The 4th Dimension ... it boggles the mind. They are rotating their xy and zw axes. They are all projected from 4d to 3d separately, each with their own 4d camera in front of each of them, that is why their "vanishing points" are at their centres, not all at the centre of the screen. Press space to stop the madness and use wasdqe and arrow keys to move around. 1 rotates the xy axes, both the z and w axes will stay fixed (not very interesting). 2 rotates the zw axes, and the xy axes remain fixed, the maths is identical to 3d rotations, you just apply a normal 2d rotation to the the zw coordinates, its the projection into 3d which makes things look weird. It actually kind of makes sense what it is doing, I will try to explain: Consider a perspective drawing of a corridor, the centre of the paper is a "vanishing point", that is because you are projecting the vertical and horizontal components on the paper by dividing them by the distance down the corridor. The further away in the z dimension, the closer the point is projected to the centre of 2d space. In 4d, you divide the xyz by the w component (distance down the 4d corridor), so the further away something is in the w direction, the closer to the centre of 3d space it is projected. When you rotate the zw components they rotate in a circle, the z component oscillating is is why the points move away/towards you, and the w changes the distance from the origin, which is why they go in and out at the same time, creating the inside out doughnut effect. If you look at it from the side as the zw rotate, it actually gives the illusion of 3d horizontal rotation, which is cool.
