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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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/*

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 * RecNode

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 * A record node.  Stores information for all the runs for a given period.

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 *

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 * Written by: Bryant Lee

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 * Date: 11/4/04

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 */

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#ifndef REC_NODE_H

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#define REC_NODE_H

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#include <map>

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class RecNode {

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 public:

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  unsigned long long currPeriod, numPeriodic, numTrials, largestorbit;

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  unsigned long long sumPeriod, sumPreperiod;

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  bool pending;

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  map<unsigned long long, unsigned long long> 

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    periodMap, // key = eventual pd., value = # points with this pd.

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    preperiodMap, // key = prepd., value = # points with this prepd.

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    orbitMap, // key = pd., value = # orbits with this pd.

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    periodicPeriodMap; //key = pd., value = # periodic points with this pd.

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 public:

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  //constructor

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  RecNode(unsigned int icPeriod, unsigned long long iNumTrials);

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  //recordOrbit

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  void recordOrbit(unsigned long long iOrbit);

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  //recordPeriod

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  //Use this to record points with eventual period "period" and

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  //preperiod "preperiod"

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  void recordPeriod(unsigned long long period, unsigned long long preperiod);

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  //recordPeriodicPeriod

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  //Use this to record _periodic_ points with period "period"

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  //This should be done in addition to recordPeriod above

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  void recordPeriodicPeriod(unsigned long long period);

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  //fraction periodic

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  double fractionPeriodic();

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  //numnonperiodic

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  unsigned long long numNonPeriodic();

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  //avgPeriod

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  double avgPeriod();

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  //avgPrePeriod

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  double avgPreperiod();

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  //maxpreperiod

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  double maxPreperiod();

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  //maxperiod

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  double maxPeriod();

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};

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#endif

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