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Random Walk & Diffusion

Hundreds of walkers take random steps from a single point. The cloud spreads as the square root of time — diffusion, built from randomness.

Random Walk & DiffusionLive

Controls

Hundreds of walkers start at the center and step randomly. The cloud spreads as √(time) — the signature of diffusion.

Presets

▶ Run in Python

Data Inspector

Walkers400
Steps0
RMS distance0.0
Law⟨r²⟩ ∝ t

Governing equation

Reading this result: With 400 walkers the RMS distance grows as √(steps) — the defining signature of diffusion.

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

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How it works

Each walker steps in a random direction each frame. Individually unpredictable, collectively they obey a precise law: mean-squared displacement grows linearly with time (⟨r²⟩ ∝ t). This is the microscopic basis of Brownian motion, heat diffusion, and the diffusion equation.

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Frequently asked questions

Is this random walk simulation tool really free?▾
Yes. Random Walk & Diffusion 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.