Disap pearing lines in Chaos graph

[LAGoff]

I saw a graph in a book on Chaos theory and it showed in the first third of the graph lines moving horizontally; then there was a break(empty space) in the second third of the graph where the lines disappeared; then in the third part of the graph, the lines reappeared. Can you tell me what this is called; even better, can you show me a picture of it; even better, can you tell me more about it?

Does this have anything to do with the glycerine/ink experiment where the ink disappears in the glycerine and then when turned the other way, it reappears again?

 

Thank you.