0 and 1 are eeffectively the same.  The transparency can range from 0 to
255.  0 is fully transparent, 255 is fully opaque.  Here's a simple
example.  It paints the background white, and then paints over it with
red.  The alpha componment of the red color is increased from 0 to 255.
   You will see the white at first, and then the red will increase in
intensity (due to the increasing alpha) until the whole panel is red.

import java.awt.*;
import javax.swing.*;
public class AlphaPanel extends JPanel {
    private int red;
    private int green;
    private int blue;
    private int currentAlpha;
    private long delay;
    public AlphaPanel(Color c, long delayInMillis) {
        this.red = c.getRed();
        this.green = c.getGreen();
        this.blue = c.getBlue();
        this.delay = delayInMillis;
        Thread t = new Thread(new Runnable() {
            public void run() {
                while (true) {
                    try {
                        Thread.sleep(delay);
                        repaint();
                    } catch (InterruptedException ie) {
                        ie.printStackTrace();
                    }
                }
            }
        });
        t.start();
    }

    protected void paintComponent(Graphics g) {
        int w = getWidth();
        int h = getHeight();

        g.setColor(Color.white);
        g.fillRect(0,0,w,h);
        g.setColor(new Color(red, green, blue, currentAlpha));
        g.fillRect(0,0,w,h);
        if (currentAlpha == 255) {
            currentAlpha = 0;
        } else {
            currentAlpha++;
        }
    }

    public static void main(String[] args) {
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.getContentPane().add(new AlphaPanel(Color.RED, 10));
        f.setSize(400,300);
        f.setVisible(true);
    }
}