Field notes / Experiment guide
Does the cube-root pattern survive longer instructions?
The first census concentrates on short rules. Does the growth pattern persist when an ant has many more colours to cycle through?
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
Longer sampled rules should retain a width exponent near one third, while the balance of slow and compact growers may change.
What we learned
The sampled rule lengths retain exponents near one third. The fraction of very slow growers decreases with length.
What this leaves open
Sampling longer rules is not an exhaustive census, and a finite run cannot certify permanent chaotic growth.
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
b3-long-rules
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: b3
Scripts
scripts/b3_sample.py: B3: random rules of length 10,12 (controls),14,16,20,24; 200 each; uniform over strings starting with R; seed 20261013.scripts/b3_stats.py: B3: rule-length extension. Input experiments/2026-10-13-b3-long-rules/results/b3_probe.csv (probe to 2^27). Decision rule: notes/frontier-2026-10-13-results.md.
Results
5 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.