Doodling Mathematically

Recently we've started watching these videos in math class. They're really neat, although if you watch more than two in a row, you'll get a headache from dizzyness. The videos are made by a lady named Vi Hart, and my teacher says she's the kind of genius who is probably working on a PhD in mathematics. Here are just three of her videos:

I have now taken to doodling cat-slugs and fractals. (There's a video somewhere on her channel about doodling fractals.)