Sierpinski pentagon

Produce a graphical or ASCII-art representation of a Sierpinski pentagon (aka a Pentaflake) of order 5. Your code should also be able to correctly generate representations of lower orders: 1 to 4.

See also

• Sierpinski pentagon

Java

<lang java>import java.awt.*; import java.awt.event.ActionEvent; import java.awt.geom.Path2D; import static java.lang.Math.*; import java.util.Random; import javax.swing.*;

public class SierpinskiPentagon extends JPanel {

   // exterior angle
   final double degrees072 = toRadians(72);

   /* After scaling we'll have 2 sides plus a gap occupying the length
      of a side before scaling. The gap is the base of an isosceles triangle
      with a base angle of 72 degrees. */
   final double scaleFactor = 1 / (2 + cos(degrees072) * 2);

   final int margin = 20;
   int limit = 0;
   Random r = new Random();

   public SierpinskiPentagon() {
       setPreferredSize(new Dimension(640, 640));
       setBackground(Color.white);

       new Timer(3000, (ActionEvent e) -> {
           limit++;
           if (limit >= 5)
               limit = 0;
           repaint();
       }).start();
   }

   void drawPentagon(Graphics2D g, double x, double y, double side, int depth) {
       double angle = 3 * degrees072; // starting angle

       if (depth == 0) {

           Path2D p = new Path2D.Double();
           p.moveTo(x, y);

           // draw from the top
           for (int i = 0; i < 5; i++) {
               x = x + cos(angle) * side;
               y = y - sin(angle) * side;
               p.lineTo(x, y);
               angle += degrees072;
           }

           g.setColor(RandomHue.next());
           g.fill(p);

       } else {

           side *= scaleFactor;

           /* Starting at the top of the highest pentagon, calculate
              the top vertices of the other pentagons by taking the
              length of the scaled side plus the length of the gap. */
           double distance = side + side * cos(degrees072) * 2;

           /* The top positions form a virtual pentagon of their own,
              so simply move from one to the other by changing direction. */
           for (int i = 0; i < 5; i++) {
               x = x + cos(angle) * distance;
               y = y - sin(angle) * distance;
               drawPentagon(g, x, y, side, depth - 1);
               angle += degrees072;
           }
       }
   }

   @Override
   public void paintComponent(Graphics gg) {
       super.paintComponent(gg);
       Graphics2D g = (Graphics2D) gg;
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
               RenderingHints.VALUE_ANTIALIAS_ON);

       int w = getWidth();
       double radius = w / 2 - 2 * margin;
       double side = radius * sin(PI / 5) * 2;

       drawPentagon(g, w / 2, 3 * margin, side, limit);
   }

   public static void main(String[] args) {
       SwingUtilities.invokeLater(() -> {
           JFrame f = new JFrame();
           f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
           f.setTitle("Sierpinski Pentagon");
           f.setResizable(true);
           f.add(new SierpinskiPentagon(), BorderLayout.CENTER);
           f.pack();
           f.setLocationRelativeTo(null);
           f.setVisible(true);
       });
   }

}

class RandomHue {

   /* Try to avoid random color values clumping together */
   final static double goldenRatioConjugate = (sqrt(5) - 1) / 2;
   private static double hue = Math.random();

   static Color next() {
       hue = (hue + goldenRatioConjugate) % 1;
       return Color.getHSBColor((float) hue, 1, 1);
   }

}</lang>