There is a set of lights near me at a cross roads which has an extra stream of traffic comkng from a row of shops off one of the roads so theres north south traffic, east west traffic and then traffic from the west that came from a little side road and out of the west entrance. If that makes sense. So 3 states the lights can be in.

Anyway, the lights are automatic, they cycle in the same pattern around the 3 states and the walk/cycle pedestrian lights follow that pattern. However, if a pedestrian presees the button, then after the extra stream of traffic from the shops has gone, an extra state is added where no cars can go in any direction and all of the pedestrian walk/cycle lights come on briefly allowi g pedestrians to cross in all directions.

Always found that mildly interesting.