A particle in a box is prepared in the same state, and its position is measured. The cloud is the computed probability, |ψ(x)|².

Each result lands as one point, and where it lands cannot be calculated in advance. Every point comes from a newly prepared particle, not the same one measured again. A thousand results pile up and come close to the computed curve.

The same is done for n = 1, 2 and 3: one peak, then two with a zero in the middle, then three. Each result is random; the shape they build is the same every time. The points are seeded draws from |ψ|², not laboratory data.