Field notes / Experiment guide
Why is the ant’s edge broader than the rotor’s?
Ant and rotor territories can grow at similar rates while their boundaries fluctuate differently. Does the difference disappear in longer runs?
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
The ant’s boundary-width exponent might drift toward the rotor’s value as the territory grows.
What we learned
The gap persists through the extended measurement windows: ants retain broader boundary fluctuations than the rotor under this estimator.
What this leaves open
Boundary width mixes shape and local roughness. The later hull experiments separate these more carefully.
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
a4-boundary-width
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: a4, a4c, run
Scripts
scripts/a4_stats.py: A4: boundary-width (Wsurf) local exponents for the rotor and the ants out to 2^32. Inputs experiments/2026-10-13-a4-boundary-width/results/a4_shape_rotor.csv, escripts/a4c_stats.py: A4: boundary-width (Wsurf) local exponents for the rotor and the ants out to 2^32. Inputs experiments/2026-10-13-a4-boundary-width/results/a4c_shape_rotor.csv,scripts/run_a4.sh: A4: boundary-width series to 2^32. usage (WSL): CARGO_TARGET_DIR=~/turmite-target-frontier2 RAYON_NUM_THREADS=1 bash experiments/2026-10-13-a4-boundary-width/scscripts/run_a4c.sh
Results
22 entries in results/ (12 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.