Connected and disconnected lattices
Posted by Dan on Aug 30th, 2009
2009
Aug 30
The lattice above is almost entirely connected to the border. There is only one “extra piece” that is woven into the lattice and could be pulled out without cutting anything. The lattice below is almost entirely disconnected from the border. There is one giant piece in the center that could be removed.
I keep saying “almost”. I have the computer grinding out thousands and millions of variations and then tracing out what’s connected to what (which is an interesting programming problem in itself). One would think that one or the other condition would be possible (completely connected or completely disconnected). However, I’ve been unable to go all the way in either direction.