Field notes / Experiment guide
How far does the ant growth pattern travel?
Is the observed growth peculiar to one ant on a square grid, or does it recur on other lattices and in related walkers?
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
Screening other geometries, internal states, noise levels and ant counts should reveal which changes preserve compact slow growth.
What we learned
The screens find related growth regimes alongside distinct thin structures and noise-driven crossovers. They motivate the more focused extension experiments.
What this leaves open
A broad screen is a way to find questions. Small cohorts, short windows and board escapes limit claims of universality.
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
ext-other-lattices-turmites-noise
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: ext, tm, tri
Scripts
scripts/ext_lattice_stats.py: Items 24, 28 (and 25 with kind=tm): classify growth of hex / cube / turmite screens.scripts/ext_long_stats.py: Items 25 and 28 follow-ups: local exponents at late times for the turmite candidates (experiments/2026-10-13-ext-other-lattices-turmites-noise/results/ext_tm_loscripts/ext_screens.py: Spec generators for the lattice/turmite screens (items 24, 25, 28). usage: python3 experiments/2026-10-13-ext-other-lattices-turmites-noise/scripts/ext_screens.scripts/ext_specs_26_27.sh: Items 26/27 experiments. usage (WSL): bash experiments/2026-10-13-ext-other-lattices-turmites-noise/scripts/ext_specs_26_27.sh (writes experiments/2026-10-13-scripts/ext_stats.py: Items 26 and 27: analyse experiments/2026-10-13-ext-other-lattices-turmites-noise/results/ext_many.csv, ext_noise.csv, ext_bg.csv (made by experiments/2026-10-1
Results
39 entries in results/ (11 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.