Mode 1: Hypercube

Displays the boundary of a 4D hypercube (from hypercube_t<Nt>.surf) as a familiar reference object. Use this mode to build intuition for 4D rotation.

Mode 2: Centre Vortices

The full vortex content of the loaded configuration. Every surface element is drawn as a translucent quad with a low-alpha outline. Colour encodes the sheet ID: each connected vortex component gets a distinct colour from a golden-ratio hue sequence in the orange-to-violet range. Sheet 1 is drawn red (and near-invisible grey in mode 3) so it stands out from the palette.

Geometry fades with distance from the selection centre (adjustable with PageUp/PageDown), which acts as a focus bubble when the full lattice is too dense to read.

Mode 3: Timeslice

A thin slab of time centred on t0, showing only the surface elements that extend through it. Time-extending vortex segments appear as cones pointing along the segment's spatial direction:

• Cone apex direction encodes the surface elements orientation (+1 along the segment, -1 against it).
• Cone tips are red; the ring base is blended toward white.

Step through time with , and . to sweep the slice through the configuration and watch vortex lines move, merge, and branch. The slab width (PageUp/PageDown) controls how many time steps contribute.

Rendering notes

• Faces are drawn translucently with depth writes disabled; outlines and cones draw afterwards with depth writes on. This keeps deep piles of overlapping surface elements readable.
• The geometry shaders cull primitives outside the focus radius and outside the time slab, and reject wrap-around artefacts (edges longer than 1.5 lattice units after periodic wrapping).
• Distance from the selection centre drives a smooth alpha fade in the fragment shaders.