RECURSION - Introduction to Java Programming: Comprehensive Version - page 735

F IGURE 18.17

The program displays a solution to the Eight Queens problem.

**18.35

( H-tree fractal ) An H-tree (introduced at the beginning of this chapter in
Figure 18.1) is a fractal defined as follows:
1. Begin with a letter H. The three lines of the H are of the same length, as
shown in Figure 18.1a.
2. The letter H (in its sans-serif form, H) has four endpoints. Draw an H cen-
tered at each of the four endpoints to an H-tree of order 1 , as shown in
Figure 18.1b. These Hs are half the size of the H that contains the four
endpoints.
3. Repeat Step 2 to create an H-tree of order 2 , 3 , . . . , and so on, as shown in
Figure 18.1c-d.

Write a program that draws an H-tree, as shown in Figure 18.1.

18.36

( Sierpinski triangle ) Write a program that lets the user to enter the order and
display the filled Sierpinski triangles as shown in Figure 18.18.

F IGURE 18.18

A filled Sierpinski triangle is displayed.

**18.37

( Hilbert curve ) The Hilbert curve, first described by German mathematician
David Hilbert in 1891, is a space-filling curve that visits every point in a square
grid with a size of 2 16, or any other power of 2.

Write a program that displays a Hilbert curve for the specified order, as shown
in Figure 18.19.

* 2, 4 * 4, 8 * 8, 16 *