Statistics is better when you can poke it.
Five small machines built from the mathematics which I found interesting about including simulations that run entirely in your browser, hand-written in plain JavaScript with no libraries. Throw darts at π, watch the bell curve assemble itself, argue with a game-show host, calibrate your eye against Pearson's r, and set Conway's cells loose.
Scatter random points on the unit square. The fraction landing inside the quarter-circle approaches π/4 — so four times that fraction approaches π.
The estimator converges at rate O(n−½): each extra digit of π costs a hundred times more points. In higher dimensions this gets stranger — see The Curse of Dimensionality.
Each ball takes eleven fair coin-flips on the way down and lands in the bin that counts its rights. The histogram is binomial(11, ½) — and the silhouette of the central limit theorem appears.
Eleven pegs, eleven coin-flips. The dashed curve is the expected binomial(11, ½) count.
Francis Galton built the original in 1873 to show that order emerges from pure chance. With enough balls, the binomial is indistinguishable from a Gaussian.
Three doors, one car, one stubborn intuition. Conditional probability says you should always switch — play a few rounds, then let the simulator keep the score honest.
Pick a door. One hides the car; two hide goats.
| Games | Won | Obs. | Theory | |
|---|---|---|---|---|
| Stay | 0 | 0 | — | 33.3% |
| Switch | 0 | 0 | — | 66.7% |
Your first pick is right ⅓ of the time — so switching wins the other ⅔.
When Marilyn vos Savant published the correct answer in 1990, around ten thousand readers — including statisticians — wrote in to tell her she was wrong. She was not.
Sixty draws from a bivariate normal distribution. Read the cloud and estimate Pearson's r by eye — calibrating intuition against the statistic is harder than it looks.
Read the cloud, then commit.
Anscombe's quartet is the standing warning: one value of r can hide very different clouds. Always plot the data.
A cellular automaton with four rules and no randomness, yet rich enough to be Turing-complete. Draw on the grid with your pointer, then press Run.
The preloaded R-pentomino — five cells — runs for 1,103 generations before settling. Gosper's glider gun fires forever.
Every machine on this page is hand-written vanilla JavaScript on <canvas> — no libraries, no frameworks. View source to see the workings.