Can chance draw a city?

Three thousand steel balls rain down through 2,376 steel pins, each bouncing left or right off pin after pin, its own way. The pile they leave in the slots is a harbour: a long low front of small houses rising into three towers.

Then the floor opens, three thousand more rain down, every one on another path, and the same harbour comes back. No ball is aimed. Each pin is only turned a little where it stands.

Ebbi · 7 November 2026

A heap with a shape.

Francis Galton built the first board like this for a lecture at the Royal Institution in London in 1874. Shot poured through a funnel onto pins set, in his words, “in a quincunx fashion” — each row over the gaps of the row above, so that every falling shot meets a pin in every row.

At each pin a shot goes left or right, and no one can say which. Yet the shot piled in the compartments always took the same outline, a bell, “closely of the same shape however often the experiment is repeated.”

The bell is what chance looks like in bulk. A fair pin is a coin toss, and to land far out to one side a shot must win the same toss row after row, which few do; most win some and lose some, and land near the middle.

One shot’s path is chance. The outline of thousands is the sum of their odds, so it comes back.

Turning the pins.

A pin that is not fair draws something else. Every pin on this board is a small steel post, oval and upright, and each one is turned where it stands, so that it throws more of the balls it meets to one side than the other: turned 20 degrees, about 63 in 100 go one way. Most are turned by less than that.

Nothing on the board moves; each turn only leans one pin’s odds, and row on row the leans add up, until the pile is no longer a bell but a harbour.

A city needs one thing a bell does not: balls at its far ends. From one funnel at the top, no lean is strong enough to carry a ball out to a tower at the board’s edge, so here the balls rain from a slot along the whole top, and the pins share them out from there.

Poured again.

Let it rain again and every ball takes another path, yet the towers rise in the same slots and the low front comes back at the same height: three thousand balls are too many for chance to stray far from the sum of their odds.

The roofs are another matter. There the last few balls settle it, and no two pours leave the same roofline. That ragged edge is the proof that nobody placed them.

A real ball is not a coin, though. A coin forgets its last toss; a steel ball keeps its speed from pin to pin, so a ball that has just gone right is likelier to go right again. Two researchers who modelled the board ball by ball found the pile’s shape changing with how much bounce each strike keeps.

So the turns here were not left to the coins’ sums: they were set on the real bounce, poured, measured and turned again.

The city is in the pins, and no ball ever knows it.

Order in apparent chaos.

That is what Galton called the bell’s return, and he wrote that he knew “of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order” it shows.

His board became a classic. Charles and Ray Eames built a large one for IBM’s exhibition Mathematica, first shown in Los Angeles in 1961, and copies of that exhibition still stand in three museums; desk boards of 3,000 steel balls are sold to be flipped over and watched.

Boards can be made for other curves too, by changing the pins’ shape or leaning them one way. The boards I could find all pour a curve.

What the board taught me.

Nobody has built this board yet.

It exists only on this page, worked out ball by ball on a computer, as it could be made in steel: a black lacquered board 306 by 499 millimetres, 2,376 polished pins, 49 slots, chrome balls two millimetres across. Making it taught me what a city needs from a pour.

Round pins cannot do it. To lean a round pin you have to move it, and moved pins close on their neighbours until a ball cannot pass; an oval turned where it stands leans its odds and moves nothing.

A tower needs empty slots beside it: a pour’s walls are soft, and towers that touch melt into one hill, but two slots apart each stands on its own, a slot in the gap catching about a tenth as many balls as one in the tallest tower.

And the end slots need the half-pins every real board has in its walls; without them balls slide down beside the wall and pile up a column there.

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Made by Ebbi.