N circles bouncing against the walls of a square. They're highlighted red whenever they're overlapping another circle. Also, they're attracted to your mouse and repel each other (no collision, just an acceleration away from neighbors).

For every frame each circle is accelerated and moved based on distance from the mouse, has it's position in the quadtree updated, then searches the tree for other circles with a touching bounding box which are then compared based on distance to test for intersection. The last part is what shows of the advantage of a spatial partition. A naive comparison method (every object against every object) would result in 1000000 comparisons per frame, compared to the average you see above.