Recursion - Java 7 for Absolute Beginners - page 259

■ Note Fibonacci numbers turn up in all kinds of interesting places. They are closely linked to the golden ratio
(important in the history of art and architecture), appear in the ratios of a number of objects in nature, and have
been used to determine when to buy stocks. While they are well beyond the scope of this topic, the origin and uses
of the Fibonacci sequence are interesting subjects in their own right.
Calculating Fractals
Fractal images involve using the output of one calculation as the input to a subsequent calculation—a
perfect task for recursion. I'll start with my personal favorite.
Drawing a Sierpinski Triangle
A Sierpinski triangle (named after Polish mathematician Waclaw Sierpinski) is a triangle consisting of
other triangles. Each smaller triangle can itself consist of other triangles. Thus, you can have triangles
within triangles within triangles to any depth you like. (Note the recursion within the preceding
sentence; just talking about recursion requires recursion.)
Here's a pair of classes that draw a Sierpinski triangle to a depth of 7 (a number I picked because I
liked the resulting output). As usual, I've created a program class that uses another class to do the
drawing.
Here's the program class:
Listing 14-4. SierpinskiTriangle.java
package com.bryantcs.examples.fractals;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import javax.swing.JFrame;
import javax.swing.JMenu;
import javax.swing.JMenuBar;
import javax.swing.JMenuItem;
public class SierpinskiTriangle implements ActionListener {
private SierpinskiTrianglePanel
sierpinskiTrianglePanel = new SierpinskiTrianglePanel();
private JFrame frame = new JFrame("Sierpinski Triangle");
private void addMenu(JFrame frame) {
JMenu file = new JMenu("File");
file.setMnemonic('F');
JMenuItem exitItem = new JMenuItem("Exit");