The derivation, with the numbers showing.
Change the seed and watch every intermediate value move. Nothing on this page is fetched — it is the same code that draws every block on the site, running here with its cover off.
The seed string is folded into a single 32-bit number with FNV-1a. Same string, same number, on every machine ever built.
That number seeds mulberry32 — a small, fully specified generator. It is not random; it is a fixed sequence you can recompute.
The first draws become a, b and the starting point. The next become the palette, the rotation, and how many states the vault holds.
400 steps are thrown away so the orbit forgets where it started, then 60,000 more are kept. If it runs past 10⁴ it has escaped and the vault is VOID.
Occupied cells are counted at five grid resolutions. The slope of log(count) against log(resolution) is the box-counting dimension.
The famous Hénon attractor lives at a = 1.4, b = 0.3. We could have pinned every seed near there and made sure every address got a handsome picture. Instead a runs from 0.90 to 1.62, which pushes a real slice of seeds out past the edge of the region where the map settles at all.
Roughly one address in five escapes and holds nothing. Another third falls into a plain repeating cycle. That is uncomfortable for a collectible and correct for a measurement, and we would rather be the second thing.