Prentice.Hall.Introduction.to.Java.Programming,.Brief.Version.9th.(2014).[sharethefiles.com]

766 Chapter 20 Recursion
FIGURE 20.17
The program displays a solution to the Eight Queens problem.
**20.35 (H-tree fractal) An H-tree (introduced at the beginning of this chapter) 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 20.1a.
2. The letter H (in its sans-serif form, H) has four endpoints. Draw an H centered
at each of the four endpoints to an H-tree of order 1, as shown in Figure
20.1b. 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 20.1c–d.
Write an applet that draws an H-tree, as shown in Figure 20.1.
**20.36 (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 * 2, 4 * 4, 8 * 8, 16 * 16, or any other power of 2.
Write a Java applet that displays a Hilbert curve for the specified order, as
shown in Figure 20.18.
(a) (b) (c) (d)
FIGURE 20.18
A Hilbert curve with the specified order is drawn.
20.37 (Sierpinski triangle) Write a program that prompts the user to enter the order
and display the filled Sierpinski triangles as shown in Figure 20.19.
**20.38 (Recursive tree) Write an applet to display a recursive tree as shown in
Figure 20.20.