PPolySim OS

L-System Fractals

A handful of rewriting rules grow into ferns, snowflakes, and dragon curves. This is how nature — and computer graphics — build organic complexity.

L-System FractalsLive

Controls

Presets

A Lindenmayer system grows a string by rewriting each symbol with a rule, then reads it as turtle commands: F draw, +/− turn, [ ] push/pop. Simple rules, botanical complexity.

Reading this result: After 5 rewrites the string holds 0 symbols — each pass replaces every symbol at once, so detail multiplies exponentially, not linearly.
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Data Inspector

Angle25°
Symbols0
AxiomX

Governing equation

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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How it works

A Lindenmayer system starts from an axiom string and repeatedly replaces each symbol using production rules. The final string is read as turtle-graphics commands (draw, turn, branch), turning a compact recursive grammar into an intricate fractal — the classic model of plant growth.

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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

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Frequently asked questions

Is this L-system fractal generator tool really free?
Yes. L-System Fractals runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.