Chladni Plates
A metal plate is driven at one frequency with sand scattered over it. At most frequencies the sand just churns. At a resonance it runs off the parts of the plate that move and piles up on the lines that stay still, drawing a figure in a few seconds: a cross, a diamond, rings, stars. The page sweeps through five of them on load. Then the dial is yours, and the share of sand sitting on the still lines is measured as it climbs.
In 1787 Ernst Chladni, a lawyer's son from Wittenberg who would rather have been studying sound, sprinkled sand on a brass plate, clamped it at the centre and drew a violin bow down its edge. The plate rang, and the sand jumped off some parts of it and settled on others, drawing a sharp, symmetrical figure. Each note he could make the plate sing gave a different one. He published the figures in a book and toured Europe showing them. Napoleon watched him in 1808 and was impressed enough to fund a prize for whoever could explain them. Sophie Germain won it, after three attempts, with the first theory of how elastic plates bend.
The surprise is how picky the plate is. Most frequencies do nothing much: the plate buzzes and the sand shivers in place. Only at a few exact frequencies, the plate's resonances, does a pattern appear, and each resonance has its own. Move the dial a few hertz off and the figure dissolves into a churn. Move it to the next resonance and a completely different figure gathers. The resonance curve above the dial shows how narrow those windows are: thin peaks on a flat floor.
Nothing tells the sand where the lines are. Each grain is kicked at random by the metal under it, harder where the metal moves more. Somewhere in the middle of the moving patches it gets thrown about. On a nodal line, where the plate does not move at all, it stops. A random walk whose step shrinks to nothing along a curve ends up on that curve, so the figure is the plate's map of where it stands still. The tile under the plate counts the grains on those lines: typically one in seven when the sand is scattered evenly, and more than nine in ten within a few seconds of a figure forming.
The same physics decides how musical instruments sound. Violin makers still sprinkle glitter on free violin plates and tune them by watching the figures. Guitar tops, cymbals, bells and loudspeaker cones are all checked the same way, and engineers map the vibration of turbine blades and car panels with the modern version, laser vibrometry, because a resonance in the wrong place cracks metal.
Pull back and fling a planet into a sky where everything pulls on everything — the dotted line bends round the stars before you let go, and two galaxies tear each other into tails.