Quincunx · Bean machine · Bell curve
Drop balls through a lattice of pegs and watch a tidy bell curve precipitate out of pure chance. Each ball just chooses left or right, over and over — yet together they trace the binomial distribution, the central limit theorem made physical.
Every ball meets each row of pegs and goes left or right. Only one thing decides where it lands: how many times it went right. With bias p = 0.5 both directions are equally likely.
Count the rights across n rows and you have the ball's bin — a number from 0 to n.
The number of rights follows the binomial distribution. There are far more paths that land near the middle than paths that veer all the way to one edge, so the central bins fill fastest.
Add rows and the binomial smooths into the normal distribution — the bell curve. That convergence is the central limit theorem you can watch happen.
Shift the bias and the peak slides to n·p, while the spread scales with √(n·p·(1−p)). The curve is widest at p = 0.5 and tightens toward either extreme.
The glowing line is that prediction. Watch the bars rise to meet it.
A self-contained demonstration of the binomial → normal limit. Built with plain HTML, CSS and canvas — no libraries, no network. After Sir Francis Galton's quincunx.