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Here is the code which generates this applet:
// ForestFire.java
import java.awt.*;
import java.awt.event.*;
import comphys.graphics.*;
import comphys.Easy;
public class ForestFire extends Animation {
double pt = 0.2; // initial probability of tree at site
double p = 0.2; // growth probability
double f = 0.1; // lightning strike probability
int L = 30; // number of trees = L * L
final int EMPTY = 0;
final int ALIVE = 1;
final int AFIRE = 2;
final int STUMP = 3;
final int SHOOT = 4;
final int LIGHT = 5;
int[][] site; // current state of forest
int[][] oldSite; // from previous time step
int[] np; // for cluster labeling
boolean instantaneous; // lightning model instantaneous spreading
int t; // time
void copyToOld () {
for (int i = 0; i <= L + 1; i++) {
for (int j = 0; j <= L + 1; j++) {
oldSite[i][j] = site[i][j];
}
}
}
void initial () {
if (site == null || site.length < L + 2) {
site = new int[L + 2][L + 2];
oldSite = new int[L + 2][L + 2];
np = new int[(L + 2) * (L + 2)];
}
// empty boundary
site[0][0] = site[0][L + 1] = EMPTY;
site[L + 1][0] = site[L + 1][L + 1] = EMPTY;
for (int i = 1; i <= L; i++) {
site[0][i] = site[i][0] = site[i][L + 1] = site[L + 1][i] = EMPTY;
}
// interior trees alive with probability p_t
for (int i = 1; i <= L; i++) {
for (int j = 1; j <= L; j++) {
if (Math.random() < pt) {
if (!instantaneous && Math.random() < f)
site[i][j] = AFIRE;
else
site[i][j] = ALIVE;
} else {
site[i][j] = EMPTY;
}
}
}
copyToOld();
t = 0;
}
void simpleSpreadingRule () {
// model on page 523
for (int i = 1; i <= L; i++) {
for (int j = 1; j <= L; j++) {
switch (oldSite[i][j]) {
case STUMP:
site[i][j] = EMPTY;
case EMPTY:
if (Math.random() < p)
site[i][j] = SHOOT;
break;
case SHOOT:
site[i][j] = ALIVE;
case ALIVE:
if (oldSite[i][j - 1] == AFIRE ||
oldSite[i][j + 1] == AFIRE ||
oldSite[i - 1][j] == AFIRE ||
oldSite[i + 1][j] == AFIRE )
site[i][j] = AFIRE;
break;
case LIGHT:
case AFIRE:
site[i][j] = STUMP;
}
}
}
}
// Hoshen-Kopelman cluster labeling algorithm
int proper (int label) {
// recursive function
if (np[label] == label)
return label;
else
return proper(np[label]);
}
void label_min (int x, int y, int left, int down) {
// both neighbors occupied, determine minimum cluster number
if (site[left][y] == site[x][down]) {
// both neighbors have same cluster label
site[x][y] = site[left][y];
} else {
// determine minimum cluster label
int cl_left = proper(site[left][y]);
int cl_down = proper(site[x][down]);
int nmax = cl_left;
int nmin = cl_down;
if (cl_down > cl_left) {
nmax = cl_down;
nmin = cl_left;
}
site[x][y] = nmin;
if (nmin != nmax)
np[nmax] = nmin; // set improper label nmax = nmin
}
}
void neighbor (int x, int y) { // determine occupancy of neighbors
int down = y - 1;
int left = x - 1;
if (site[x][down] * site[left][y] > 0) { // both neighbors occupied
label_min(x, y, left, down);
} else if (site[x][down] > 0) { // down neighbor occupied
site[x][y] = site[x][down];
} else { // left neighbor occupied
site[x][y] = site[left][y];
}
}
int maxClusterNumber;
void assign () {
// assign cluster numbers to occupied sites
for (int i = 0; i < np.length; i++)
np[i] = 0;
int ncluster = 0; // cluster number
for (int y = 1; y <= L; y++) {
for (int x = 1; x <= L; x++) {
if (site[x][y] < 0) { // site occupied
int down = y - 1; // square lattice
int left = x - 1;
if (site[x][down] + site[left][y] == 0) {
++ncluster; // new cluster
site[x][y] = ncluster;
np[ncluster] = ncluster; // proper label
} else {
neighbor(x, y);
}
}
}
}
// assign proper labels to cluster array
maxClusterNumber = 0;
for (int y = 1; y <= L; y++) {
for (int x = 1; x <= L; x++) {
site[x][y] = proper(site[x][y]);
if (site[x][y] > maxClusterNumber)
maxClusterNumber = site[x][y];
}
}
}
boolean[] clusterOnFire;
