L-Systems

Stochastic rewrite rules: plants, snowflakes, dragon curves.

patterns.lsystem · v1 · renderer canvas

Plant · 6 iterations · 24.0° · 1 stochastic rule

The rule for X has four possible replacements and picks one every time it fires — hundreds of thousands of independent choices in a single plant. That is the whole difference between a diagram of a tree and a tree: a deterministic L-system draws the same specimen every time, and nothing in nature does.

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

Plant · 6 iterations · 24.0° · 1 stochastic rule

Controls · from schema()

Width

200 2048

Height

200 2048

System

Iterations

0 14

Zero uses the preset's own depth. Each iteration rewrites every symbol at once, so the string grows geometrically.

Turn angle

0 180

Zero uses the preset's own angle. The single most dramatic control here — a plant at 90° is a lattice.

Randomness

0 1

How freely the branching rules choose between their alternatives, and how much the turns and internodes wander. Only the plant has alternatives; the other three are textbook figures and ignore this.

Line weight

0.4 6

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 NOAA Space Weather.

seed token H80B6VPJSHCJC9FNQXJTZJA0ZC

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 bytes

rejections

duration

815 µs

palette

axiom

rules

{"X":["F+[[X]-X]-F[-FX]+X","F-[[X]+X]+F[+FX]-X","F[+X][-X]FX","F[-X]F[+X]-X"],"F":["FF"]}

iterations

angle

estimated symbols

15,658

Seed receipt

Class C · Observational

Planetary K-index 1.00 — the geomagnetic field was quiet when this was made.

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

source: NOAA Space Weather
observed: 2026-10-30T11:07:00+00:00
latency: 257ms
mixed with: csprng — always

https://www.swpc.noaa.gov/products/planetary-k-index ↗

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

L-Systems

Result

Measurements

Seed receipt

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