How do I simulate a random walk?

Open this page and use the live Lissajous Curves tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a random walk from your own measurements.

Use case · powered by Lissajous Curves

Lissajous Curves for a random walk

Simulate a random walk live in your browser. This runs the real Lissajous Curves solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

Lissajous CurvesLive

harmonic motion in two axes

Controls

Speed1×

Combine two perpendicular sine waves. The frequency ratio a:b sets the number of lobes; the phase δ morphs the shape — the patterns you see on an oscilloscope.

Presets

Frequency a (x)

Frequency b (y)

Phase δ (×π)

▶ Run in Python

Data Inspector

Ratio3:2

Phase0.50π

Closedrational

Governing equation

x = A sin (3 t + 0.50 π), y = B sin (2 t), 3 : 2

Reading this result: Reduced to 3:2, the curve closes into a stable 3-by-2 lobe figure; because the ratio is a whole-number fraction it never drifts, and the phase δ only morphs and rotates that fixed pattern.

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

or unlock everything with Pro →

About this simulation

The full Lissajous Curves tool models a random walk with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

More you can do with Lissajous Curves

Lissajous Curves for compound interest Lissajous Curves for a population curve Lissajous Curves for a loan payoff Lissajous Curves for a logistic map Lissajous Curves for a Fibonacci sequence Lissajous Curves for a fractal tree Lissajous Curves for a Fourier series Lissajous Curves for a Taylor approximation

Other ways to simulate a random walk

Visual Node Graph for a random walk Symbolic Math for a random walk Vector Fields for a random walk Notebook for a random walk Fractal Explorer for a random walk Fourier Series for a random walk

Frequently asked questions

How do I simulate a random walk?: Open this page and use the live Lissajous Curves tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a random walk from your own measurements.