// Direct algorithm,  Evgeny Demidov,  11 November 2002
  
  import java.awt.*;
  import java.awt.image.*;
  import java.awt.event.*;
  import java.util.StringTokenizer;
  
  public class applet-math-fractal-direct extends java.applet.Applet implements MouseListener {
  double maxIZI2=10., Ymid=.0, Xmid=-.5, DelX=3.,  paramC,paramD;
  int MaxIt = 256,  maxColor = 96, w, h, pixArr[];
  Image img;             IndexColorModel RainbowColor;
  long generTime;        boolean   showXY = true;
  FormulaD formD;        TextField tfXY;
  
  public void init() {
    String s=getParameter("XYmidDelCD"); if (s != null) {
      StringTokenizer st = new StringTokenizer(s);
      Xmid = Double.valueOf(st.nextToken()).doubleValue();
      Ymid = Double.valueOf(st.nextToken()).doubleValue();
      DelX = Double.valueOf(st.nextToken()).doubleValue();
      paramC = Double.valueOf(st.nextToken()).doubleValue();
      paramD = Double.valueOf(st.nextToken()).doubleValue();}
    s=getParameter("MaxIt"); if (s != null) MaxIt=Integer.parseInt(s);
    s=getParameter("MaxIZI2");
    if (s != null) maxIZI2 = Double.valueOf(s).doubleValue();
    s=getParameter("MaxColor"); if (s != null) maxColor=Integer.parseInt(s);
    int M=maxColor/3,  M2=2*M;  maxColor = 3*M;     // maxColor is 3*int
    long M4 = (long)M*M*M*M;
    byte rColor[] = new byte[maxColor+2], bColor[] = new byte[maxColor+2],
         gColor[] = new byte[maxColor+2];
    for (int i = 1; i < M2; i++){                   // set Color Map
      long dum = M - i;  dum *=dum;  dum *=dum;
      gColor[i] =  bColor[(i+M) % maxColor] = rColor[(i+M2) % maxColor] =
          (byte)(255 - (255*dum)/M4);}
    rColor[maxColor+1] = gColor[maxColor+1] = bColor[maxColor+1] = (byte)200;
    RainbowColor = new IndexColorModel( 8, maxColor+2, rColor,gColor,bColor);
    w = getSize().width;   h = getSize().height;
    s=getParameter("showXY");
    if ( (s != null) && (s.equalsIgnoreCase("N")) ) showXY = false;
    else{
      setLayout(new BorderLayout());
      if (Ymid < 0.) s = ""+Xmid+" "+Ymid+"*i; "+(float)DelX;
         else s = ""+Xmid+" +"+Ymid+"*i; "+(float)DelX;
      tfXY = new TextField( s );
      add("South",  tfXY);
      h -= tfXY.getPreferredSize().height;}
    pixArr = new int[w*(h+2)];
    s=getParameter("Formula");
    if (s != null)
      try{  formD = (FormulaD)Class.forName( s ).newInstance();
      }catch(Exception e){}
    else  formD = new DirectJ3();
    Draw(Xmid, Ymid, DelX/w, formD, paramC, paramD );
    addMouseListener(this);
  }
  
  public void destroy() {  removeMouseListener(this); }
  public void mouseClicked(MouseEvent e) {}      //1.1 event handling
  public void mousePressed(MouseEvent e) {}
  public void mouseEntered(MouseEvent e) {}
  public void mouseExited(MouseEvent  e) {}
  
  public void mouseReleased(MouseEvent e) {
    Xmid = Xmid+(e.getX()-w/2)*DelX/w;
    Ymid = Ymid-(e.getY()-h/2)*DelX/w;
    if ( e.isControlDown() ) {
      if ( e.isShiftDown() )  DelX *=4.;  else  DelX *=2.;}
    else {
      if ( e.isShiftDown() )  DelX /=4.;  else  DelX /=2.;}
    Draw(Xmid, Ymid, DelX/w, formD, paramC, paramD);
    if (showXY) {
      if (Ymid < 0.) tfXY.setText( ""+Xmid+" "+Ymid+"*i; "+(float)DelX);
         else  tfXY.setText( ""+Xmid+" +"+Ymid+"*i; "+(float)DelX);};
    repaint();
  }
  
  public void paint(Graphics g) {
    g.drawImage(img, 0, 0, this);
    if (DelX > .01) drawLabel(g);
    showStatus( "Time=" + generTime + " msec");
  }
  
  public void drawLabel(Graphics gra) {
   double  R=0.,I=0., StZ=DelX/w;
   gra.setColor(Color.white);
   int x,y;
   String s=getParameter("sqrRID"); if (s != null) {
     StringTokenizer st = new StringTokenizer(s);
     double sqrRmid = Double.valueOf(st.nextToken()).doubleValue(),
     sqrImid = Double.valueOf(st.nextToken()).doubleValue();
     int sqr = (int)(Double.valueOf(st.nextToken()).doubleValue()/StZ);
     x = (w - sqr)/2 + (int)((sqrRmid-Xmid)/StZ);
     y = (h - sqr)/2 + (int)((Ymid - sqrImid) /StZ);
     gra.drawRect(x,y, sqr,sqr);}
   gra.setFont(
     new Font( gra.getFont().getName(), Font.BOLD, 15 ) );
   int maxLabel=0;
   while (true) {
     s=getParameter("lb"+maxLabel);
     if (s == null) break;
     StringTokenizer st = new StringTokenizer(s);
     x=w/2+(int)((Double.valueOf(st.nextToken()).doubleValue()-Xmid)/StZ);
     y=h/2+(int)((Ymid-Double.valueOf(st.nextToken()).doubleValue())/StZ);
     gra.drawString(st.nextToken(), x,y);
     maxLabel++; }
  }
  
