Polygons + Chaos Game

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:

1. Mark three points in a plane to form a triangle.
2. Randomly select any point on the canvas as your starting 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. Mark the new position.
6. Repeat steps 3 to 6.

Below is a graphic animating this process. You can change the number of vertices to change the base shape as well as change the ratio of each move after choosing a point. These dynamic parameters are just one example of how you can modify the process to create even more fractals from different polygons, different restrictions on choosing the next vertex, etc.