How do I simulate a Markov chain?

Open this page and use the live Euler vs RK4 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 Markov chain from your own measurements.

Use case · powered by Euler vs RK4

Euler vs RK4 for a Markov chain

Simulate a Markov chain live in your browser. This runs the real Euler vs RK4 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

Numerical Methods — Euler vs RK4Live

ODE integration accuracy

Controls

Solving dy/dt = y (true answer eᵗ). Euler drifts badly at large step sizes; RK4 hugs the exact curve. Shrink the step and both improve — RK4 far faster.

Presets

Step size h

▶ Run in Python

Data Inspector

Step h0.50

Euler error8.695

RK4 error2.07e-2

RK4 order4th

Governing equation

y_{n + 1} = y_{n} + h f (t_{n}, y_{n}), h = 0.50

Reading this result: Halving the step roughly halves Euler's error (1st order) but cuts RK4's by ~16× (4th order): that steep payoff is why RK4 dominates for smooth problems.

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

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About this simulation

The full Euler vs RK4 tool models a Markov chain 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 Euler vs RK4

Euler vs RK4 for compound interest Euler vs RK4 for a population curve Euler vs RK4 for a loan payoff Euler vs RK4 for a logistic map Euler vs RK4 for a Fibonacci sequence Euler vs RK4 for a fractal tree Euler vs RK4 for a Fourier series Euler vs RK4 for a Taylor approximation

Other ways to simulate a Markov chain

Visual Node Graph for a Markov chain Symbolic Math for a Markov chain Vector Fields for a Markov chain Notebook for a Markov chain Fractal Explorer for a Markov chain Fourier Series for a Markov chain

Frequently asked questions

How do I simulate a Markov chain?: Open this page and use the live Euler vs RK4 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 Markov chain from your own measurements.