Curvex

Meet Curvex, an old oscilloscope who draws looping patterns from two simple swings.

Feed one wave into the sideways motion of a dot and another into its up and down motion. The dot traces a closed curve called a Lissajous figure, named after Jules Antoine Lissajous, who made them with mirrors on tuning forks in 1857.

The shape depends on the ratio of the two frequencies a and b and on the phase difference δ. Equal frequencies give a line, an ellipse or a circle. A ratio of 1 to 2 gives a figure of eight. A ratio of 3 to 2 gives a pretzel with more lobes.

The number of lobes along each edge tells you the frequency ratio. Before digital meters, engineers compared an unknown signal with a known one this way. If the pattern stood still, the frequencies were in an exact whole number ratio.

The curves still turn up in physics labs, in old science fiction films, and in logos, including the Australian Broadcasting Corporation's.