I just noticed something about this. Zuko is the first one to reach out. He knows that Katara hates his guts. He knows that she doesn’t trust him. But he trusts her, enough to hope that when he reaches out to her, she will reach back. And she does.
I think this all the time. Try going in pitch black with a picher of water, a flashlight, and a bowl. As you pour the water in to the bowl shine the flashlight across the water. It will move sightly with the light.