Field notes / Experiment guide
A census of the worlds ants build
What kinds of long-run behaviour emerge when we enumerate short left/right rules instead of choosing a few attractive examples?
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 census asks whether recurrent compact growth is common and which rules instead build repeating escape paths or grow very slowly.
What we learned
The sweep supplies the rule catalogue used by later growth and highway studies. Exact repeats of shorter rules can be removed without changing the main growth summary appreciably.
What this leaves open
Classifications are bounded by the run budget and board size. A rule that has not built a highway yet is not proved never to build one.
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
census-sweeps
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: 1B, census, confirmed, equiv, non, regen, sweep, unresolved, v2
Scripts
scripts/census.pyscripts/equiv_census.py: Frontier item 23: how many census rules are exact repeats u^k of a shorterscripts/regen_frontier_stats.sh: Regenerates every analysis text output of the frontier work from the raw data files (deterministic; run twice and diff to check).
Results
13 entries in results/ (1 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.