I'm not completely though it yet, but I find the graph theory aspects of the brain to be really interesting. It turns out that the vast majority of neurons are connected to their immediate neighbors (unsurprising), but the minimum path length between any two neurons is significantly shortened by a very small number of "distant" connections.

Which leads me to wonder about variations on Conway's Game of Life, where specific random cells have "neighbors" that are spatially distant, and what the dynamics of that sort of system would look like.