Sierpinski’s triangle has always fascinated me. As I learned more about it, I found that there were multiple ways to create or generate it. One that I found particularly interesting is called a chaos game. Here are the steps:

Mark three points in a plane to form a triangle. Randomly select any point on the canvas as your starting position. Randomly select any one of the three vertex points. Move half the distance from your current position to the selected vertex. Mark the new position. Repeat steps 3 to 6.

Below is a graphic animating this...