Methods & Data Dictionary

Nothing here touches the path library or the network at page-load: a scheduled builder does all the reading and writes one JSON snapshot, and every board renders only that file. The builder is incremental — each new .wrd is analysed exactly once into an append-only index — so even a multi-million-path library is processed once, ever.

Three sources, three provenances. LIB the kept .wrd library — geometry-rich, but only the tail (length ≥ 3000 or radius ≥ 300). POP combined histograms over every walk ever run — the uncensored truth for means and exponents. LOG the per-machine performance.log — throughput and luck. Any full-population claim must come from POP; the library alone is a censored sample.

One row per kept path in path_stats.csv. Each column is a single linear pass over the trace (the convex hull is O(N log N); the sealed-chamber flood fill is bounded). Everything the boards show derives from this table plus the population and fleet logs.

Flory exponent ν

Fit ⟨R²⟩ ∼ N^2ν across length bins. The 2-D self-avoiding-walk value is ν = 3/4 exactly (Nienhuis 1982); kinetic-growth walks are believed to share it asymptotically.

Fractal dimension D

Mean box-counting slope of a trace; theory D = 1/ν = 4/3.

Asphericity

From the gyration-tensor eigenvalues, ((λ₁−λ₂)/(λ₁+λ₂))²; a known universal mean for 2-D SAWs.

Winding-angle law

Variance of the angle wound about the origin grows ∝ ln N (Duplantier & Saleur 1988).

First-passage scaling

Median step to reach radius r grows as r^1/ν = r^4/3.

Asphyxiation curve

Ensemble-mean free neighbours 100/50/10 steps before the trap — the universal shape of dying.

Mean trapping length

The [POP] mean walk length. The 4-direction lattice value is ≈70.7 (Hemmer & Hemmer 1984); the 8-direction constant has no published figure and is measured here.

RNG integrity

Chirality must split 50/50 (binomial p) and the 8 step directions must be equiprobable across the ensemble (χ² vs uniform); the roses must be round.

Correlation matrix

Pearson r between the curated measures, from streamed sums, sums-of-squares and cross-products.

Shape space

PCA of the correlation matrix (a Jacobi eigen-decomposition); a reservoir sample of paths is projected onto the top two components. The nearest twin is the closest pair in standardised descriptor space.

Record history

Because the index is written oldest-first, a forward pass with running maxima recovers when each record fell; for i.i.d. draws the count grows as ln n + γ and the next break waits ~n paths.

The bestiary

Each walk is placed into one personality species by priority rules on orbits, outward bias, straight-run length, hull fill, reach and tortuosity, using library-adaptive cut-offs.

Rarity / Path of the Day

Mean absolute z-score across length, reach, gyration, tortuosity and hull area over the recent window.

schema

v3

compiled

2026-08-01 11:52:15 (34m ago)

library

45.5K kept paths

Blocks present in the current snapshot:

⭳ Download the raw snapshot (JSON) everything on every board, in one file