So I saw this video the other day while strolling through my feed. It was a video of the demonstration of the Sierpinski Triangle and how you can make it with a bunch of points. The idea is to draw 3 vertices of an equilateral triangle, and then choose a random point. Then take the midpoint between a random vertex and that point, then plot that point. Then for the new point take a random vertex and plot the midpoint again. Then keep doing that over and over again until something beautiful appears.

The first 3 points

n = 3

n = 10

n = 100

n = 1000

n = 20000

Animation