Field notes / Experiment guide
Why do some ants spend more time at the edge?
Two ants can have similar territory shapes yet spend different amounts of time near fresh ground. Can simple rule features predict that difference?
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.
A closer look
The idea under test
The boundary occupation factor, kappa, might be set by letter balance, early letters or the mixture of colours at the edge.
What we learned
Kappa varies reproducibly between rules, but these simple predictors did not explain it in the original analysis. The proposed half-plane mechanism was not built.
What this leaves open
This is an early negative result. Later prefix and growth-control experiments refine the question; it does not rule out every predictor of kappa.
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
a1-kappa
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: a1, a1b, a1c, a1d
Scripts
scripts/a1_edge_q.py: A1, exploratory (not pre-registered): does the edge-weighted turn probability q_edge = sum_c share_boundary(c) * [rule[c] == R] explain kappa across the 40 mixiscripts/a1_kappa_proxy.py: A1 proxy (NOT the half-plane model): how much of the across-rule variance of kappa is carried by the rule string alone?scripts/a1b_icc.py: A1b: ICC of kappa across rules with 12 patched seeds per rule. Design/decision: notes/frontier-2026-10-13-results.md. usage: uv run experiments/2026-10-13-a1-kascripts/a1c_predict.py: A1c (exploratory, after A1b): predict the rule-mean kappa (core band, b2_probe + item21 + patched rules, >= 6 runs) from the rule string.scripts/a1d_stats.py: A1d: probe statistics of the memoryless persistent walker (pw:Q:SEED).
Results
7 entries in results/ (0 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.