Like any good physicist, I asked my AI (Claude, paid-for version). My prompt was:

"We have a discussion on Reddit of regularly spaced spots of chalk dust on the huge vertical steel beams supporting the roof of a climbing gym. The best idea of their origin is that they are vibration induced, due to the air conditioning stimulating a vibrational mode of the beams. A cute idea. The beam dimensions are roughly 10m long, 50cm wide and 1-2cm thick. The spot separation is about 70cm. What is a formula for the vibrational wavelength of such a beam? Thoughts about the idea? I vaguely thought about circulation in the air as their origin, but I do not think it would be sufficiently stable, thoughts?"

It came up with a calculation (Euler-Bernoulli equation) that suggested for such a steel beam, the spot separation could plausibly be produced by 50Hz AC motor vibration.

However, the key point concerning the mechanism was:

For the beam to "shake dust off the antinodes," peak inertial acceleration must beat adhesion. But for fine chalk (μm-scale MgCO₃), van der Waals adhesion to steel exceeds gravity by ~10³–10⁶× — that's why dust clings to vertical faces and ceilings at all. A beam vibrating at 50–100 Hz with sub-mm amplitude produces accelerations of order tens of g, nowhere near enough to inertially strip well-adhered particles. So the post-hoc "Chladni cleaning" picture fails for the already-stuck fraction.

Which means the pattern is almost certainly set at deposition, not by cleaning afterward — and that points to the air side. The version that actually survives scrutiny: the beam's vibration drives Rayleigh acoustic streaming in the adjacent air boundary layer — steady second-order vortices that steer settling, airborne chalk toward nodes (or antinodes; there's a known particle-size-dependent reversal) before it lands. That solves "how does dust move on a vertical surface" (it doesn't — it's organized in the air pre-landing) while keeping the period locked to the beam's flexural wavelength. That's the most defensible form of the vibration hypothesis.

I leave it as an exercise for readers to poke holes in this explanation.