Field notes / Experiment guide
Is the exponent spread really changing empty space?
Two territories can have the same width but different numbers of visited cells. Does changing filling fraction explain why their area exponents differ?
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
Decomposing area into bounding-box size and filling fraction should separate shape growth from progressive filling.
What we learned
The saved decomposition measures those contributions rather than treating width and area exponents as interchangeable.
What this leaves open
This is a decomposition of existing trajectories, not a mechanism test. Consult the saved analysis before interpreting any particular rule’s contribution.
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
h1-lacunarity-decomposition
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: h1, run
Scripts
scripts/h1_decomp.py: dependencies = ["polars", "numpy", "scipy"]scripts/h1_lacunarity.py: H1 (research-frontier-2026-10-13-pm.md): is the rule-specific part of the area exponent carried by drift of the filling fraction eta = A/(W_x W_y)?scripts/run_1e10.sh: Item 17: push the length<=10 primitive rules still unresolved at 1e9 to 1e10 steps (lean ant, grid 32768).scripts/run_1e11.sh: B5 (frontier 2026-10-13): first 240 rules (in the fixed-seed shuffled chunk order of run_1e10.sh)scripts/run_1e11b.sh: B5 extension (2026-10-13): the remaining survivors of the 1e10 run (list positions 241..), same protocol as run_1e11.sh, chunks 20.. .
Results
1 entries in results/ (0 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.