Some puzzles like this don't settle into a steady state, leaving the logical equivalent of a "flip-flop" circuit, the classic paradoxical "This statement is false."-type problem, or two self-defeating, self-reinforcing arrangements like in the "Life" game.

I think if you seed the initial statement differently, it might settle on a different possibility, though of course, this particular implementation uses the underscores for placement, so that will have to change.