Watch the film · 6:00 · 1080p HD
UTFANSWF Proper: Living Geometry
A continuous view inside the connected structure—distinct layers, shared junctions and motion within motion.
Follow what changes
A guide to the film.
- Opening: a living mathematical structure.
- From reference to structure: the spherical construction unfolds.
- Connected cone regions: 32 regions and 90 registered interfaces.
- Beneath the surface: a continuous cutaway reveals the interior.
- Slant intersections: local responses meet within the same structure.
- Local motion and shared response: separate phases contribute to a collective mode.
- Finite nonlinear structure: reduced source coefficients shape the response.
- Rotation within rotation: common rotation and local phase remain distinct.
- Layers and local interiors: connections remain visible across the cutaway.
- A connected operating environment: different local roles within one construction.
- The whole remains in motion: continuing structure and response.
- Closing statement, author credit and paper DOI.
What the visualization represents
Mathematical sources. Explicit visual choices.
The film uses the P5/H6 adjacency, shell Schur eigenspectrum and five-wedge reduced coefficients from saved UTFANSWF Proper calculations. The color key distinguishes outer structure, layers, inner regions and local features.
The camera path, display growth, layer radii, cutaway, phase sweeps and travelling indicators make those relationships visible. Their screen motion is illustrative, not a newly calculated physical trajectory or independent scientific validation.
Created 18 October 2026 · Ronald L. Alexander · DOI: 10.5281/zenodo.23451622