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
*/
/*
* RecNode
* A record node. Stores information for all the runs for a given period.
*
* Written by: Bryant Lee
* Date: 11/4/04
*/
#ifndef REC_NODE_H
#define REC_NODE_H
#include <map>
class RecNode {
public:
unsigned long long currPeriod, numPeriodic, numTrials, largestorbit;
unsigned long long sumPeriod, sumPreperiod;
bool pending;
map<unsigned long long, unsigned long long>
periodMap, // key = eventual pd., value = # points with this pd.
preperiodMap, // key = prepd., value = # points with this prepd.
orbitMap, // key = pd., value = # orbits with this pd.
periodicPeriodMap; //key = pd., value = # periodic points with this pd.
public:
//constructor
RecNode(unsigned int icPeriod, unsigned long long iNumTrials);
//recordOrbit
void recordOrbit(unsigned long long iOrbit);
//recordPeriod
//Use this to record points with eventual period "period" and
//preperiod "preperiod"
void recordPeriod(unsigned long long period, unsigned long long preperiod);
//recordPeriodicPeriod
//Use this to record _periodic_ points with period "period"
//This should be done in addition to recordPeriod above
void recordPeriodicPeriod(unsigned long long period);
//fraction periodic
double fractionPeriodic();
//numnonperiodic
unsigned long long numNonPeriodic();
//avgPeriod
double avgPeriod();
//avgPrePeriod
double avgPreperiod();
//maxpreperiod
double maxPreperiod();
//maxperiod
double maxPeriod();
};
#endif