[hardwired]

Code:

C:\jexp\jep-2.4.1>java -jar jep-2.4.1.jar
Failed to load Main-Class manifest attribute from
jep-2.4.1.jar

Couldn't run your jar or find any source files so I made up something that may answer your question(s).

Code:

import java.awt.*;
import java.awt.event.*;
import java.awt.geom.*;
import java.awt.image.BufferedImage;
import java.util.Random;
import javax.swing.*;

public class AnimationTest implements ActionListener, Runnable {
    AnimationPanel animationPanel = new AnimationPanel();
    Thread thread;
    boolean running = false;

    public void actionPerformed(ActionEvent e) {
        String ac = e.getActionCommand();
        if(ac.equals("START")) 
            start();
        if(ac.equals("STOP"))
            stop();
        if(ac.equals("CLEAR"))
            animationPanel.clear();
    }

    private void start() {
        if(!running) {
            running = true;
            thread = new Thread(this);
            thread.setPriority(Thread.NORM_PRIORITY);
            thread.start();
        }
    }

    private void stop() {
        running = false;
        if(thread != null)
            thread.interrupt();
        thread = null;
    }

    public void run() {
        while(running) {
            try {
                Thread.sleep(250);
            } catch(InterruptedException e) {
                running = false;
                System.out.println("interrupted");
            }
            animationPanel.addDot();
        }
    }

    private JPanel getAnimationPanel() {
        return animationPanel;
    }

    private JPanel getUIPanel() {
        JPanel panel = new JPanel();
        String[] ids = { "start", "stop", "clear" };
        for(int i = 0; i < ids.length; i++) {
            JButton button = new JButton(ids[i]);
            button.setActionCommand(ids[i].toUpperCase());
            button.addActionListener(this);
            panel.add(button);
        }
        return panel;
    }

    public static void main(String[] args) {
        AnimationTest test = new AnimationTest();
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.add(test.getAnimationPanel());
        f.add(test.getUIPanel(), "Last");
        f.pack();
        f.setLocation(200,200);
        f.setVisible(true);
    }
}

class AnimationPanel extends JPanel {
    Random seed = new Random();
    BufferedImage image;
    Path2D.Double path;

    public void addDot() {
        int x = seed.nextInt(100) - 5 + 300;
        int y = 225 - seed.nextInt(100);
        Graphics2D g2 = image.createGraphics();
        g2.setPaint(new Color(210,200,230));
        g2.fill(new Ellipse2D.Double(x-2, y-2, 4, 4));
        g2.dispose();
        repaint();
    }

    public void clear() {
        int w = image.getWidth();
        int h = image.getHeight();
        Graphics2D g2 = image.createGraphics();
        g2.setBackground(getBackground());
        g2.clearRect(0, 0, w, h);
        g2.dispose();
        repaint();
    }

    protected void paintComponent(Graphics g) {
        if(image == null)
            init();
        // Looks like you want the dots to appear
        // under/behind the graph.
        g.drawImage(image, 0, 0, this);
        Graphics2D g2 = (Graphics2D)g;
        g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                            RenderingHints.VALUE_ANTIALIAS_ON);
        g2.setPaint(Color.blue);
        g2.draw(path);
    }

    public Dimension getPreferredSize() {
        return new Dimension(600,450);
    }

    private void init() {
        int w = getWidth();
        int h = getHeight();
        int type = BufferedImage.TYPE_INT_RGB;
        image = new BufferedImage(w, h, type);
        Graphics2D g2 = image.createGraphics();
        g2.setBackground(getBackground());
        g2.clearRect(0, 0, w, h);
        g2.dispose();
        path = initWave(w, h);
    }

    private Path2D.Double initWave(int w, int h) {
        Path2D.Double sineWave = new Path2D.Double();
        for(int x = 0; x < w; x++) {
            double y = h/2.0 - Math.sin(((double)x/w)*2*Math.PI)*(h-2)/2.0;
            if(x > 0)
                sineWave.lineTo(x, y);
            else
                sineWave.moveTo(x, y);
        }
        return sineWave;
    }
}

Edit:
type "java applet monte carlo inria" in google showed this thread as number one. I looked around a little and couldn't find what you described.