Recursive graphics: The Sierpinski Triangle

The Sierpinski triangle is a very nice example of a recursive pattern (fractal). It was described by the mathematician Sierpinski in 1915. Although it looks complex, it can be generated with a very short recursive method.

First, let's try to understand the recursion.

Do you see the pattern? Imagine that you have a method called

//draws a black-filled triangle with vertices (x1, y1), (x2,y2), (x3,y3)
drawFilledTriangle(int x1, int y1, int x2, int y2, int x3, int y3)

//draws a Sierpinski triangle with vertices (x1, y1), (x2, y2), (x3, y3)
render(int x1, int y1, int x2, int y2, int x3, int y3, int depth) {

    ...
}