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

iteration count (line 28). The method returns COUNT_LIMIT if the sequence is
bounded (line 31).
The loop in lines 8–9 examines each point (x, y) for - ˛2 6 x 6 2 and
- ˛2 6 y 6 2 with interval 0.01 to see if its corresponding complex number
c = x + yi is in the Mandelbrot set (line 10). If so, paint the point black (line
12). If not, set a color that is dependent on its iteration count (line 15). Note that
the point is painted in a square with width u and height 1. All the points are
scaled and mapped to a grid of 400-by-400 pixels (lines 14–15). Note that the
values 77, 58, and 159 are set arbitrarily. You may set different numbers to get
new colors.
Complete the program to draw a Mandelbrot image, as shown in Figure
15.13a.
**15.21 (Julia set) The preceding exercise describes Mandelbrot sets. The Mandelbrot
set consists of the complex c value such that the sequence z n + 1 = z 2 n + c is
bounded with z 0 fixed and c varying. If we fix c and vary z 0 (= x + yi), the
point (x, y) is said to be in a Julia set for a fixed complex value c, if the function
z n + 1 = z 2 n + c stays bounded. Revise Exercise 15.20 to draw a Julia set
as shown in Figure 15.13b. Note that you only need to revise the count
method by using a fixed c value (- ˛0.3 + 0.6i).
15.22 (Use the Rational class) Write a program that computes the following summation
series using the Rational class:
1
2 + 2 3 + 3 4 + c + 98
99 + 99
100
You will discover that the output is incorrect because of integer overflow (too
large). To fix this problem, see Programming Exercise 15.17.
Programming Exercises 597