LI Exp G - Hopf Fiber Density | PAPP 6-Stage

3D Model

Experiment G is a “fiber-aware” Hopf visualization: instead of projecting 4D vertices point-to-point, it reconstructs the full Hopf fiber circle for each sampled point on S², then measures how many 4D vertices lie near that circle and how evenly they populate it.

Using 7 PAPP-generated polychora (total 42,852 S³ vertices), the model probes 288 fibers (radius 0.15) and builds a disc heightfield where dense + uniform fibers become peaks, sparse fibers become valleys, and clumped occupation produces ridges (uniformity mean 0.315, count range 12–472).

The surface is then extruded into a watertight manifold (χ=2). Mesh: 57,170 verts / 114,336 faces, per-vertex color + normals.

Color key: gold/amber = populated fibers, blue/violet = sparse, red tint = clumped.

Generated by PAPP Framework.