I also play trains with my kid, and I might be thinking about the same stuff. When I build a track, I think "given a position and direction, could I reach every

I also play trains with my kid, and I might be thinking about the same stuff. When I build a track, I think "given a position and direction, could I reach every other (position,direction) pair from here?". There's a certain minimum complexity required for a track to have that property, but I haven't really broken it down in a principled way.