Freddie The Robot

A relatively straightforward gif created using Processing. Each individual dot oscillates sinusoidally along a fixed radial path. Adjacent dots have different oscillation frequencies, which results in interesting patterns.

This follows the mathematics of the pendulum wave phenomenon, which is explained very well in this paper. The difference here is that the pendula have been arranged in a circle, rather than a straight line. As a bonus, staring at the centre of the image induces an illusion effect, where some of the dots appear to have dark centres.