// Symbolic x=x*x+c Iterations,  Evgeny Demidov, 1 July 2002
  import java.awt.*;
  import java.awt.event.*;
  import java.util.StringTokenizer;
  
  public class applet-math-fractal-iterate1 extends java.applet.Applet
         implements MouseMotionListener, KeyListener {
  Image buffImage;          Graphics buffGraphics;
  int maxIt = 10, N = 1, numIt,  w,h,h2,  iXo,iYo,  lbSize = 30,
      xFun[],yFun[],  xGist[],yGist[], xIt[],yIt[];
  double C = -.5, maxIYI = 2., Xo = 0., Yo = 0., delX = 4., Step;
  Label     lbIt, lbN, lbC;
  TextField tfIt, tfN, tfC;
  
  public void init() {
    h = Integer.parseInt(getParameter("height")) - lbSize;    h2 = h / 2;
    w = Integer.parseInt(getParameter("width"));
    String s=getParameter("XYoDel"); if (s != null) {
      StringTokenizer st = new StringTokenizer(s);
      Xo = Double.valueOf(st.nextToken()).doubleValue();
      Yo = Double.valueOf(st.nextToken()).doubleValue();
      delX = Double.valueOf(st.nextToken()).doubleValue();}
    s=getParameter("MaxIt"); if (s != null) maxIt=Integer.parseInt(s);
    s=getParameter("N"); if (s != null) N=Integer.parseInt(s);
    s = getParameter("C");  if (s != null) C = Double.valueOf(s).doubleValue();
    xFun = new int[h];    for (int i = h-1; i >= 0; i--) xFun[i] = i;
    yFun = new int[h];
    buffImage = createImage(w, h);
    buffGraphics = buffImage.getGraphics();
    lbC = new Label("C");             add(lbC);
    tfC = new TextField( "" + C, 9);  add(tfC);
    lbN = new Label("N");             add(lbN);
    tfN = new TextField( "" + N, 3);  add(tfN);
    lbIt = new Label("It");                add(lbIt);
    tfIt = new TextField( "" + maxIt, 3);  add(tfIt);
    tfC.addKeyListener(this);   tfN.addKeyListener(this);
    tfIt.addKeyListener(this);
    addMouseMotionListener(this);
  
    Step = delX / h;
    iXo = h2 - (int)(Xo/Step);   iYo = h2 + (int)(Yo/Step);
    draw();
  }
  
  public void destroy() {  removeMouseMotionListener(this); }
  public void keyTyped(KeyEvent e) {}
  public void keyPressed(KeyEvent e) {}
  public void keyReleased(KeyEvent e) {
    final int keyEnter = 10;
    if (e.getKeyCode() == keyEnter) {
      try{
        N = Integer.parseInt( tfN.getText() );
        maxIt = Integer.parseInt( tfIt.getText() );
        C = Double.valueOf(tfC.getText()).doubleValue();
      }catch ( NumberFormatException ne) {}
      draw();    repaint();
    }
    e.consume();
  }
  
  public void mouseMoved(MouseEvent e) {}
  public void mouseDragged(MouseEvent e) {
    C = Yo + Step*(h2 - (e.getY() - lbSize));
    tfC.setText( Float.toString((float)C) );
    draw();    repaint();
    e.consume();
  }
  
  public void draw() {
    xGist = new int[maxIt<<1 + 1];    yGist = new int[maxIt<<1 + 1];
    xIt = new int[maxIt+1];    yIt = new int[maxIt+1];
    for (int i = 0; i <= maxIt; i++)
      xIt[i] = h + (int)((w-h-1)*(double)i/(maxIt));
    generateFun();        iterations();
    buffGraphics.setColor(Color.white);
    buffGraphics.fillRect(0, 0, w  - 1, h - 1);
    buffGraphics.setColor(Color.black);
    buffGraphics.drawRect(0, 0, w  - 1, h - 1);
    buffGraphics.drawLine(h, 0, h, h - 1);
    buffGraphics.drawLine(0, iYo, w  - 1, iYo);
    buffGraphics.drawLine(iXo, 0, iXo, h - 1);
    buffGraphics.setColor(Color.green);
    int iYe = (int)((Yo-Xo)/Step);
    buffGraphics.drawLine(0, h+iYe, h, iYe);
    buffGraphics.setColor(Color.blue);
    buffGraphics.drawPolyline( xFun, yFun, h );
    buffGraphics.setColor(Color.red);
    buffGraphics.drawPolyline( xGist, yGist, numIt<<1 );
    buffGraphics.drawPolyline( xIt, yIt, numIt+1 );
    for (int i = 0; i <= maxIt; i++)
      buffGraphics.fillRect(xIt[i]-1, yIt[i]-1, 3, 3);
  }
  
  public void paint(Graphics g) {
    g.drawImage(buffImage, 0, lbSize, this);
    showStatus( "It=" + numIt);
  }
  
  public void iterations() {
    double X = 0.,  Y;         int bakX, bakY;
    xGist[0] = ( bakX = h2 - (int)(Xo/Step) );
    yGist[0] = yIt[0] = h2 + (int)(Yo/Step);
    for (int i = 1; i <= maxIt; i++) {
      Y = X;
      for (int n = N; n > 0; n--)   Y = Y*Y + C;
      int i2 = i<<1;
      for (int n = N; n > 0; n--)   
      xGist[i2 - 1] = bakX;
      yGist[i2 - 1] = ( bakY = h2 - (int)((Y - Yo)/Step) );
      xGist[i2] = ( bakX = h2 + (int)((Y - Xo)/Step) );
      yGist[i2] = yIt[i] = bakY;
      X = Y;    numIt = i;
      if (Math.abs(Y) > maxIYI) break;
    }
  }
  
  public void generateFun() {
    for (int i = h - 1; i >= 0; i--) {
      double X = Xo + (i-h2)*Step;
      for (int n = N; n > 0; n--)   X = X*X + C;
      yFun[i] = h2 - (int)((X - Yo)/Step);
    }
  }
  
  public void update(Graphics g)   {  paint(g);  }
  
  }