THE FOLD / SPAWN / THE SANDBOX / THE POISSON DISK
THE POISSON DISK
random points that never crowd — blue noise
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Poisson-disk sampling scatters points that are random but never closer than a radius r to one another — “blue noise.” Bridson’s algorithm does it in O(n): a background grid (cell r/√2, so each cell holds at most one point) and an active list; for each active point it throws k candidates into the annulus [r, 2r] and accepts the first with no neighbor closer than r. The even, gap-respecting spread is why it is used for stippling, texture, and sensor placement.
LIT verified live: across 30 runs every pair of accepted samples is at least r apart (the minimum gap equals r, never less) — window.__poisson. FIG no framing; exact.
LIT verified live: across 30 runs every pair of accepted samples is at least r apart (the minimum gap equals r, never less) — window.__poisson. FIG no framing; exact.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-sandbox — the spatial playground where points must be sown evenly, none crowding another. Poisson-disk sampling is that even sowing. AVAN (AI) built the instrument: the r/√2 background grid, the annulus candidate throw, the neighbor rejection, and the exhaustive minimum-gap check.
Credit as content: Robert Bridson (2007). The weave: David names the sandbox; I grow the sample set from an active front, reject any candidate too close, and confirm no two accepted points ever fall within r.
Credit as content: Robert Bridson (2007). The weave: David names the sandbox; I grow the sample set from an active front, reject any candidate too close, and confirm no two accepted points ever fall within r.
3 ONE DIMENSION
From an active point, throw k candidates into the ring between r and 2r. Accept the first whose nearest existing neighbor is ≥ r away; otherwise the point is exhausted and leaves the active front.
4 TWO DIMENSIONS · INTERACTIVE
A Poisson-disk point set; every point’s exclusion disk of radius r is shown, and the minimum pairwise gap is checked to be ≥ r.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: an even, gap-respecting scatter.
AVAN’s addition (the inverse-companion): make randomness even by forbidding any two points within r — grow from an active front, throwing candidates into the [r,2r] ring and rejecting the too-close. The inverse of ‘uniform random points clump and leave gaps’ is ‘blue noise — random yet minimally spaced.’ Magenta is the clumps and voids of plain uniform sampling; green is the elbow-room scatter. Random, but never crowded.
LIT Genuine Bridson Poisson-disk sampling (Bridson 2007). Verified live: across 30 runs the background-grid + active-list algorithm produces point sets in which every pair of accepted samples is at least r apart, with the measured minimum gap equal to r and never below it (window.__poisson.allApart).
FIG No framing: the r/sqrt2 background grid, the annulus candidate throw, the neighbor rejection, and the exhaustive minimum-gap check run in-browser and hold. The AVAN inverse is honest — forbidding any two points within r while growing from an active front makes randomness even (blue noise); magenta is the clumps and voids of plain uniform sampling, green the elbow-room scatter. Random, but never crowded.
FIG No framing: the r/sqrt2 background grid, the annulus candidate throw, the neighbor rejection, and the exhaustive minimum-gap check run in-browser and hold. The AVAN inverse is honest — forbidding any two points within r while growing from an active front makes randomness even (blue noise); magenta is the clumps and voids of plain uniform sampling, green the elbow-room scatter. Random, but never crowded.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE SANDBOX · David Lee Wise (ROOT0), with AVAN