Physics / Math
Galton board (3D)
Real balls on a peg lattice pile into a two-dimensional bell.
What happens
Balls fall through a lattice of pegs and pile up in bins. There is no coin flip anywhere on this board: every ball is a sphere under gravity, bouncing off round pegs with restitution and friction, and the bell is what those collisions produce. The board is a real board - a slot a few peg pitches deep between two glass panes - so the physics inside is honestly three-dimensional while the statistics live along x, where the histogram is. The lattice rows are offset by half a pitch: on a square grid the balls fall straight down the corridors between pegs and arrive undeflected. Tilt the board to bias the result: that moves the mean because gravity gains a horizontal component, not because a parameter was nudged.
Equations used in the module
Equations each peg: a real collision, no coin flip P(k) = C(n, k) / 2^n (the bell it tends to) σ = √n / 2, the bell is Gaussian for large n
