Two Dimensional Divergence Applet

import java.awt.*;
import java.applet.*;
import java.lang.*;
import expr.*;

public class Divergence2 extends Applet
{
     Panel         controls1 = new Panel();
     Panel         controls2 = new Panel();
     Panel         controls3 = new Panel();
     Panel         controls4 = new Panel();
 
     private       TextField PText         = new TextField("x^2", 35);
     private       TextField QText         = new TextField("y^2", 35);
     private       TextField xMinText      = new TextField("-1", 10);
     private       TextField xMaxText      = new TextField("1", 10);
     private       TextField yMinText      = new TextField("-1", 10);
     private       TextField yMaxText      = new TextField("1", 10);
 
     Expr          Pequation;
     Expr          Qequation;

     Variable      x     = Variable.make("x");
     Variable      y     = Variable.make("y");
     Variable      Picon = Variable.make("Pi");
     Variable      PIcon = Variable.make("PI");
     Variable      picon = Variable.make("pi");
     Variable      Econ  = Variable.make("E");
     Variable      econ  = Variable.make("e");

     String        UserInput;

     double        xmin, xmax, ymin, ymax, absmax;

     Graphics      sG;
     Graphics      bG;
     Image         bI;

     Color         black        = new Color(0, 0, 0);
     Color         back         = new Color(247, 243, 234);
     Color         lines        = new Color(128, 128, 255);
     Color         white        = new Color(255, 255, 255);

     int           width = 423;           // applet width and height
     int           top   = 175;           // height of text panels
     int           left  =  90;           // left margin

     int           steps = 50;            // number of frames in animation

     int           n = 60;                // display is 61 by 61
     int           grid = 4;              // courseness is 4

     double[][]    foo = new double[61][61];  
     double[][]    rho = new double[61][61];
     double        xx, yy, p1, p2, q1, q2, dx, dy;

     public void init()
     {
             setBackground(back);
             bI = createImage(this.size().width, this.size().height);
             bG = bI.getGraphics();
             
             drawback();

             picon.set_value(Math.PI);
             Picon.set_value(Math.PI);
             PIcon.set_value(Math.PI);
             econ.set_value(Math.E);   
             Econ.set_value(Math.E);

             controls1.setBackground(back);
             controls1.setFont(new Font("Courier", Font.BOLD, 12));
             controls1.add(new Label(" P(x, y): "));     
             controls1.add(PText);
             controls2.setBackground(back);
             controls2.setFont(new Font("Courier", Font.BOLD, 12));
             controls2.add(new Label(" Q(x, y): "));     
             controls2.add(QText);
             controls3.setBackground(back);
             controls3.setFont(new Font("Courier", Font.BOLD, 12));
             controls3.add(new Label(" Min x:"));
             controls3.add(xMinText);
             controls3.add(new Label(" Max x:"));
             controls3.add(xMaxText);
             controls4.setBackground(back);
             controls4.setFont(new Font("Courier", Font.BOLD, 12));
             controls4.add(new Label(" Min y:"));
             controls4.add(yMinText);
             controls4.add(new Label(" Max y:"));
             controls4.add(yMaxText);
             add(controls1);
             add(controls2);
             add(controls3);
             add(controls4);
     }

     public void paint(Graphics g)
     {
            g.drawImage(bI, 0, top, this);
            sG = getGraphics();
     }

     public void update(Graphics g)
     {
            g.drawImage(bI, 0, top, this);
     }

     public void drawback()
     {
            bG.setColor(back);
            bG.fillRect(0, 0, width, width - top);
            bG.setColor(black);
            for (int i = 0; i < (n + 1) * grid + 1; i = i + grid)
            {
                bG.drawLine(left, i, left + (n + 1) * grid, i);
                bG.drawLine(left + i, 0, left + i, (n + 1) * grid);
            }

     }

     public Color boxcolor(double z)
     {
            Color tcolor;
            int  red, blue;

            if (z >= 0.0)
            {
                 z = Math.min(z, 1.0);
                 blue = (int) Math.round(255.0 * (1 - z));
                 tcolor = new Color(255, blue, blue);              
            }
            else
            {
                 z = Math.max(z, -1.0);
                 red = (int) Math.round(255.0 * (z + 1));
                 tcolor = new Color(red, red, 255);
            }
            return tcolor;
     }

     public boolean mouseDown(Event evt, int mx, int my)
     {
            if (my < top) return true;

            // Get Functions and Ranges from Panels
            
            try
            {
                  Pequation = Parser.parse(PText.getText());
            }
            catch (Syntax_error e)
            {
                  System.err.println ("Syntax error: " + e);
            }

            try
            {
                  Qequation = Parser.parse(QText.getText());
            }
            catch (Syntax_error e)
            {
                  System.err.println ("Syntax error: " + e);
            }

            UserInput = xMinText.getText().trim();
            xmin = Double.valueOf(UserInput).doubleValue();
            UserInput = xMaxText.getText().trim();
            xmax = Double.valueOf(UserInput).doubleValue();
            UserInput = yMinText.getText().trim();
            ymin = Double.valueOf(UserInput).doubleValue();
            UserInput = yMaxText.getText().trim();
            ymax = Double.valueOf(UserInput).doubleValue();

            drawback();
            sG.drawImage(bI, 0, top, this);
            
            dx = (xmax - xmin)/n;
            dy = (ymax - ymin)/n;

            bG.setColor(boxcolor(0.0));

            absmax = 0.0; 
            xx = xmin;
            for (int i = 0; i < n + 1; i = i + 1)
            {
                yy = ymax;
                for (int j = 0; j < n + 1; j = j + 1)
                {
                    rho[i][j] = 0.0;
                    x.set_value(xx - dx/2);
                    y.set_value(yy);
                    p1 = Pequation.value();
                    x.set_value(xx + dx/2);
                    p2 = Pequation.value();
                    x.set_value(xx);
                    y.set_value(yy - dx/2);
                    q1 = Qequation.value();
                    y.set_value(yy + dx/2);
                    q2 = Qequation.value();
                    foo[i][j] = (p2 - p1 + q2 - q1)/dx;
                    absmax = Math.max(absmax, Math.abs(foo[i][j]));
                    bG.fillRect(left + 1 + grid * i, 1 + grid * j,
                                grid - 1, grid - 1);
                    yy = yy - dy;                   
                }
                sG.drawImage(bI, 0, top, this);
                xx = xx + dx;                
            }

            if (absmax > 0.0001)
            {
                bG.setColor(back);
                bG.fillRect(left, 0, (n + 1) * grid + 1, (n + 1) * grid + 1);
                for (int step = 0; step < steps; step = step + 1)
                {   
                    for (int i = 0; i < n + 1; i = i + 1)
                    {
                        for (int j = 0; j < n + 1; j = j + 1)
                        {
                            rho[i][j] = rho[i][j] + foo[i][j] / (absmax * steps);
                            bG.setColor(boxcolor(rho[i][j]));
                            bG.fillRect(left + grid * i,  grid * j,
                                        grid, grid);
                      
                        }   
                    }
                sG.drawImage(bI, 0, top, this);
                }
            }

            return true;
     }

}