Lissajous.
A plotter for Lissajous curves. Two perpendicular oscillations — x = sin(a·t + φ) and y = sin(b·t) — drawing on the same square. Turn the a knob slowly and watch the figure breathe: at rational ratios it closes into a knot or a pretzel; in between it walks an endless dense path, the simplest visible resonance of two clocks. The readout shows the live continued-fraction expansion of a/b, which is how the curve's geometry talks back to its arithmetic.
What you're looking at.
Two harmonic motions, perpendicular and independent: x = sin(a·t + φ), y = sin(b·t). Plot one against the other and the pen traces a Lissajous figure. When a/b is rational — say p/q in lowest terms — the curve closes after q periods of x and p periods of y, and you get one of the canonical shapes: the figure-eight (1:2), the pretzel (2:3), the lattice of bumps (3:4). The reduced fraction in the readout tells you exactly how many times the pen crosses each axis before retracing itself.
When a/b is irrational the curve never closes. Its orbit on the (x, y) torus is dense — given enough time it passes arbitrarily close to every point of the square. This is the simplest visual of an ergodic trajectory: the long-run space-average equals the time-average, and "long run" is the only thing that matters. Drag a by a few hundredths off an integer and watch the pretzel slowly rotate into a fuzzy carpet.
Engineering aside: dual-channel oscilloscopes once used Lissajous figures to measure unknown frequencies — feed the unknown signal into x, a calibrated reference into y, then tune the reference until the figure stops drifting and locks closed. The continued-fraction expansion under the canvas is more than ornament: its convergents are, in a precise sense, the best rational approximations to a/b — the same approximations a patient oscilloscope operator would have stumbled into by hand.