Brownian Motion Generator
Create a reproducible continuous-time style random process.
Also known as: wiener process
seeded
Output
About this tool, tips & examples
What it does
The Brownian Motion Generator simulates a Wiener process — the continuous-time random walk that underpins diffusion physics and most of quantitative finance. Configure the volatility (step size) and an optional drift term, generate up to 10,000 steps, and reuse a seed to reproduce the exact same path. The output is the running series, ready to chart or export as CSV or JSON.
Common use cases
- Finance demos — drifting Brownian motion is the core of the geometric-Brownian-motion price models used in options pricing; simulate paths to illustrate volatility and drift visually.
- Teaching stochastic processes — show how the same volatility produces wildly different paths, and how drift bends the ensemble.
- Testing analytics code — feed charting, smoothing, or anomaly detection a series whose statistical properties you control.
- Placeholder time series — realistic-looking wandering data for dashboard mockups.
Settings
- Steps — the length of the path, 1 to 10,000 points.
- Volatility — the scale of each random increment; higher values make a wilder path.
- Drift — a constant per-step trend added on top of the noise; positive drift trends up, zero is the pure Wiener process.
- Seed — the same seed and parameters always regenerate the identical path.
Privacy note
Paths are computed locally in your browser and never uploaded. The output is a synthetic mathematical simulation — not market data and not a prediction of anything.
FAQ
What’s the difference between this and a random walk? A random walk moves in discrete jumps (±1 per step); Brownian motion is its continuous limit, with normally distributed increments. For the discrete version, see the Random Walk tool.
Why do two runs look so different? That’s the nature of the process — variance grows with time, so paths diverge. Fix the seed to freeze one path for repeatable demos.
Can I simulate a stock price with this? This generates arithmetic Brownian motion. For a simple price-like series, add drift and exponentiate the result yourself — or use it directly to explain the concepts.