Mazes

DFS, Kruskal and Wilson side by side — algorithm as bias.

patterns.maze · v1 · renderer canvas

Randomised DFS: 262 deep, 10% dead ends · Kruskal: 116 deep, 32% dead ends · Wilson's: 121 deep, 28% dead ends

Every one of these is a spanning tree: 480 cells, 479 passages, exactly one route between any two points. They are not drawn from the same distribution. DFS carves until it cannot and then backs up, so its longest route runs 262 cells and only 10% of cells are dead ends; Kruskal leaves 32%; Wilson's leaves 28% and is the only one of the three that is provably uniform over all possible mazes — the other two are biased by their own convenience.

[data-canvas-stage] { display: none; }

Drawn in the browser

This generator does not send you an image. The server sends a short description of one — the parameters below, plus a 32-byte key — and the drawing is done here, from the same byte stream the server would have used. That needs JavaScript, so with it switched off there is nothing to show.

The description itself is still public: /api/v1/g/patterns.maze returns it, and the maths is in resources/js.

Randomised DFS: 262 deep, 10% dead ends · Kruskal: 116 deep, 32% dead ends · Wilson's: 121 deep, 28% dead ends

Controls · from schema()

Width

200 2048

Height

200 2048

Algorithm

Cell size

8 64

In pixels. Grown automatically if the grid would otherwise be too large to carve.

Wall thickness

0.04 0.5

As a fraction of a cell.

Colour the floor by

Distance is where the bias becomes visible: DFS stretches one long gradient, the other two spread outwards.

Colour

Palette size

2 12

Entropy source

Picking a source changes the story on the receipt, never the quality: anything below class A is mixed with the OS CSPRNG before it reaches you. This result actually came from Live Weather.

seed token R0PK209VGTYB98AJV5N2TWKGQG

Re-render keeps this token. Generate replaces it. That is the whole idea.

Burned into the corner before the file is written, so the image keeps its provenance wherever it ends up:

entropy in

16 bytes

stream used

4,345 bytes

rejections

532

duration

4,372 µs

palette

grid

15 × 32

cells each

480

passages each

479

statistics

{"dfs":{"dead_ends":0.096,"mean_depth":155,"max_depth":262},"kruskal":{"dead_ends":0.325,"mean_depth":54.2,"max_depth":116},"wilson":{"dead_ends":0.281,"mean_depth":65.1,"max_depth":121}}

Seed receipt

Class C · Observational cached

It was 0.1°C in Yakutsk, Russia, with a 16 km/h wind, when this was made.

Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.

source: Live Weather
observed: 2026-09-14T17:21:40+00:00
latency: 0ms
mixed with: csprng — always

https://open-meteo.com/en/docs#latitude=62.035&longitude=129.675 ↗

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The token is the seed, so this link recomputes the result rather than looking it up. No database, and it works for as long as v1 does.

This page and /api/v1/g/patterns.maze run the same code. There is no private endpoint.

Mazes

Result

Measurements

Seed receipt

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