# Paths

### Paths

Consider a 200x200 square grid. A spanning tree is a subset of edges that, for any vertices x and y, allows for exactly one path joining x and y using these edges. Choose one spanning tree uniformly at random. The picture shows not the tree itself, but two things about it: one is the path in the tree that joins opposite corners. The other is the distance in the tree to the lower left corner, shown as height (and coded by color). Several aspects of this picture remain to be explained.- Russell Lyons