(a) (b)
**14.10 (Display a graph) Rewrite the preceding exercise by reading data from a Web URL such as
**14.11 (Mandelbrot fractal ) Mandelbrot fractal is a well–known image created from a Mandelbrot
set (see Figure 14.9). A Mandelbrot set is defined using the following iteration:
c is a complex number and the starting point of iteration is
For a given c, the iteration
will produce a sequence of complex numbers:
It can be shown that the
sequence either tends to infinity or stays bounded, depending on the value of c. For example,
if c is 0, the sequence is
which is bounded. If c is i, the sequence is
{0,, 1 , , 1 ,, },iiiii−+ − −+
which is bounded. If c is
the sequence is
which is unbounded. It is known that if the absolute value of a complex
value i
in the sequence is greater than 2, then the sequence is unbounded. The Mandelbrot
set consists of the c value such that the sequence is bounded. For example, 0 and i are in the
Mandelbrot set. A Mandelbrot image can be created using the following code: