Markov Chain Simulator

What do tomorrow's weather, your shifting mood, and the word your phone
suggests next all have in common? They can be described by a Markov chain —
a simple rule where the next step depends only on where you are right now,
never on the whole history behind you.

Markov Chain Simulator turns that one elegant idea into a hands-on "graph lab"
you can poke at. Tap a state, watch it hop to the next, and see deep ideas
like steady states and probability matrices appear on their own — no heavy
math background needed, from curious kids to grown-up data lovers.


WHAT YOU CAN DO

☀️ Weather
Sunny, cloudy, or rainy? Tap Step to hop between states along glowing,
probability-labelled arrows, and watch how often each kind of day shows up.

😊 Mood
The exact same machinery on a friendly example — drift between Happy, Okay,
and Grumpy and discover the long-run balance of your "moods".

🛒 Customer
Loyal, Browsing, or Gone? See how a business models customers who stay or
churn — and why some states are hard to escape.

💬 Text Maker
Words are states too. Watch sentences build themselves one word at a time,
each chosen from the current word's probabilities — the very trick behind
your keyboard's next-word suggestions.


SEE THE IDEAS, DON'T JUST READ THEM

- A live state graph — glowing nodes, directed arrows, and the current state
lit up as you step through it.
- Step, Run x100, and Reset — go one hop at a time or take hundreds instantly.
- A visit bar that fills in real time as the chain explores.
- The transition matrix shown as a clean heatmap (every row sums to 1).
- A steady-state donut: start anywhere and the long-run shares always settle
to the same place.
- Crisp formulas (rendered with KaTeX) and a plain-language "why it works"
on every screen.


THE BIG IDEA

Markov chains quietly run the modern world — weather models, Google's
original PageRank, language models, queueing systems, and board games all
lean on the same memoryless rule:

"To know what happens next, you only need to know where you are now."

Download Markov Chain Simulator and watch that rule build patterns, settle
into balance, and even write sentences.

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Note: this app uses an internet connection to display the math formulas and ads.