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.
For 1D, this becomes p(right). For 2D, it biases the direction softly.
0°
0°
Advanced
Seeded mode is for reproducible demos/tests only (not secure).
More presets
Transition matrix P
Paste as text
Initial distribution π0
0.10
Advanced
Visualization
Trajectories
MSD
Tip: drag nodes to rearrange the state graph.
Distribution
Probability table (sample)
Details
Notes
These visualizations help build intuition. They do not guarantee prediction accuracy or cryptographic security.
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.