Time for action – drawing the Sierpinski gasket

For the purpose of demonstration we will draw a Sierpinski gasket, also known as Sierpinski triangle or Sierpinski Sieve with OpenGL. This is a fractal pattern in the shape of a triangle created by the mathematician Waclaw Sierpinski. The triangle is obtained via a recursive and, in principle, infinite procedure. Perform the following steps to draw the Sierpinski gasket:

1. First, we will start out by initializing some of the OpenGL-related primitives. This includes setting the display mode and background color. A line-by-line explanation is given at the end of this section.

   def display_openGL(w, h):
     pygame.display.set_mode((w,h), pygame.OPENGL|pygame.DOUBLEBUF)
   
     glClearColor(0.0, 0.0, 0.0, 1.0)
     glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)
     
     gluOrtho2D(0, w, 0, h)

2. The algorithm requires us to display points, the more the better. First, we set the drawing color to red. Second, we define the vertices (I call them points myself) of a triangle...