I live by the flip, I die by the flip! Its probably my favourite aspect of the game and I change settings to really make Culture Conquest an option.
The Aztecs, for the first time in my experience, have a dominant late game position (due to a recent double conquest) but due to my settings have opted to neglect culture. I placed Haarlem between the Aztecs and the Iroquois, confident I could resist a flip. However, the Aztecs then conquered the Iroquois and left Haarlem surrounded on three sides by the Aztecs and bound to flip. So in the culture vacuum created by the Fall of Niagra I surrounded it with new settlements, stopped teching, migrated loads of workers into the 3x new dutch cities and bought culture buildings. I also built a fourth city east of Grand River to try and flip it too, but it was destroyed.
Anyhoo. Niagra Falls was size 12 and controlled all tiles in its small square, but now it has just two tiles left to work on, but is stubbornly hanging in there. A squadron of Aztec soldiers just ran into Niagra Falls and shows how the AI knows when a city is at risk of flipping. I don't actually know how many musketeers are in there. It appears to scroll away off to the side, so is likely more than the mere 13 musketeers shown!
I will be taking my lesson from Montezuma and filling Haarlem with every land unit I can find, because even if I take Niagra Falls I think Haarlem is going to flip to the Aztecs in time (even though I put my Forbidden Palace into it). I'm half trying for Teotihuacan to flip too, but alas I fear that I Teotihuacan't pull that off (as he has 11 Musketeers in there also and is a more established city).
Look at the variation in culture output caused primarily by doubling the cost of all culture buildings. As dutch with no culture building bonus I shouldn't really be doing culture as my option but the Aztecs are so backwards I couldn't resist. Plus, in the ancient era I was using Agriculture to create high population growth and city size, migrating the population to frontier towns then slaving it to build the culture buildings. Great fun (unless you are a worker)!