void instantaneousSpreadingRule () {
// model on page 524
for (int i = 1; i <= L; i++) {
for (int j = 1; j <= L; j++) {
switch (oldSite[i][j]) {
case STUMP:
oldSite[i][j] = site[i][j] = EMPTY;
case EMPTY:
if (Math.random() < p)
oldSite[i][j] = SHOOT;
break;
case SHOOT:
oldSite[i][j] = ALIVE;
case ALIVE:
site[i][j] = -1; // needs to be assigned to a cluster
if (Math.random() < f)
oldSite[i][j] = LIGHT;
break;
case LIGHT:
oldSite[i][j] = AFIRE;
site[i][j] = EMPTY;
break;
case AFIRE:
site[i][j] = EMPTY;
oldSite[i][j] = STUMP;
break;
}
}
}
// use Hoshen-Kopelman algorithm (page 426) to label clusters
assign();
// determine which clusters are on fire
if (clusterOnFire == null ||
clusterOnFire.length < maxClusterNumber + 1)
clusterOnFire = new boolean[maxClusterNumber + L];
for (int i = 1; i <= maxClusterNumber; i++)
clusterOnFire[i] = false;
for (int i = 1; i <= L; i++) {
for (int j = 1; j <= L; j++) {
if (oldSite[i][j] == LIGHT)
clusterOnFire[site[i][j]] = true;
}
}
for (int i = 1; i <= L; i++) {
for (int j = 1; j <= L; j++) {
if (site[i][j] == EMPTY) {
site[i][j] = oldSite[i][j];
} else {
if (clusterOnFire[site[i][j]]) {
if (oldSite[i][j] == LIGHT)
site[i][j] = LIGHT;
else
site[i][j] = AFIRE;
} else {
site[i][j] = oldSite[i][j];
}
}
}
}
}
void takeStep () {
copyToOld();
if (instantaneous) {
instantaneousSpreadingRule();
} else {
simpleSpreadingRule();
}
++t;
}
Color lightGreen = new Color(51, 255, 0);
Color darkGreen = new Color(0, 153, 0);
Color brown = new Color(204, 153, 0);
class Forest extends Plot {
public void paint () {
clear();
setWindow(0, L, 0, L);
for (int i = 1; i <= L; i++) {
for (int j = 1; j <= L; j++) {
switch (site[i][j]) {
case EMPTY:
osg.setColor(brown);
break;
case ALIVE:
osg.setColor(darkGreen);
break;
case AFIRE:
setColor("yellow");
break;
case STUMP:
setColor("black");
break;
case SHOOT:
osg.setColor(lightGreen);
break;
case LIGHT:
setColor("red");
break;
}
boxArea(i - 1, i + 0.1, j - 1, j + 0.1);
}
}
}
}
Forest forest;
TextField pTextField, fTextField;
Checkbox instantaneousBox;
Reader LReader, ptReader;
void pGet () {
try {
p = new Double(pTextField.getText()).doubleValue();
} catch (Exception e) {
pTextField.setText("" + Easy.format(p, 4));
}
}
void fGet () {
try {
f = new Double(fTextField.getText()).doubleValue();
} catch (Exception e) {
fTextField.setText("" + Easy.format(f, 4));
}
}
public void init () {
initial();
add(forest = new Forest());
add(LReader = new Reader("L = ", L));
add(ptReader = new Reader("p_t = ", pt, 4));
Panel pPanel = new Panel(new GridLayout(1, 2));
pPanel.add(new Label("P(new tree) ="));
pTextField = new TextField("" + Easy.format(p, 4));
pTextField.addActionListener(new ActionListener () {
public void actionPerformed (ActionEvent ae) {
pGet();
}
});
pPanel.add(pTextField);
add(pPanel);
Panel fPanel = new Panel(new GridLayout(1, 2));
fPanel.add(new Label("P(set fire) ="));
fTextField = new TextField("" + Easy.format(f, 4));
fTextField.addActionListener(new ActionListener () {
public void actionPerformed (ActionEvent ae) {
fGet();
}
});
fPanel.add(fTextField);
add(fPanel);
add(instantaneousBox = new Checkbox("Lightning!", instantaneous));
instantaneousBox.addItemListener(new ItemListener() {
public void itemStateChanged (ItemEvent ie) {
instantaneous = instantaneousBox.getState();
}
});
addControlPanel();
}
public void step () {
takeStep();
forest.repaint();
}
public void reset () {
L = LReader.readInt();
pt = ptReader.readDouble();
pGet();
fGet();
initial();
forest.repaint();
}
public static void main (String[] args) {
ForestFire forestFire = new ForestFire();
forestFire.frame("Forest Fire Automaton Model", 430, 600);
}
}
The following applet is based on the program Hopfield.java, which is an implementation of Problems 15.12 and 15.13 on pages 523-4 of the textbook.
