Home▸Probability & Statistics▸The Binomial Distribution and the Galton Board

🔔 The Binomial Distribution and the Galton Board

A 3D Galton board where falling beads bounce left or right at each row of pegs, piling into bins that trace out the binomial distribution in real time.

Probability & Statistics3DAdvanced60 FPS

Beads fall through staggered rows of pegs, bouncing left or right like independent coin flips, and pile up in bins whose heights trace out the binomial distribution live in 3D.

🔬 What It Demonstrates

Every peg is a Bernoulli trial with probability p of bouncing right. After n rows, the bin a bead lands in records its total number of "successes" — a live sample from Binomial(n, p).

🎮 How to Use

Set the number of peg rows and the bounce probability, then watch beads accumulate. Toggle the theoretical curve overlay to compare the growing histogram against the exact binomial PMF.

💡 Did You Know?

Francis Galton built the first quincunx board in the 1880s to show that many small independent random effects sum to a bell curve — an early, physical proof of the Central Limit Theorem.

⚙ Under the hood

A 3D Galton board where falling beads bounce left or right at each row of pegs, piling into bins that trace out the binomial distribution in real time.

распределениевероятностьшаббегункистатистикадиффузиямоделированиеThree.js

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install