Sierpiński triangle

This is a quick test of the Sierpiński triangle.

No audio was added to the game.

The rules of the paper game are:

1. Take three points in a plane to form a triangle.
2. Randomly select any point inside the triangle and consider that your current position.
3. Randomly select any one of the three vertex points.
4. Move half the distance from your current position to the selected vertex.
5. Plot the current position.
6. Repeat from step 3.

I have created this program to simulate the game. 

You can read more about the Sierpiński triangle here: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle

Edit: added a continuous mode so you can watch the triangles form in real time.