polynomials lookup map
class Func {
private:
string str;
list<FuncNode*> fList; //list representation of function (poly repres.)
int* fTable; //lookup representation of function (table repres.)
int shiftSize; //#symbols in shift
int type; //0 = table, 1 = polynomial, 2= optimized polynomial
unsigned int span; //span (table repres. only)
unsigned int tablesize; //(table repres. only)
//-- member vars used for OPT functions ONLY
vector<int> optTerms;
map<StorageKey, byte> optLookupMap; //takes a vector of term values, returns answer
map<int, int> optFindTerm; //key = term #, val = coord in "compact" array
//--
//generates the index-th term of the image of x
byte timage(byte *word, int wordLength, int index);
unsigned int timage(unsigned int * word, int wordLength, int index);
// (used in opt polynomial functions only: for precomputing to lookup table)
// generates value of function based on inputs
byte timage_by_inputs(byte *inTerms, int numTerms,
const map<int,int> &optFindTerm);
public:
//constructor
Func(const string & iStr, int iShiftSize, bool opt);
//destructor
~Func();
//print
void print(ofstream & fout);
//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);
//return true if this is an opt polynomial function
bool isOpt();
};
#endif