import java.awt.Color;
import javax.swing.JComponent;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.geom.Point2D;
import java.awt.geom.Line2D;

public class SpiralComponent extends JComponent
{
   public void paintComponent(Graphics g)
   {
      Graphics2D g2 = (Graphics2D) g;
      final int GRID_SIZE = 10;

      Point2D end = new Point2D.Double(100,100);

      for (int n = 0; n < ...; n++)
      {
        Point2D start = end;

        end = ...; 

        g2.draw(new Line2D.Double(start, end));
      }
   }
}