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
*/
#include "RecNode.h"
#include <map>
//constructor
RecNode::RecNode(unsigned int icPeriod, unsigned long long iNumTrials) {
currPeriod = icPeriod;
sumPeriod = 0;
sumPreperiod = 0;
numPeriodic = 0;
numTrials = iNumTrials;
largestorbit = 0;
//for FProbPeriod: pending flag says that this RecNode is not filled in yet
// which is helpful in case of a crash
//for FPeriod and FDense: this is not used
pending = true;
}
//recordOrbit
void RecNode::recordOrbit(unsigned long long orbit) {
map<unsigned long long, unsigned long long>::iterator mult;
if((mult = orbitMap.find(orbit)) != orbitMap.end()) {
mult->second++;
}
else {
orbitMap.insert(pair<unsigned long long, unsigned long long>(orbit,1));
}
}
//recordperiod
void RecNode::recordPeriod(unsigned long long period,
unsigned long long preperiod) {
map<unsigned long long, unsigned long long>::iterator mult;
if(period > largestorbit)
largestorbit = period;
sumPeriod += period;
sumPreperiod += preperiod;
if((mult = periodMap.find(period)) != periodMap.end()) {
mult->second++;
}
else {
periodMap.insert(pair<unsigned long long, unsigned long long>(period,1));
}
if((mult = preperiodMap.find(preperiod)) != preperiodMap.end()) {
mult->second++;
}
else {
preperiodMap.insert(pair<unsigned long long,unsigned long long>(preperiod,1));
}
}
//recordPeriodicPeriod
void RecNode::recordPeriodicPeriod(unsigned long long period) {
map<unsigned long long,unsigned long long>::iterator mult;
if((mult = periodicPeriodMap.find(period)) != periodicPeriodMap.end()) {
mult->second++;
}
else {
periodicPeriodMap.insert(pair<unsigned long long,unsigned long long>(period,1));
}
}
//fractionperiodic
double RecNode::fractionPeriodic() {
return ((double) numPeriodic)/((double) numTrials);
}
//numnonperiodic
unsigned long long RecNode::numNonPeriodic() {
return numTrials - numPeriodic;
}
//avgperiod
double RecNode::avgPeriod() {
return ((double) sumPeriod)/((double) numTrials);
}
//avgpreperiod
double RecNode::avgPreperiod() {
return ((double) sumPreperiod)/((double) numTrials);
}
//maxpreperiod
double RecNode::maxPreperiod() {
map<unsigned long long, unsigned long long>::const_reverse_iterator rit;
rit = preperiodMap.rbegin();
if(rit !=
(map<unsigned long long, unsigned long long>::const_reverse_iterator)
preperiodMap.rend())
return rit->first;
else
return 0;
}
//max period
double RecNode::maxPeriod() {
map<unsigned long long,unsigned long long>::const_reverse_iterator rit;
rit = periodMap.rbegin();
if(rit !=
(map<unsigned long long,unsigned long long>::const_reverse_iterator)
periodMap.rend())
return rit->first;
else
return 0;
}