// Helium Periodic Orbits,   Evgeny Demidov,  2 Apr 2003
  import java.awt.*;
  import java.awt.event.*;
  import java.awt.image.*;
  import java.util.StringTokenizer;
  public class applet-math-fractal-hepo extends java.applet.Applet implements MouseListener,
    KeyListener, ActionListener, Runnable {
    Thread thIntegrate;
    int w,h,w2,h2,w4,  delay=0,
        Mx=100, My=25, x1,x2,y1,y2;
    double Q1_0= .6, P1_0=0, Q2_0= .5, P2_0=0,
           Q1_1, P1_1, Q2_1, P2_1, Q12,Q22, E,  ds=.001, ds2, ds8,t;
    Image buffImage; Graphics buffGraphics;
    boolean bRun = false,  bClear = true;
    Label     lbDs,  lbDelay;
    TextField tfDs,  tfDelay;
    Button    btRun, btClear;
  
  public void init() {
    w = getSize().width;   h = getSize().height;
    w2 = w/2; h2 = h/2; w4 = w/4;
    buffImage = createImage(w, h);
    buffGraphics = buffImage.getGraphics();
    String s=getParameter("Delay");
    if (s != null) delay = Integer.parseInt(s);
    s=getParameter("coord");
    if (s != null){
      StringTokenizer st = new StringTokenizer(s);
      Q1_0 = Double.valueOf(st.nextToken()).doubleValue();
      P1_0 = Double.valueOf(st.nextToken()).doubleValue();
      Q2_0 = Double.valueOf(st.nextToken()).doubleValue();
      P2_0 = Double.valueOf(st.nextToken()).doubleValue();}
    Q2_0 = Q1_0;  E = -1;
    P1_0 = Math.sqrt(14 - 4*Q1_0*Q1_0); P2_0 = -P1_0;
  
    Q1_1 = Q1_0; P1_1 = P1_0;  Q2_1 = Q2_0; P2_1 = P2_0;
    Q12 = Q1_1*Q1_1;  Q22 = Q2_1*Q2_1;
  //  E = ((P1_1*P1_1 - 16.)/Q12 + (P2_1*P2_1 - 16.)/Q22)/8. + 1/(Q12 + Q22);
    ds2 = ds*2; ds8 = ds/8;
    x1  = (int)(Mx*Q1_1); y1  = (int)(My*P1_1);
    x2  = (int)(Mx*Q2_1); y2  = -(int)(My*P2_1);
  
    lbDs = new Label("ds", Label.RIGHT); add(lbDs);
    tfDs = new TextField( "" + ds, 3);   add(tfDs);
    lbDelay = new Label("Delay", Label.RIGHT); add(lbDelay);
    tfDelay = new TextField( "" + delay, 4);   add(tfDelay);
    tfDs.addKeyListener(this);
    tfDelay.addKeyListener(this);
    btRun = new Button("Run ");  btRun.addActionListener(this);  add(btRun);
    btClear = new Button("Clear"); btClear.addActionListener(this); add(btClear);
    addMouseListener(this);
  }
  public void destroy() {
    removeMouseListener(this);
  }
  
  public void run() {
    double Q1_12, Q2_12, R12;
    while(true) {
      if ( Thread.currentThread() != thIntegrate ) return;
      for (int i=0; i < 3; i++){
       Q1_0 = Q1_1; Q2_0 = Q2_1;    P1_0 = P1_1; P2_0 = P2_1;
  
       Q1_12 = Q1_0 + P1_0*Q22*ds8;
       Q2_12 = Q2_0 + P2_0*Q12*ds8;
       Q12 = Q1_12*Q1_12;    Q22 = Q2_12*Q2_12;  R12 = Q12 + Q22;  R12 *= R12;
  
       P1_1 = P1_0 + Q1_12*(2. - P2_0*P2_0/8. + Q22*(E - Q22/R12))*ds2;
       P2_1 = P2_0 + Q2_12*(2. - P1_0*P1_0/8. + Q12*(E - Q12/R12))*ds2;
  
