Extreme high voltage path of least resistance changes? In this video, there is an extremely high voltage being sent through a blank breadboard. The arcs go through different, seemingly random new paths. What causes this? How could you determine what the next path would be?
https://www.youtube.com/watch?v=5MISuVItKgo

 A: 
Why does electricity travel through the air through different paths?

In general, an arc is heating the air along its path, which causes the air to expand and rise, which, in turn, affects the path of the arc, causing it to wander. As an example, you can observe a constantly moving discharge path of an arc through an open air gap around $19$ seconds into the video.
When the open air gap between the electrodes is replaced by a breadboard, the paths along x and y, as discussed in the video, become more favorable than other random paths, which explains a general "square" pattern, but, since the air is still constantly moving, at any given time, some "square" paths are more favorable than others.
Perhaps, this would not be the case for a DC arc, which, once established, would be less likely to drastically change its path. 
A: In electric discharges, there is a randomness. There is the theory of diffusion-limited aggregation where random walks of ions and molecules may explain lightning, Lichtenberg figures, chemical trees, snowflakes, etc. In this case, ionizing radiation may play a role, as for example in this muon spark chamber.
In this systen, the square pattern is responsible for the directions. And maybe a discharge somehow erases or burns away its own path, so that it does not become permanent.
