Method and limits
- Bit y × 3 + x of the decimal seed number controls cell (x, y), counted from the top-left. The row images make the encoding visible.
- Use the eight rotations/reflections of the original 3 × 3 frame. Translations inside the frame are not deduplicated. We simulate each representative once.
- Track only live cells and their neighbours in a sparse unbounded plane. Cells outside the current footprint are dead; there is no wrapping or clipping.
- Stop at extinction or an exact whole-pattern recurrence, allowing translation. Compare with the preceding 128 generations.
- Otherwise stop after 1,200 generations and label the seed unresolved. A repeat outside the 128-generation comparison window is also not proved by this census.
Why R-pentomino can be “unresolved”
R-pentomino's standard transient ends at generation 1,103, leaving stable/oscillating ash and escaping gliders. The complete footprint keeps spreading, so it need not repeat as one translated object. “Unresolved” here is a limit of the whole-pattern test, not a claim that its known evolution is unknown.
Compare the R-pentomino snapshots · Read the 3×3 methuselah guide
Reproduce and check the data
Download the standalone reproduction script. Put it in an empty folder and run node reproduce-3x3-census.mjs with Node.js 20 or later. It needs no packages or repository access and writes the JSON, CSV and SHA-256 files next to the script, replacing files with the same names. Compare them with the downloads above.
The public script embeds the same engine and stopping rules used for the dataset. Its generated files are checked byte-for-byte against the published data; the engine is also checked against the dense update rule for all 512 seeds and classic oscillator/spaceship periods.
Version 1 was generated on 2026-10-11. Download SHA-256 checksums to compare the exact files. Footprint dimensions are reported as short and long sides; JSON displacement components are absolute and sorted. Neither describes orientation-specific axes.