Field notes / Experiment guide
What happens when the rotor’s world has a preferred direction?
The rotor walker is a comparison model with arrows stored on the grid. Does biasing those initial arrows destroy cube-root growth?
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 alternatives are a continuous change with bias or a range of biases that preserves the exponent before a crossover.
What we learned
With adequate board size the width exponent persists through moderate bias, then becomes ballistic at stronger bias. Area and shape respond earlier.
What this leaves open
An initial apparent failure was a board-size effect. Width alone can hide elongation and changing area 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
c2-arrow-bias
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: c2, c2b, c2c, escape, run
Scripts
scripts/c2_escape.py: C2 follow-up: all biased-arrow runs left the 8192 board, so per-run exponents over k=20..26 do not exist.scripts/c2_stats.py: C2: rotor with north-biased initial arrows. Input experiments/2026-10-13-c2-arrow-bias/results/c2_probe.csv. Decision rule in notes/frontier-2026-10-13-results.scripts/c2b_escape.py: C2b: biased-arrow runs (small biases, grid 32768); original text: all biased-arrow runs left the 8192 board, so per-run exponents over k=20..26 do not exist.scripts/c2b_stats.py: C2: rotor with north-biased initial arrows. Input experiments/2026-10-13-c2-arrow-bias/results/c2b_probe.csv. Decision rule in notes/frontier-2026-10-13-resultsscripts/c2c_escape.py: C2 follow-up: all biased-arrow runs left the 8192 board, so per-run exponents over k=20..26 do not exist.scripts/run_c2.sh: C2: biased-arrow rotor vs unbiased control. usage (WSL): RAYON_NUM_THREADS=1 bash experiments/2026-10-13-c2-arrow-bias/scripts/run_c2.shscripts/run_c2b.sh: C2b: small biases on a larger grid. usage (WSL): RAYON_NUM_THREADS=1 bash experiments/2026-10-13-c2-arrow-bias/scripts/run_c2b.shscripts/run_c2c.sh: C2c: bias 0.2, 0.25, 0.3 on a 32768 board. usage (WSL): RAYON_NUM_THREADS=3 bash experiments/2026-10-13-c2-arrow-bias/scripts/run_c2c.sh
Results
21 entries in results/ (9 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.