Diffusion-Limited Aggregation

Dendritic crystals, grown one sticky particle at a time.

patterns.dla · v1 · renderer canvas

7,000 particles · 440×400 lattice · from a point · stickiness 1.00

Grown outward from one seed cell, so the cluster is a star whose arms competed for every arrival. At full stickiness a particle freezes at the first thing it touches, which is almost always a tip — hence the thinnest, most dendritic form the rule produces. Colour runs along the palette in arrival order, so the ramp is the history of the growth rather than a restatement of its shape.

[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.dla returns it, and the maths is in resources/js.

7,000 particles · 440×400 lattice · from a point · stickiness 1.00

Controls · from schema()

Width

200 2048

Height

200 2048

Grow from

Particles

200 40000

Every one of them is walked until it touches, which is the entire cost of the render. The run ends at this count or when the cluster reaches the edge of its lattice, whichever comes first — and the finished cluster is then fitted to the frame, so fewer particles means a chunkier crystal rather than a smaller one.

Lattice

1 10

The lattice the crystal grows on, as a divisor of the canvas. A finer lattice grows a cluster with finer branches, and costs a great deal more walking: halving this roughly triples the render.

Stickiness

0.02 1

The chance a particle freezes when it touches. Below 1 it can work its way into the crevices before committing, which thickens the branches and pushes the fractal dimension towards 2 — frost at one end of this slider, sponge at the other.

Glow

0 0.3

A wide, faint halo under every particle, added rather than painted. Haloes overlap where the cluster is dense, so the trunk lights up and a lone tip does not.

Ground

Colour

Palette size

2 12

Grain

0 0.08

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 RANDOM.ORG.

seed token 5A737A5HDHEYS15VQZ0RZ6185W

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

8 bytes

rejections

duration

155 µs

palette

background

#010103

particles

7,000

lattice

440×400

fractal dimension

≈1.71 (planar DLA, measured)

Seed receipt

Class A · Cryptographic

Atmospheric radio noise, sampled in Dublin moments ago.

source: RANDOM.ORG
observed: 2026-10-30T11:13:42+00:00
latency: 234ms
mixed with: csprng — always

https://www.random.org/randomness/ ↗

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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.dla run the same code. There is no private endpoint.

Diffusion-Limited Aggregation

Result

Measurements

Seed receipt

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