Field notes / Experiment guide
How often does apparent chaos turn into a highway?
An ant can wander for billions of steps before finding a repeating path that carries it away. Does the chance of that late switch stay constant per decade of time?
New to these ants? Start here.
An ant moves on a grid of coloured squares. Each colour tells it to turn left (L) or right (R). It advances that square to the next colour, then steps forward. A rule such as RLR is the list of turns, starting at colour zero. On a blank grid the same rule always makes the same trajectory.
Territory means every cell visited so far. Its boundary consists of visited cells with an unvisited neighbour. A highway is a repeating pattern of motion that carries the ant away. A tether means repeated returns to a small home region.
Growing like the cube root of time means taking eight times as many steps to double a linear size. The rotor walker is a comparison model that follows and rotates arrows stored on cells. A seed makes a random starting pattern reproducible; the ant itself can still move deterministically.
We distinguish c, the chance of discovering a cell per boundary step, from kappa (κ), time at the boundary normalized by perimeter divided by area. Explaining their values is harder than using them to account for growth.
The idea under test
Extending surviving rules by another decade should produce a similar fraction of new highways if the onset tail remains flat.
What we learned
The new-highway count falls below the flat-rate prediction. The observed tail thins, while some board escapes still have no classified highway.
What this leaves open
One more decade cannot show whether every survivor eventually switches. Board escape is not itself evidence of a highway.
Read the evidence and reproduction recipe ↗
Inside the experiment
Methods, registered predictions, exact commands and saved analysis. These are the working research documents; expand them for the detail behind the introduction.
Methods and original experiment record
b5-late-highways
Migrated legacy investigation (2026-10-14). Its files used to sit in the flat data/ directory (and calib/, occ/, snaps/, dumps*, knock* where listed) with the label prefix below; experiments/_migration/map.tsv gives the exact old -> new path of every file. This stub was generated from file names and script docstrings. It is not the original write-up: the question, timestamped hypotheses, commands and results are in notes/ (mainly notes/frontier-results.md, notes/frontier-status.md, notes/research-frontier*.md; search for the label), and the producing command is usually in the script docstring or a run_*.sh here.
Old labels / prefixes: b5
Scripts
scripts/b5_restart6.sh: Restart the B5 driver with 6 rayon threads (12 rules per chunk = exactly 2 rounds of 6) at the next chunk boundary. Safe: chunks are resumable.scripts/b5_stats.py: B5: highway onsets in (1e10, 1e11] for a 240-rule unbiased sample of the rules still unresolved at 1e10 (experiments/2026-10-13-highways-unresolved-rules-1e10-1
Results
2 entries in results/ (1 are .log/.done markers); csv/json/txt outputs, *_stats.txt hold the summaries quoted in the notes.
Notebook
No committed Jupyter notebook is available for this experiment yet.