Write a program that uses recursion to draw a Koch snowflake fractal of any given order....

Write a program that uses recursion to draw a Koch snowflake fractal of any given order. A Koch snowflake of order 0 is an equilateral triangle. To create the next-higher-order fractal, each line segment in the shape is modified by replacing its middle third with a sharp protrusion made of two line segments, each having the same length as the replaced one, as shown in Figure 13-11.

The following is the necessary information to compute the three new points (x₂, y₂), (x₃, y₃), and (x₄, y₄) in terms of (x₁, y₁) and (x₅, y₅).

Let:

The first three Koch snowflakes produced by the program might look like Figure 13-12.