Field notes / Experiment guide
Do thin turmites have the same visit profile as compact ants?
Can the radial visit-density argument be carried over to stateful walkers with square-root-like 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.
A closer look
The idea under test
If the same uniform-occupation assumptions hold, the growth law should predict the accumulated profile.
What we learned
Several thin square-root walkers escape the board before a usable profile is obtained. Missing profiles cannot count as support for the formula.
What this leaves open
Thin geometry and board censoring make this a different regime from a compact two-dimensional territory.
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
w2
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: w2
Scripts
scripts/w2_select.py: W2 selection: 10 sqrt-class and 10 chaotic-class 2x2 turmite tables, seed 20261013, from the 2^20 screen.scripts/w2_stats.py: W2: visit-density profile of 2x2 turmites at 2^28 vs the uniform-occupancy formula (1/(1-a))(1-(r/R)^(2(1-a)/a)) with the run's own a (k=22..28)
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.