The center shows a scene graph: a planet node orbits in a 4D plane, moon nodes orbit the planet in different planes, and each world transform is the composition of its ancestors' rotations and translations — the same parent–child machinery as three.js, with 4D rotors in place of quaternions.
The background field is instancing: hundreds of copies of one 16-cell, each with its own 4D rigid transform stored per instance on the GPU, all drawn in a single call. The geometry uploads once; moving an instance costs 20 floats.
Push instances to 1024 and check the edge count in the corner — the frame rate barely notices. Alt-drag rotates the shared 4D frame: hierarchy and field turn together through the hidden dimension.