Field notes / Experiment guide
Why do some stateful ants grow a different way?
Adding an internal state produces many walkers with square-root-like area growth. Are they compact territories with a new exponent, or thin structures?
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
A simple transition-table feature might distinguish these walkers from compact cube-root-like growers.
What we learned
No single table feature cleanly separates the classes. The square-root class instead has increasingly thin, effectively one-dimensional geometry.
What this leaves open
These are screened transition tables, with symmetry duplicates and finite observation times; the result is not a full classification theorem.
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
d1-turmite-sqrt-cluster
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: d1, d1b, run
Scripts
scripts/d1_tables.py: D1: table features of the sqrt(t) turmite cluster vs the cube-root-like cluster. Design and decision rule: notes/frontier-2026-10-13-results.md.scripts/d1b_specs.py: dependencies = ["numpy"]scripts/d1b_stats.py: D1b: 2-state 3-colour random tables: classes, 'state 0 never leaves state 0' enrichment, single-feature AUCs, area/extent^2. Design/prediction: notes/frontier-2scripts/run_d1b.sh
Results
8 entries in results/ (3 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.