To Generate Hénon's Strange Attractor

/**
* @author Henon's Strange Attractor Generator
* @author Robert J Morton
* @version 30 October 1997 */

import java.awt.*;

public class Henon extends java.applet.Applet implements Runnable
{
   int XBIAS = 150, YBIAS = 150;                      //pixel co-ordinates of real point 0,0
   int XMAX  = 300, YMAX  = 300;                      //dimensions of the display area (pixels)
   double Scale = 100;                                //pixels per unit real eg 100 pixels = 1.00d
   double x = 0, y = 0, z;                            //real co-ordinates of 'chaotic body'
   int i, j;                                          //its pixel co-ordinates within the visible x-y plane
   Color A[][], colour,                               //colour array and current plot colour
         bgc = Color.lightGray,                       //background colour
         fgc,                                         //foreground colour
         axc = Color.gray;                            //axes colour
   Thread HenonThread;                                //declare a thread reference variable
   long TimeFrame = 150, T;                           //inter-plot time frame (milliseconds)


   public void init() {
      A = new Color[XMAX][YMAX];                      //create colour array for the display area
      for(i = 0 ; i < XMAX ; i++)                     //clear the colour array to background colour
         for(j = 0 ; j < YMAX ; j++)
            A[i][j] = bgc;
      for(i = 0 ; i < XMAX ; i++) A[i][YBIAS] = axc;  //create the x-axis graticule
      for(j = 0 ; j < YMAX ; j++) A[XBIAS][j] = axc;  //create the y-axis graticule
      fgc = new Color(0, 128, 64);                    //colour for the plots
      T = System.currentTimeMillis()  + TimeFrame;    //end of first plot's time frame
   }                                       

   public void paint(Graphics g) {                    //PAINT / RE-PAINT THE PICTURE SO FAR
      for(j = 0 ; j < YMAX ; j++) {                   //for each of the YMAX lines in the picture
         int I = 0;                                   //starting dot of next single-colour stretch of line
         i = 0;                                       //to find next pixel in current line with a different colour 
         colour = A[I][j];                            //make colour of first dot the reference colour
         while(++i < XMAX) {                          //while not yet reached end of current line
            if(colour != A[i][j]) {                   //if this dot a different colour from previous dot
               g.setColor(colour);                    //set colour to colour of previous dot
               g.drawLine(I, j, i - 1, j);            //draw line from start dot to previous dot
               colour = A[I = i][j];                  //make reference colour that of this dot
            }
         }
         g.setColor(colour);                          //set colour for final stretch of current line
         g.drawLine(I, j, i - 1, j);                  //draw the last stretch of the current line
      }
   }

   public void update(Graphics g) {                   //called in response a request for a repaint()
      z = x;                                          //z inherits last time's value of x
      x = 1.4 * x * x + 0.3 * y - 1;                  //advance x
      y = z;                                          //advance y
      int i = XBIAS + (int)(x * Scale);               //Compute the pixel co-ordinates
      int j = YBIAS - (int)(y * Scale);               // corresponding to the new values of x and y.
      A[i][j] = fgc;                                  //put the plot on the 'canvas'
      g.setColor(fgc);                                //set colour for plot
      g.drawLine(i, j, i, j);                         //draw the plot in the applet window
   }

   public void run() {                                //run the Track Recorder painting thread
      while(true) {                                   //permanent loop
         repaint();                                   //paint in the next plot
         long s = T - System.currentTimeMillis();     //get time left in this plot's time frame
         if(s < 5) s = 5;                             //in case machine isn't fast enough
         try { Thread.currentThread().sleep(s);       //sleep for the time remaining
         } catch (InterruptedException e) { }         //catch interrupt from GUI or browser
         T = System.currentTimeMillis() + TimeFrame;  //get when next plot's time frame will end
      }
   }

   public void start() {                              //Start the program thread by
      HenonThread = new Thread(this);                 //creating the thread object
      HenonThread.start();                            //and starting it running by
   }                                                  //requesting a call to run()

   public void stop() { HenonThread.stop(); }         //Stop this a program thread

/*  Robert J Morton, the author of this program, 
    is a poor but Right Honourable Fellow of the
    Ancient and Noble Order of the Long-term Unemployed.

    Offers of work please to: robmorton@clara.net  */
}