[user-the-name]

"Pick a random vertex of the triangle and find its midpoint with p" is actually "Take the whole triangle, and scale it down to half size, and place it so that it shares a random vertex". This is the basic structure of the Sierpinski triangle, so repeating this process creates the fractal shape of the Sierpinski.

[asxd]

Thanks. I wasn't quite sure what "pick a random vertex of the triangle and find its midpoint with p" meant. What's the midpoint of a vertex?

[kzrdude]

It sounds like they mean the point (vertex + p) / 2.

[asxd]

D'oh. Seems obvious in the morning. The perils of late-night posting.