# L-Systems — Randomly

> Stochastic rewrite rules: plants, snowflakes, dragon curves. One of 63 generators at [Randomly](https://randomly.cluxnei.dev), a library of random generators seeded from verifiable real-world entropy. Free HTTP API, no key, no signup.

## `patterns.lsystem` — L-Systems

Stochastic rewrite rules: plants, snowflakes, dragon curves.

| | |
|---|---|
| **Key** | `patterns.lsystem` |
| **Module** | `patterns` |
| **Version** | `1` — a permalink carries this, and a replay against a different version returns `409` rather than something else |
| **Formats** | `application/json`, `text/plain`, `image/png` |
| **Studio** | https://randomly.cluxnei.dev/g/patterns/lsystem |
| **API** | `GET https://randomly.cluxnei.dev/api/v1/g/patterns.lsystem` |

`value` is a **render spec** — algorithm, parameters, palette and a render key — not pixels. Ask for `format=png` to get the image.

| Parameter | Type | Default | Accepts | What it does |
|---|---|---|---|---|
| `width` | int | `900` | `200` – `2048` | Width |
| `height` | int | `600` | `200` – `2048` | Height |
| `preset` | enum | `plant` | `plant`, `koch`, `dragon`, `sierpinski` | System |
| `iterations` | int | `0` | `0` – `14` | Iterations — Zero uses the preset's own depth. Each iteration rewrites every symbol at once, so the string grows geometrically. |
| `angle` | float | `0` | `0` – `180` | Turn angle — Zero uses the preset's own angle. The single most dramatic control here — a plant at 90° is a lattice. |
| `stochastic` | float | `1` | `0` – `1` | Randomness — 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. |
| `thickness` | float | `2` | `0.4` – `6` | Line weight |
| `palette` | enum | `viridis` | `golden`, `analogous`, `complementary`, `triadic`, `split`, `viridis`, `magma`, `mono` | Colour |
| `colours` | int | `7` | `2` – `12` | Palette size |

Out-of-range numbers are **clamped, not rejected**, so a request never fails for being
ambitious — but it may not do what you meant. Unknown keys are dropped and missing ones
fall back to the defaults above.

```bash
curl -s 'https://randomly.cluxnei.dev/api/v1/g/patterns.lsystem?width=900&height=600&preset=plant' -H 'Accept: text/plain'
curl -o out.png 'https://randomly.cluxnei.dev/api/v1/g/patterns.lsystem?width=900&height=600&preset=plant&format=png'
```

## The receipt

Every result carries one, naming the physical source of the randomness and linking to the
third party's own record of it:

```json
"receipt": {
  "source": "seismic",
  "source_label": "USGS Seismic Feed",
  "class": "C",
  "caveat": "Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.",
  "narrative": "A magnitude 3.6 earthquake, 67 km N of Culebra, Puerto Rico, 39.6 km down — 52 minutes ago.",
  "proof_url": "https://earthquake.usgs.gov/earthquakes/eventpage/us7000th33",
  "mixed_with_csprng": true,
  "degraded": false
}
```

Pick the source with `?source=`, or leave it at the default `auto`:

- **Class A** (Cryptographic) — `csprng`, `anu-qrng`, `random-org`
- **Class B** (Public beacon) — `nist-beacon`, `drand`, `bitcoin`. Published openly — anyone can look this value up after the fact.
- **Class C** (Observational) — `seismic`, `space-weather`, `atmosphere`, `iss`. Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.

## More

- [The full API contract](https://randomly.cluxnei.dev/api.md)
- [Everything in one file](https://randomly.cluxnei.dev/llms-full.txt)
- [The catalogue as JSON](https://randomly.cluxnei.dev/api/v1/generators)
- [This generator in the browser](https://randomly.cluxnei.dev/g/patterns/lsystem)