Field notes / Experiment guide
Are unusually fast and slow exponents reproducible?
The census contains rules far from the central growth-exponent peak. Do they remain unusual under new starting patterns?
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
Repeated patched starts should distinguish a persistent rule effect from an exceptional trajectory or transient.
What we learned
The experiment remeasures the selected extreme rules alongside random core controls, retaining seed variation rather than trusting a single fitted slope.
What this leaves open
Selection was based on extreme original estimates, so regression toward the centre is expected. The result is not an unbiased sample of all rules.
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
item21-slow-outliers
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: item21
Scripts
scripts/item21_select.py: Item 21: pick the extreme exponent outliers among blob rules (alpha_w > 0.40 or < 0.27) plus 30 random corescripts/item21_stats.py: Item 21: re-measurement of exponent outliers. Input experiments/2026-10-13-item21-slow-outliers/results/item21_probe.csv (probe 27 < experiments/2026-10-13-item
Results
7 entries in results/ (2 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.