/* This java applet program generates a fractal image of a fern.
 * The algorithm is based on the Iterated Function System (IFS). 
 * It is generated by four affine maps of the plane.
 * They are of the form x'=Ax+(e,f), where A=(a,b|c,d) is a 2x2 matrix. 
 * There is a slight subtlety in the drawing of the picture. The four 
 * mappings are not used with equal probability. The probabilities p are 
 * given in the table. This does not affect the actual IFS Attractor, 
 * but does affect the computergraphical appearance. You could use for
 * example the table below.
 *  #    a      b      c      d      e      f       p 
 *  1    0      0      0      0.16   0      0       0.01 
 *  2    0.85   0.04   -0.04  0.85   0      1.6     0.85 
 *  3    0.2    -0.26  0.23   0.22   0      1.6     0.07 
 *  4    -0.15  0.28   0.26   0.24   0      0.44    0.07 
 *
 * Write the HTML code as:
 * <applet code= Fern.class width=600 height=400> </applet>
 * C.A. Bertulani, 08/15/2000
*/
import java.awt.*;
import java.applet.*;

public class Fern extends Applet {
  double mxx,myy,bxx,byy;

  public void Fernplot(Graphics g)
  {
     int i;
     double x, y, xn, yn, r;
     int pex,pey;
     int max, seed;
     max=15000;
     seed=68111;
     x=0.5;                         /* starting point */
     y=0.0;
     convert(0.0,1.0,1.0,-0.5);
     setBackground(Color.black);
     g.setColor(Color.green);
     for(i=1; i<=max; i++)                /* iterations */
     {
        r=Math.random();  /* generate a random number */
        if (r <= 0.02)                    /* case 1 */
        {
           xn = 0.5;
           yn = 0.27*y;
        }
        else if((r>0.02) && (r<=0.17))    /* case 2 */
        {
          xn = -0.139*x + 0.263*y + 0.57;
          yn =  0.246*x + 0.224*y - 0.036;
        }
        else if ((r>0.17) && (r<=0.3))    /* case 3 */
        {
          xn = 0.17*x  - 0.215*y + 0.408;
          yn = 0.222*x + 0.176*y + 0.0893;
        }
        else                              /* case 4 */
        {
          xn = 0.781*x + 0.034*y + 0.1075;
          yn = -0.032*x + 0.739*y + 0.27;
        }
        x=xn;
        y=yn;
        pex=(int)(mxx*x+bxx);
        pey=(int)(myy*y+byy);
        g.drawLine(pex,pey,pex,pey);   /* output to screen */
     }
  }

   void convert(double xiz,double ysu,double xde,double yinf)
  {//to convert to screen coordinates. Gives mxx, bxx for
    //x_screen=mxx*x_world + byy same for y.
    double maxx,maxy,xxfin,xxcom,yyin,yysu;
    maxx=600;
    maxy=450;
    xxcom=0.15*maxx;
    xxfin=0.75*maxx;
    yyin=0.8*maxy;
    yysu=0.2*maxy;
    mxx=(xxfin-xxcom)/(xde-xiz);
    bxx=0.5*(xxcom+xxfin-mxx*(xiz+xde));
    myy=(yyin-yysu)/(yinf-ysu);
    byy=0.5*(yysu+yyin-myy*(yinf+ysu));
  }

  public void paint(Graphics g)
  {
    Fernplot(g);
    showStatus("Done");
  }
}