**18.27 (Koch snowflake fractal) The text presented the Sierpinski triangle fractal.  In this exercise, you will write a program to display another fractal, called the Koch snowflake, named after a famous Swedish mathematician. A Koch snowflake is created as follows:

1.    Begin with an equilateral triangle, which is considered to be the Koch fractal of order (or level) 0, as shown in Figure 18.14a.

2.    Divide each line in the shape into three equal line segments and draw an out- ward equilateral triangle with the middle line segment as the base to create a Koch fractal of order 1, as shown in Figure 18.14b.

3.    Repeat Step 2 to create a Koch fractal of order 2, 3, . . . , and so on, as shown in Figure 18.14c–d.

 

 

              

(a)                                          (b)                                          (c)                                          (d)

FIGURE  18.14     A Koch snowflake is a fractal starting with a triangle.