// Helium Zee Poincare map,   Evgeny Demidov,  12 Apr 2003
  import java.awt.*;
  import java.awt.event.*;
  import java.awt.image.*;
  import java.util.StringTokenizer;
  public class applet-math-fractal-poincare-dzee extends java.applet.Applet implements MouseListener,
    KeyListener, ActionListener{
    int w,h,w2,h2,  Mx=70, My=50, it = 5;
    double Qo=3.5, Po=2.8, dP = .2,
           Q1_1, P1_1, Q2_1, P2_1, Q12, Q22,
           Pmax = 7,  ds=.0005, ds2, ds8,t;
    Image buffImage; Graphics buffGraphics;
    boolean   bClear = true;
    Label     lbDs;
    TextField tfDs;
    Button    btClear;
  
  public void init() {
    w = getSize().width;   h = getSize().height;
    w2 = w/2; h2 = h/2;
    buffImage = createImage(w, h);
    buffGraphics = buffImage.getGraphics();
    String s=getParameter("ds");
    if (s != null) ds = Double.valueOf(s).doubleValue();
    ds2 = ds*2; ds8 = ds/8;
    s=getParameter("dp");  if (s != null){
      StringTokenizer st = new StringTokenizer(s);
      it = Integer.parseInt(st.nextToken());
      Qo = Double.valueOf(st.nextToken()).doubleValue();
      Po = Double.valueOf(st.nextToken()).doubleValue();
      dP = Double.valueOf(st.nextToken()).doubleValue();}
    s=getParameter("mxy");  if (s != null){
      StringTokenizer st = new StringTokenizer(s);
      Mx = Integer.parseInt(st.nextToken());
      My = Integer.parseInt(st.nextToken());}
  
    lbDs = new Label("ds", Label.RIGHT); add(lbDs);
    tfDs = new TextField( "" + ds, 5);   add(tfDs);
    tfDs.addKeyListener(this);
    btClear = new Button("Clear"); btClear.addActionListener(this); add(btClear);
    addMouseListener(this);
    clear();
    buffGraphics.setColor(Color.black);
    for (int i = 0; i < it; i++){ 
      Po += dP;
      integrate();}
  }
  public void destroy(){
    removeMouseListener(this);
  }
  
  public void integrate() {
    double Q1_0, P1_0, Q2_0, P2_0, Q1_12, Q2_12, R12;
    t = 0;
    Q1_1 = Qo; P1_1 = Po;    Q2_1 = 0.; P2_1 = -4.;
    while(t < 50.){
      Q1_0 = Q1_1; Q2_0 = Q2_1;    P1_0 = P1_1; P2_0 = P2_1;
      Q12 = Q1_1*Q1_1;  Q22 = Q2_1*Q2_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*(1. - Q22/R12))*ds2;
      P2_1 = P2_0 + Q2_12*(2. - P1_0*P1_0/8. - Q12*(1. + Q12/R12))*ds2;
  
      Q1_1 = Q1_12 + P1_1*Q22*ds8;
      Q2_1 = Q2_12 + P2_1*Q12*ds8;
      t += ds;
      if( (Math.abs(P1_1) > Pmax) || (Math.abs(P2_1) > Pmax) ) break;
      if (Q2_1*Q2_0 < 0.){
        int x  = (int)(Mx*Q1_1), y  = (int)(My*P1_1);
        buffGraphics.drawLine( x,h2-y, x,h2-y);}
    }
    repaint();
  }
  
  public void mouseClicked(MouseEvent e){}       // event handling
  public void mousePressed(MouseEvent e) {
    int mx0 = e.getX(),  my0 = h2 - e.getY();
    Qo = (double)mx0/Mx;  Po = (double)my0/My;
    buffGraphics.setColor(Color.red);
    integrate();
  }
  public void mouseReleased(MouseEvent e){}
  public void mouseEntered(MouseEvent e) {}
  public void mouseExited(MouseEvent e)  {}
  public void actionPerformed(ActionEvent e){
    clear(); repaint();
  }
  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;
      }catch ( NumberFormatException ne) {}
    }
    e.consume();
  }
  
  public void clear(){
    buffGraphics.setColor(Color.white);
    buffGraphics.fillRect(0, 0, w, h);
    buffGraphics.setColor(Color.lightGray);
    buffGraphics.drawLine(0,0,0,h);
    buffGraphics.drawLine(0,h2,w,h2);
  }
  
  public void paint(Graphics g) {
    g.drawImage(buffImage, 0, 0, this);
    showStatus("Q=" + (float)Qo + "  P=" + (float)Po + "   s=" + (float)t );
  }
  public void update(Graphics g){ paint(g); }
  
  }