Applet to Generate the Mandelbrot Set

/** Mandelbrot Set Generator by Robert J Morton 27 October 1997 */

import java.awt.*;

public class Mandelbrot extends java.applet.Applet implements Runnable
{
   int XBIAS = 220, YBIAS = 130;                      //pixel co-ordinates of real point 0,0
   int XMAX = 340, YMAX = 260;                        //dimensions of the display area (pixels)
   double Scale = 100;                                //pixels per unit real eg 100 pixels = 1.00d
   int i, j, v = 0;
   boolean finished = false;
   Color C[], A[][], colour;                          //colour array and current plot colour
   Thread Brot;                                       //declare a thread reference variable

   public void init() {
      C = new Color[20];                              //create colour array
      C[ 0] = Color.lightGray;                        //create colours for the display
      C[ 1] = new Color(  0,   0, 128);               //series diverged after 2 iterations
      C[ 2] = new Color(  0, 136,   0);               //series diverged after 3 iterations
      C[ 3] = new Color(144,   0,   0);               //series diverged after 4 iterations
      C[ 4] = new Color(  0, 152, 152);               //series diverged after 5 iterations
      C[ 5] = new Color(160,   0, 160);               //series diverged after 6 iterations
      C[ 6] = new Color(168, 168,   0);               //etc.
      C[ 7] = new Color(176, 176, 176);
      C[ 8] = new Color( 16,  16, 184);
      C[ 9] = new Color( 16, 192,  16);
      C[10] = new Color(200,  16,  16);
      C[11] = new Color( 16, 208, 208);
      C[12] = new Color(216,  16, 216);
      C[13] = new Color(224, 224,  16);
      C[14] = new Color(232, 232, 232);
      C[15] = new Color( 64,  64, 240);
      C[16] = new Color( 64, 248,  64);
      C[17] = new Color(252,  64,  64);
      C[18] = new Color(255, 255,  64);
      C[19] = new Color(255, 255, 255);
      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] = Color.black;
   }                                       

   public void paint(Graphics g) {                    //PAINT / RE-PAINT THE PICTURE SO FAR
      for(j = 0 ; j < YMAX ; j++) {                   //for each of the 180 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()
      if(v < YMAX) {                                  //if last line not yet painted
         int I = 0;                                   //start pixel for current colour
         int i = 0;                                   //current pixel of current colour
         colour = A[I][v];                            //make colour of first dot the reference colour
         while(++i < XMAX) {                          //for each pixel on the current line...
            double x = .01, y = .01, z,               //reset values to start another convergence test
            cx = (double)(i - XBIAS) / Scale,         //Convert current pixel co-ordinates to real
            cy = (double)(YBIAS - v) / Scale;         // co-ordinates on the complex plane.
            for(int k = 0 ; k < 128 ; k++) {          //if not yet completed 128 iterations
               z = x * y;                             //compute and add in the next term of the
               x = x * x - y * y + cx;                //complex series
               y = z + z + cy;
               if(x < -2.5 || x > 1.5 ||              //if the value of the complex quantity has
                  y < -2.0 || y > 2.0) {              //gone beyond the bounds of the display area
                  if(k > 19) k = 19;                  //max number of iterations for divergence
                  A[i][v] = C[k];                     //store the pixel colour
                  break;
               }
            }
            if(colour != A[i][v]) {                   //if colour has changed
               g.setColor(colour);                    //set colour according to number of iterations
               g.drawLine(I, v, i - 1, v);            //draw the plot
               colour = A[I = i][v];                  //set current colour as reference colour
            }
         }
         g.setColor(colour);                          //set colour for final stretch of current line
         g.drawLine(I, v, i - 1, v);                  //draw the last stretch of the current line
         v++;                                         //advance downwards to the next line
      } else finished = true;
   }

   public void run() {                                //run the Track Recorder painting thread
      while(true) {                                   //permanent loop
         if(!finished) repaint();                     //paint in the next plot
         try { Thread.currentThread().sleep(5);       //sleep for the time remaining
         } catch (InterruptedException e)  { }        //catch interrupt from GUI or browser
      }
   }

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

   public void stop() { Brot.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  */
}