A few interactive statistical ideas: watch a distribution form, estimate π from random points, or play against a Gaussian. Curiosity belongs in the lab, too.
Toy 01 · the bean machine
Galton board
Drop balls through a lattice of pegs. Each peg is a coin flip; the pile at the bottom is a Normal distribution assembling itself in real time. Skew the coin with Bias and watch the curve lean. The dashed line is the Gaussian the histogram is chasing.
Balls
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Mean bin
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σ
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Toy 02 · darts & destiny
Monte Carlo π
Throw random darts at a square. The fraction landing inside the quarter-circle, times four, is π — a transcendental constant falling out of pure noise. The more darts, the closer it creeps.
π estimate
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Darts thrown
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Relative error
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Toy 03 · a game against noise
Pong vs. a Gaussian
The opponent is perfect at physics and imperfect at aim: it computes exactly where the ball will land, μ, then aims at μ + σz with z ~ N(0, 1). Slide σ to zero and it becomes a wall. Turn on AI’s mind to see the bell it samples from. First to 7 wins.