@hidden The video shows different algebraic surfaces. I've mentioned the classification of algebraic surfaces, where there is a beautiful shore and a dark ocean of unknown material. All the surfaces in the video are at (0, 0) in the map - the safest and best-understood part of the shore.

Specifically, they are "rational" surfaces, meaning that they can be traced out like this: (P(x, y) / Q(x, y) , R(x, y) / S(x, y)) where P, Q, R, S are polynomials in the variables x and y. The terminology comes from the fact that "polynomial divided by polynomial" is called a "rational function." These surfaces are nice because they can be traced out by a flat sheet (just let (x, y) move around in the xy-plane). That also explains why they can be nicely plotted in a video.

A funny thing about algebraic shapes is that their bulges and cavities tend to occur opposite to each other. You can see this in some frames of the video. Despite their flowing appearance in the video, they are also extremely rigid, in the sense that a tiny shred of the surface uniquely determines the entire thing. I find them beautiful, but more than that, I feel that there is something uniquely old about them, like you can feel the antiquity dripping from their tired souls.