Nuna-shaped pixels
Claim
It is proposed, and not yet tested, that an image rendered on this tile rather than the square might carry more visual detail per unit area.
Construction
The idea is recorded in the project's master reference as a longer-range, theoretical item: that an image rendered with nuna-tile-shaped pixels rather than square ones might carry more visual detail per unit area than an equivalent-resolution square-pixel image.
The lattice is already in place for it. On the lattice construction — not the wave construction, which fails in phase — tiles cover the plane exactly at pitch s = r√2, each covering area 4r², in four orientations.
Status
There is no proof here, and no experiment on file. The reference itself proposes the shape of the test: a rasteriser-and-compare experiment, rendering the same source image on both lattices at matched area per cell and comparing the results.
Two things can be said from the geometry alone, and they pull in opposite directions. In favour: a nuna cell has the same area as a square cell of the same width, by Claim A, so a like-for-like comparison is straightforward to set up. Against: the tile carries about 18 per cent more boundary than that square, by Claim P, so each cell shares a longer edge with its neighbours, and whether that helps an eye resolve an edge or hinders it is exactly the open question.
Note
This one is yours to argue. The page states the proposal and stops.
Open questions
- The experiment has not been run. Until it is, nothing here should be quoted as a result.
- What “more detail” would mean, measurably. Edge fidelity, perceptual error against a reference, compressed size at matched quality — the claim needs a metric before it can be tested.
- Whether the four tile orientations are a resource for the rasteriser or just four ways to make the same error.
Checks
| What | How | Source |
|---|---|---|
| The proposal, as recorded | Listed under downstream projects: nuna-shaped pixels, likely starting as a rasterise-and-compare experiment | nuna_master_reference.md |
| Area parity with the square | 4r2 = d2, recomputed from the tile path | _src/core.py |
| Perimeter cost | 3πr = 942.478 against a square's 8r = 800 at equal width, a factor of 1.178 | reference/geometry-constants.md |
| Experimental result | None on file. | — |