Galton board.
A toy for the central limit theorem. Balls fall through a triangular peg lattice — gravity tilts a touch according to the bias slider, so each ball drifts toward one side at every peg — and the bins at the bottom keep a running tally. The empirical histogram is what actually happened; the cobalt curve drawn over it is the Binomial(N, p) you'd predict if every peg were a perfect coin flip — which the physics only approximates, but which a normal bell hugs more tightly as N grows. The original device, Galton's quincunx, is one of the cleanest "math is real" demos you can build.
What you're looking at.
Each ball begins as the same kind of "experiment" — a sequence of tiny chance events as it ricochets between pegs. Individually the path is unpredictable; in aggregate the central limit theorem guarantees the bins at the bottom are roughly normal, with mean Np and standard deviation √(Np(1-p)). Slide bias away from 0.5 and watch the peak march sideways; raise rows and the bell narrows relative to its mean — the law of large numbers is the same idea looked at once.
The bars are real outcomes; the cobalt line over them is the theoretical prediction, scaled to the same total count so they're comparable at a glance. Physics being physics, the empirical distribution won't match the Binomial exactly — bouncing balls aren't perfect coin flips — but the shape and the parameters track very closely. That mismatch is itself a story: real systems are full of "almost Gaussian," and the CLT is what guarantees the almost.