PPolySim OS

Markov Chain

Systems that hop between states by fixed probabilities forget where they started — they settle into one stationary distribution. Watch it converge.

Markov ChainLive
A100.0%
B0.0%
C0.0%

Controls

A system hops between states by fixed probabilities. From any start it converges to the same stationary distribution — the math behind PageRank and queueing.

Presets

▶ Run in Python

Data Inspector

Step0
P(A)1.000
P(B)0.000
P(C)0.000

Governing equation

Reading this result: State A has the stickiest self-loop (0.70), so it keeps the largest share of the stationary distribution no matter where you start.

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

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How it works

A Markov chain moves between states according to a transition matrix. No matter the starting state, an ergodic chain converges to a unique stationary distribution — the principle behind Google PageRank, queueing theory, and Markov-chain Monte Carlo.

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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

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Frequently asked questions

Is this Markov chain simulation tool really free?
Yes. Markov Chain 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.