Here is the code which generates this applet:
// Hopfield.java
import comphys.graphics.*;
import comphys.Easy;
public class Hopfield extends Animation {
static final int plotWidth = 400;
static final int plotHeight = 400;
static final int maxN = 100;
int N;
int[][][][] J; // connection strength
int[][] B; // bias term
int[][][] L;
int M;
int P; // probability
int[] H; // Hamming distances
double sumH;
int[] X, Y; // visited neurons
int t;
void initial () {
N = 10;
M = 1;
P = 30;
J = new int [10][10][10][10];
B = new int [10][10];
L = new int [10][10][10];
H = new int [26];
X = new int [26];
Y = new int [26];
}
void initializeNetwork() {
int i, j, k, l, m;
for (i = 0; i < N; ++i)
for (j = 0; j < N; ++j)
for (k = 0; k < N; ++k)
for (l = 0; l < N; ++l)
J[i][j][k][l] = 0;
for (m = 0; m < M; ++m)
for (i = 0; i < N; ++i)
for (j = 0; j < N; ++j)
for (k = 0; k < N; ++k)
for (l = 0; l < N; ++l)
J[i][j][k][l] += Letter[m][i][j] * Letter[m][k][l];
for (i = 0; i < N; ++i)
for (j = 0; j < N; ++j)
J[i][j][i][j] = B[i][j] = 0;
for (i = 0; i < N; i++)
for (j = 0; j < N; j++)
for (k = 0; k < N; k++)
for (l = 0; l < N; l++)
B[i][j] += J[i][j][k][l];
if (L.length < M)
L = new int [M][N][N];
for (m = 0; m < M; ++m)
for (i = 0; i < N; ++i)
for (j = 0; j < N; ++j)
if (Math.random() > P / 100.0)
L[m][i][j] = Letter[m][i][j];
else L[m][i][j] = -Letter[m][i][j];
t = 0;
iNext = 0;
jNext = -1;
}
boolean regularSweep;
boolean bias;
int iNext;
int jNext = -1;
void takeStep() {
if (++jNext == N) {
jNext = 0;
if (++iNext == N)
iNext = 0;
}
for (int m = 0; m < M; ++m) {
int i = 0;
int j = 0;
if (regularSweep) {
i = iNext;
j = jNext;
} else {
i = (int) (Math.random() * N);
j = (int) (Math.random() * N);
}
X[m] = j;
Y[m] = i;
double E_flip = 0;
for (int k = 0; k < N; ++k)
for (int l = 0; l < N; ++l)
E_flip += J[i][j][k][l] * L[m][k][l];
if (bias)
E_flip -= 0.5 * B[i][j];
E_flip *= 2 * L[m][i][j] / (double) M;
if (E_flip < 0)
L[m][i][j] = -L[m][i][j];
}
computeHammingDistances();
++t;
}
void computeHammingDistances() {
sumH = 0;
for (int m = 0; m < M; ++m) {
H[m] = 0;
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
int d = Letter[m][i][j] - L[m][i][j];
H[m] += d * d;
}
}
sumH += H[m] / (double) (4 * N * N);
}
}
boolean running;
class Network extends Plot {
public void paint () {
clear();
int Lx = (int) Math.sqrt(M);
if (Lx * Lx != M)
Lx += 1;
int Ly = Lx;
int margin = plotWidth / (N * Lx);
int letterSize = (plotWidth - (Lx + 1) * margin) / Lx;
int pixelSize = letterSize / N;
int radius = pixelSize / 4;
if (radius < 1)
radius = 1;
int m = 0;
int x = 0;
int y = 0;
while (m < M) {
for (int j = 0; j < N; ++j) {
for (int i = 0; i < N; ++i) {
