Here’s an excellent “wavy” animation discovered by Till Hartmann. It’s a great illustration of a collective phenomena. When you observe closely, each dot travels along a regular circle-path. Since most of the circles are mutually out of phase, they form illusive waves floating steadily across the screen. Things like this happen all over the place; just take water or sound waves for example. They work in basically the same way – the small back-and-forth motions of individual molecules lead to compression larger-scale patterns moving throughout the medium.
It’s a simple demonstration of how large-scale, collective phenomena can emerge from very simple small-scale behaviour.