Random Walk & Markov Chain Visualizer

Why this stochastic process visualizer?

Compare random walk diffusion, bias, and boundary conditions visually.
Build Markov chains from a transition matrix and see probability evolution.
Estimate stationary behavior (power iteration) and try absorbing-chain analysis when applicable.
Copy a settings-only URL and download results (JSON/CSV/PNG).

How to use (3 steps)

Choose a mode: Random Walk or Markov Chain.
Adjust settings (steps, paths, or transition matrix).
Run, then download or copy a settings-only URL.

Visualize

Random walk & Markov chain

Two lightweight modes: random-walk trajectories/MSD and Markov probability evolution/graphs.

Dimension

Steps

Paths

Drift strength: 0

For 1D, this becomes p(right). For 2D, it biases the direction softly.

Drift direction (deg)

0°

Neighbors

Boundary

Advanced

RNG

Animation speed

Visualization

Trajectories

MSD

Distribution

Probability table (sample)

Details

Notes

These visualizations help build intuition. They do not guarantee prediction accuracy or cryptographic security.

How to use this tool effectively

This guide helps you use Random Walk & Markov Chain Visualizer in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.

How it works

The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.

When to use

Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.

Common mistakes to avoid

Changing multiple parameters at once, which hides the true cause of output movement.
Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
Comparing with another tool without aligning defaults, constants, and rounding rules.
Using rounded display values as exact downstream inputs without re-checking precision.

Interpretation and worked example

Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.

Frequently asked questions

What is a random walk?

A random walk is a process that moves step-by-step in random directions. It is a basic model for diffusion and noise.

What is a Markov chain?

A Markov chain is a process where the next state depends only on the current state, via a transition matrix.

Does a stationary distribution always converge?

Not always. Periodic or reducible chains may not converge from every initial distribution, even if a stationary distribution exists.

Is my input uploaded?

No. Everything runs locally in your browser.

What should I do first on this page?

Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.

How to use Random Walk & Markov Chain Visualizer effectively

How this tool helps

Tools are designed for quick scenario comparisons. They work best when you keep one question per run, define success criteria first, and avoid switching objectives mid-stream. This reduces decision noise and produces results you can defend in follow-up review.

Input validation checklist

Before running, verify that required values are in the right format, that optional flags are intentionally set, and that baseline assumptions reflect current conditions. Invalid assumptions are often mistaken for tool bugs, so validation is part of interpretation quality.

Scenario planning pattern

Build three rows: conservative, expected, and aggressive cases. Keep data sources transparent for each case and compare output spacing. The pattern helps you spot non-linear jumps and decide whether a model is stable under plausible variation.

When to revisit inputs

Revisit inputs when input scale changes, time window shifts, or downstream decisions add new constraints. If constraints change, your previous output remains a useful reference but should not be treated as final guidance.