https://youtu.be/-E62sgpSX2U

Three 4D tori. 4D rigid rotations occur in 2 perpendicular planes. The rate of rotation in each plane is independent of the other. In this video the ratio between the two periods -- the horological ratio or horatio -- is pi so the pattern would never repeat. Four different rotations are shown.

Instead of a projection all four dimensions are drawn, with the viewer's knowledge of the object being shown allowing the viewer to distinguish them. In this case we draw eight parallel circular slices of each torus in the xy plane, while the centers of these circles are laid out in the wz plane. The tori themselves are motionless, instead the viewer is orbiting them, so the three tori are moving as though they were somehow connected into a single rigid system.