if (L[m][j][i] == 1) {
if (H[m] == 0)
setColor("black");
else setColor("red");
} else setColor("yellow");
osg.fillRect(margin +
x * (margin + letterSize) + i * pixelSize,
margin +
y * (margin + letterSize) + j * pixelSize,
pixelSize - 2, pixelSize - 2);
}
}
if (running && H[m] != 0) {
setColor("green");
osg.fillOval(margin + radius +
x * (margin + letterSize) + X[m] * pixelSize,
margin + radius +
y * (margin + letterSize) + Y[m] * pixelSize,
2 * radius, 2 * radius);
}
if (++x == Lx) {
++y;
x = 0;
}
++m;
}
setColor("blue");
osg.drawString("t = " + t, 40, plotHeight - 10);
osg.drawString("Total Hamming Distance = " + Easy.format(sumH, 4),
150, plotHeight - 10);
}
}
Network network;
Reader MReader, PReader, sweepReader, biasReader;
public void init () {
initial();
add(network = new Network());
add(MReader = new Reader("Memories =", M));
add(PReader = new Reader("% Errors =", P));
add(sweepReader = new Reader("Regular sweep", regularSweep));
add(biasReader = new Reader("Bias term", bias));
addControlPanel();
initializeNetwork();
computeHammingDistances();
}
public void step () {
takeStep();
computeHammingDistances();
if (sumH == 0) {
stopAnimation();
running = false;
} else {
running = true;
}
network.repaint();
}
public void reset () {
M = MReader.readInt();
if (M < 1)
M = 1;
if (M > 26)
M = 26;
P = PReader.readInt();
if (P < 0)
P = 0;
if (P > 100)
P = 100;
regularSweep = sweepReader.readBoolean();
bias = biasReader.readBoolean();
initializeNetwork();
computeHammingDistances();
running = false;
network.repaint();
}
public static void main (String[] args) {
Hopfield hopfield = new Hopfield();
hopfield.frame("Hopfield neural network model", 430, 600);
}
int Letter[][][] = {
{
{-1, -1, -1, -1, +1, +1, -1, -1, -1, -1},
{-1, -1, -1, +1, +1, +1, +1, -1, -1, -1},
{-1, -1, +1, +1, -1, -1, +1, +1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, +1, +1, -1},
{-1, +1, +1, +1, +1, +1, +1, +1, +1, -1},
{+1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{+1, +1, +1, -1, -1, -1, -1, +1, +1, +1},
{+1, +1, -1, -1, -1, -1, -1, -1, +1, +1},
{+1, +1, -1, -1, -1, -1, -1, -1, +1, +1},
{+1, +1, -1, -1, -1, -1, -1, -1, +1, +1}
}, {
{-1, +1, +1, +1, +1, +1, +1, -1, -1, -1},
{-1, +1, +1, +1, -1, -1, +1, +1, -1, -1},
{-1, -1, +1, +1, -1, -1, +1, +1, -1, -1},
{-1, -1, +1, +1, -1, -1, +1, +1, -1, -1},
{-1, -1, +1, +1, +1, +1, +1, -1, -1, -1},
{-1, -1, +1, +1, +1, +1, +1, -1, -1, -1},
{-1, -1, +1, +1, -1, -1, +1, +1, -1, -1},
{-1, -1, +1, +1, -1, -1, +1, +1, -1, -1},
{-1, +1, +1, +1, -1, -1, +1, +1, -1, -1},
{-1, +1, +1, +1, +1, +1, +1, -1, -1, -1}
}, {
{-1, -1, +1, +1, +1, +1, +1, +1, -1, -1},
{-1, +1, +1, +1, +1, +1, +1, +1, -1, -1},
