ncube is a single-serving site with a hypercube in it, smoothly prolapsing in the three dimensions that your screen can display. There's a panel with sliders that let you set the number of dimensions the cube has and warp it into other shapes. Things seem to get out of hand quickly if I mess with the geometrical sliders, though. This isn't a chill hypercube. This is a hypercube that's going places.
It's the work of Nuno David, who confesses everything (and posts the source) on Github.
It works by rotating the hyperdimensional vertices and applying a chain of perspective projections to them until the 3rd dimension is reached. Everything is generated in real time just from the dimension number.
Stare at it long enough and you'll move minds.
