This is the Sierpinsky Triangle. Its generated by drawing a Triangle and then connecting the middle points of each side to form an upside down triangle. And repeat.
Some sea shells (e.g. Cymbiola innexa)
Generating a Sierpinsky Triangle by playing the “Chaos Game”
You can do the same for a square, which will give you the socalled Sierpinsky Carpet:
There is also a 3 dimensional variant of this fractal, called the Menger Sponge: