Every figure on these boards comes from one blind process — a walk that steps to a random unvisited neighbour until it traps itself — measured once and aggregated cheaply. This page is the reference: the pipeline that turns raw traces into a snapshot, a dictionary of every per-path measure, the science each panel tests, and a live look at the current snapshot with a link to download it.
The pipeline
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.
*.wrd traces — full (x, y) traces of the kept "interesting" walkspath_stats.csv (≈50 columns/path)path_stats_summary.jsonThree 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.
Per-path data dictionary
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.
| Column | Meaning |
|---|---|
| Identity | |
| file | Filename Length_Serial_Client.wrd |
| serial / client | The path's serial number and the machine that found it |
| mtime | When the file was written (used for growth and record history) |
| family | Marathoner (N≥3000), Voyager (R_max≥300), Legend (both), or other |
| Size & displacement | |
| length | Steps taken, N (points − 1) — the headline number |
| end_r | End-to-end distance R from origin to the death point |
| manhattan | |dx|+|dy| at death |
| max_r | Farthest radius the walk ever reached — the Voyager criterion |
| rg | Radius of gyration — the polymer-physics size measure |
| bbox_w / bbox_h / aspect | Bounding-box width, height and long/short ratio |
| hull_area / hull_perim / hull_v | Convex-hull area, perimeter and vertex count |
| fill_bbox / fill_hull | Points per unit bounding-box / hull area — coil density |
| fractal_d | Box-counting dimension of the trace (2-D SAW theory: 4/3) |
| asphericity | Gyration-tensor shape, 0 = disc … 1 = rod |
| Direction & turning | |
| d0 … d7 | Counts of each of the 8 step directions |
| diag_frac | Fraction of steps that were diagonal (cover √2) |
| longest_run | Longest unbroken straight run, in steps |
| chirality | Net signed turning (+ = CCW, − = CW) |
| winding_deg / orbits | Total angle wound about the origin, and full turns |
| turn_entropy | Shannon entropy of the turn-angle histogram |
| reversal_rate / repeat_frac | Share of turns ≥90°, and share that repeat the heading |
| drift_mag / drift_deg / death_deg | Centroid drift magnitude & bearing; death bearing |
| Death & constraint | |
| self_contacts | Times the walk brushed its own trail and survived |
| choice_entropy | Mean log₂(free neighbours) — how constrained the walk was |
| enclosed_area | Unvisited cells sealed into chambers at death (−1 if skipped) |
| free_m10 / free_m50 / free_m100 | Free neighbours 10/50/100 steps before the trap |
| Origin & tempo | |
| esc50 / esc100 / esc200 / esc300 | First step to reach radius 50/100/200/300 (−1 = never) |
| closest_return | Nearest approach to home after first passing radius 100 |
| outward_bias | Fraction of steps that increased the radius |
| tortuosity | N ÷ R — steps spent per cell of net progress |
| peak_frac | Where R_max happened, as a fraction of the walk |
Methods the panels test
- Flory exponent ν
- Fit ⟨R²⟩ ∼ N2ν 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 r1/ν = r4/3.
- 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.
This snapshot
- schema
- v3
- compiled
- 2026-11-01 13:53:25 (8m ago)
- library
- 52.3K kept paths
Blocks present in the current snapshot:
⭳ Download the raw snapshot (JSON) everything on every board, in one file