       Q1_1 = Q1_12 + P1_1*Q22*ds8;
       Q2_1 = Q2_12 + P2_1*Q12*ds8;
       Q12 = Q1_1*Q1_1;  Q22 = Q2_1*Q2_1;
       t += ds;
      }
      E = ((P1_1*P1_1 - 16.)/Q12 + (P2_1*P2_1 - 16.)/Q22)/8. + 1/(Q12 + Q22);
      repaint();
      try {  Thread.sleep( delay );
      } catch (InterruptedException e) {}
    }
  }
  
  public void stop() {
    thIntegrate = null;
  }
  public void mouseClicked(MouseEvent e){}       // event handling
  public void mousePressed(MouseEvent e) {
    int mx0 = e.getX() - w4,  my0 = h2 - e.getY();
    if (mx0 > 0){
      Q1_1 = Q1_0 = 2*(double)mx0/Mx;
      P1_1 = P1_0 = (double)my0/My;
      x1  = (int)(Mx*Q1_1); y1  = (int)(My*P1_1);
      Q12 = Q1_1*Q1_1;}
    else{
      Q2_1 = Q2_0 =-2*(double)mx0/Mx;
      P2_1 = P2_0 =-(double)my0/My;
      x2  = (int)(Mx*Q2_1); y2  = -(int)(My*P2_1);
      Q22 = Q2_1*Q2_1;}
    E = ((P1_1*P1_1 - 16.)/Q12 + (P2_1*P2_1 - 16.)/Q22)/8. + 1/(Q12 + Q22);
    repaint();
  }
  public void mouseReleased(MouseEvent e){}
  public void mouseEntered(MouseEvent e) {}
  public void mouseExited(MouseEvent e)  {}
  public void actionPerformed(ActionEvent e){
    if ( e.getActionCommand().equals("Clear") ) { bClear = true;   repaint();}
    else{
     if (bRun) {
       bRun = false;  btRun.setLabel("Run "); thIntegrate = null;}
     else { bRun = true;  btRun.setLabel("Stop");
       thIntegrate = new Thread(this); thIntegrate.start();}
    }
  }
  public void keyTyped(KeyEvent e) {}
  public void keyPressed(KeyEvent e) {}
  public void keyReleased(KeyEvent e) {
    final int keyEnter = 10;
    if (e.getKeyCode() == keyEnter) {
      try{
        ds = Double.valueOf(tfDs.getText()).doubleValue();
        ds2 = ds*2; ds8 = ds/8;
        delay = Integer.parseInt( tfDelay.getText() );
      }catch ( NumberFormatException ne) {}
    }
    e.consume();
  }
  
  public void paint(Graphics g) {
    if (bClear){
      buffGraphics.setColor(Color.white);
      buffGraphics.fillRect(0, 0, w, h);
      buffGraphics.setColor(Color.lightGray);
      buffGraphics.drawLine(w4,0,w4,h);
      buffGraphics.drawLine(0,h2,w2,h2);
      buffGraphics.drawLine(w2,h,w,h-w2);
      bClear = false;}
    buffGraphics.setColor(Color.blue);
    int x,y, xx;
    x  = (int)(Mx*Math.abs(Q1_1)); y  = (int)(My*P1_1);
    if (Q1_1 < 0.) y = -y;
    buffGraphics.drawLine( w4+(x1>>1),h2-y1, w4+(x>>1),h2-y);
    y1 = y;
    buffGraphics.setColor(Color.red);
    xx  = (int)(Mx*Math.abs(Q2_1)); y  = (int)(My*P2_1);
    if (Q2_1 > 0.) y = -y;
    buffGraphics.drawLine( w4-(x2>>1),h2-y2, w4-(xx>>1),h2-y);
    buffGraphics.setColor(Color.black);
    buffGraphics.drawLine( w2+x1,h-x2, w2+x,h-xx);
    x1 = x;  x2 = xx;  y2 = y;
    g.drawImage(buffImage, 0, 0, this);
    showStatus("E="+(float)E+"   s="+(float)t );
  }
  public void update(Graphics g){ paint(g); }
  
  }