Antonio Marquez-Raygoza explains the Sierpinski Triangle.
So I was me and I was in math class watching paint dry it was starting to crack when suddenly I realized there was a page for which the internet was invented.
There is some stunning imagery there, covering the length and breadth of Triforce of Fractals. It also comes with Mathematica code examples so you can follow at home, if you've got a copy (I unfortunately don't).
This cow does not cower. Infinity cannot bully this bull, cannot bloviate this bovine. By all appearances this cow is wearing infinity on its mane. Its horns are probably made of ℵ ℵ … down 4 or 5 levels, an immutability surpassed only by that of the tusks of the Alephant.
… and cows.
If you're looking for a matching soundtrack, R2Bl3nd, who's maybe best known for his adaption of Windows 7 x64 Paint.exe, has interpreted an image of the triangle as a wave file for you:
There's another auditory interpretation of the triangle at the bottom of Antonio's page, but that sounds less chiptune and more like a Lovecraftian Merry-Go-Round.
And now I want Mathematica for Christmas.