Motion of water bubbles at the surface of hot water

I've been thinking about this now and then, when boiling water. As the water becomes hotter the bubbles are rising in increasing numbers. The bubbles seem to either repel each other or merge to form bigger bubbles (or pop on contact) and then they seem to be moving toward the edge of the pot. After a while they pop.

This motion doesn't seem totally random, is it explained in some sort of theory?
Is this an example of brownian motion? (don't know what it is, but have heard it several times)

(title is wrong, should obviously be air bubbles in water)