  public void Draw( double Xmid, double Ymid, double Step,
    FormulaD form, double parC, double parD){
    double X,Y;
    int pix=w, ix,iy;
    generTime = System.currentTimeMillis();
    for (iy=0, Y=Ymid+Step*h/2; iy < h; iy++, Y-=Step) {
     for (ix=0, X=Xmid-Step*(w/2-1); ix < w; ix++, X+=Step, pix++) {
        pixArr[pix] =form.iterate(X, Y, parC, parD, maxIZI2, MaxIt, maxColor);
     }
    }
    img = createImage(new MemoryImageSource(w, h, RainbowColor, pixArr, w, w));
    generTime = System.currentTimeMillis()-generTime;
  }
  
  }
  
  abstract class FormulaD{
   abstract int iterate(double x, double y, double paramC, double paramD,
     double max, int MaxIt, int maxCol);
  }
  
  class DirectJ2 extends FormulaD{
   int iterate(double re, double im, double Cr, double Ci, double max,
     int MaxIt, int maxCol){
      double I=im, R=re,  I2=I*I, R2=R*R;   int n=0;
      if (R2+I2 > max) return 0;
      do  {  I=(R+R)*I+Ci;  R=R2-I2+Cr;  R2=R*R;  I2=I*I;  n++;
      } while ((R2+I2 < max) && (n < MaxIt) );
      if (n == MaxIt) return maxCol;  else return n % maxCol;
   }
  }
  class DirectJ2DE extends FormulaD{
   int iterate(double re, double im, double Cr, double Ci, double max,
     int MaxIt, int maxCol){
      double I=im, R=re,  I2=I*I, R2=R*R, Dr=.7,Di=.7,D, K=18;   int n=0;
      do  {
        D = (R*Dr - I*Di);  Di = (R*Di + I*Dr);  Dr = D;
        I=(R+R)*I+Ci;  R=R2-I2+Cr;  R2=R*R;  I2=I*I;  n++;
      } while ((R2+I2 < 100.) && (n < MaxIt) );
      if (n == MaxIt) return maxCol;
      else{
       R = -K*(Math.log(Math.log(R2+I2)*Math.sqrt((R2+I2)/(Dr*Dr+Di*Di)))-n*.693);
       if (R < 0) R=0;
       return (int)R % maxCol; };
   }
  }
  class DirectJ3 extends FormulaD{
   int iterate(double re, double im, double Cr, double Ci, double max,
    int MaxIt, int maxCol){
     double I=im, R=re,  I2=I*I, R2=R*R;   int n=0;
     do  {  I=(3.*R2-I2-1.08)*I;
            R=(R2-3.*I2-1.08)*R+1.032;  R2=R*R;  I2=I*I;  n++;
     } while ( (R2+I2 < 242.8415) && (n < MaxIt) );
     if (n == MaxIt) return maxCol;  else return n % maxCol;
   }
  }
  class DirectJ3a extends FormulaD{
   int iterate(double re, double im, double Cr, double Ci, double max,
    int MaxIt, int maxCol){
     double I=im, R=re,  I2=I*I, R2=R*R;   int n=0;
     do  {  I=(3.*R2-I2-1.6875)*I;
            R=(R2-3.*I2-1.6875)*R+.984;  R2=R*R;  I2=I*I;  n++;
     } while ( (R2+I2 < 3421.45) && (n < MaxIt) );
     if (n == MaxIt) return maxCol;  else return n % maxCol;
   }
  }
  class ManExp extends FormulaD{
    public int iterate(double cr, double ci, double Re0, double Im0, double max,
     int MaxIt, int maxCol){
      double I=Im0, R=Re0, r,i, exp;   int n=0;
      do{
        exp = Math.exp(R);
        i=Math.sin(I)*exp;  r=Math.cos(I)*exp;
        R=cr*r-ci*i;  I=ci*r+cr*i;  n++;
      } while ((R < 50.) && (n < MaxIt) );
      if (n == MaxIt) return maxCol;  else return n % maxCol;
    }
  }
  class Biquad extends FormulaD{
   int iterate(double A, double B, double Cr, double Ci, double max,
    int MaxIt, int maxCol){
      double X, X2=0;   int n=0, n0;
      do  {  X2 += A; X = X2*X2+B; X2 = X*X;  n++;
      } while ((X2 < 1000.) && (n < MaxIt) );
      n0 = n;  n = 0;
      if(A < 0){ X = Math.sqrt(-A); X2 = X*X;
       do  {  X2 += A; X = X2*X2+B; X2 = X*X;  n++;
       } while ((X2 < 1000.) && (n < MaxIt) );
       if (n == MaxIt){
        if (n0 == MaxIt) return maxCol;
        else return 2*maxCol/3;}
       else{
        if (n0 == MaxIt) return maxCol/2;
        else return ((n+n0)/2) % maxCol;}}
      else{
       if (n0 == MaxIt) return maxCol/2;
       else return n0 % maxCol;}
   }
  }
  class HenonDyn extends FormulaD{
   int iterate(double Xo, double Yo, double a, double b, double max,
    int MaxIt, int maxCol){
      double X=Xo, X2=X*X, X1, Y=Yo;   int n=0;
      do{ X1 = a + X2 + b*Y;  Y = X;  X = X1;  X2 = X*X;   n++;
      } while ((X2 < 1000.) && (n < MaxIt) );
      if (n == MaxIt) return maxCol;
      return n % maxCol;
   }
  }