Basically what is happening is that there is a current between the two nodes. Electricity doesn't just flow in the path of least resistance, that's a popular misconception, it's actually flowing in multiple directions in a certain proportion that is related to a current divider. That basically means that the less resistance there is in a path, the more current will flow through it, but it's really flowing in all directions like an electric field towards it (until you get all quantum mechanicsy). Every path was ultimately going to connect, but once a single path is connected between the two nodes, it's already established a much easier path to travel through than burning through the other paths and will cease to burn other paths.

Also, there is always current going from one node to the other, it's just that it only burns in certain spots after they've heated up enough in proportion to how much current is travelling through a path. The current would optimally like to travel along the electric field lines but because of the dynamic resistance of the wood that's changing as more and more current runs through it and burns it up, it travels along the path that you see in the gif.