{-1, +1, +1, +1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, +1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, +1, +1, +1, +1, +1, -1, -1},
{-1, -1, +1, +1, +1, +1, +1, +1, -1, -1}
}, {
{+1, +1, +1, +1, +1, +1, +1, +1, -1, -1},
{+1, +1, +1, +1, +1, +1, +1, +1, +1, -1},
{-1, +1, +1, -1, -1, -1, -1, +1, +1, -1},
{-1, +1, +1, -1, -1, -1, -1, +1, +1, -1},
{-1, +1, +1, -1, -1, -1, -1, +1, +1, -1},
{-1, +1, +1, -1, -1, -1, -1, +1, +1, -1},
{-1, +1, +1, -1, -1, -1, -1, +1, +1, -1},
{-1, +1, +1, -1, -1, -1, -1, +1, +1, -1},
{+1, +1, +1, +1, +1, +1, +1, +1, -1, -1},
{+1, +1, +1, +1, +1, +1, +1, -1, -1, -1}
}, {
{+1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{+1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{+1, +1, -1, -1, -1, -1, -1, -1, -1, -1},
{+1, +1, -1, -1, -1, -1, -1, -1, -1, -1},
{+1, +1, +1, +1, +1, +1, -1, -1, -1, -1},
{+1, +1, +1, +1, +1, +1, -1, -1, -1, -1},
{+1, +1, -1, -1, -1, -1, -1, -1, -1, -1},
{+1, +1, -1, -1, -1, -1, -1, -1, -1, -1},
{+1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{+1, +1, +1, +1, +1, +1, +1, +1, +1, +1}
}, {
{-1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{-1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, +1, +1, +1, +1, -1, -1, -1},
{-1, +1, +1, +1, +1, +1, +1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{-1, +1, +1, -1, -1, -1, -1, -1, -1, -1}
}, {
{-1, +1, +1, +1, +1, +1, +1, +1, +1, -1},
{+1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{+1, +1, +1, -1, -1, -1, -1, -1, -1, -1},
{+1, +1, -1, -1, -1, -1, -1, -1, -1, -1},
{+1, +1, -1, -1, -1, -1, -1, -1, -1, -1},
{+1, +1, -1, -1, -1, -1, +1, +1, +1, +1},
{+1, +1, -1, -1, -1, -1, -1, +1, +1, +1},
{+1, +1, +1, -1, -1, -1, -1, +1, +1, +1},
{+1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{-1, +1, +1, +1, +1, +1, +1, +1, +1, +1}
}, {
{-1, +1, +1, -1, -1, -1, -1, -1, +1, +1},
{-1, +1, +1, -1, -1, -1, -1, -1, +1, +1},
{-1, +1, +1, -1, -1, -1, -1, -1, +1, +1},
{-1, +1, +1, -1, -1, -1, -1, -1, +1, +1},
{-1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{-1, +1, +1, +1, +1, +1, +1, +1, +1, +1},
{-1, +1, +1, -1, -1, -1, -1, -1, +1, +1},
{-1, +1, +1, -1, -1, -1, -1, -1, +1, +1},
{-1, +1, +1, -1, -1, -1, -1, -1, +1, +1},
{-1, +1, +1, -1, -1, -1, -1, -1, +1, +1}
}, {
{-1, -1, +1, +1, +1, +1, +1, +1, -1, -1},
{-1, -1, +1, +1, +1, +1, +1, +1, -1, -1},
{-1, -1, -1, -1, +1, +1, -1, -1, -1, -1},
{-1, -1, -1, -1, +1, +1, -1, -1, -1, -1},
{-1, -1, -1, -1, +1, +1, -1, -1, -1, -1},
{-1, -1, -1, -1, +1, +1, -1, -1, -1, -1},
{-1, -1, -1, -1, +1, +1, -1, -1, -1, -1},
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Questions or comments:
phygons@acsu.buffalo.edu