What determines how many catapults spawn in a lane?

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Once the fort and keep are down in a lane, catapults begin to spawn with minion waves. At first, it's just one catapult. But on really long games, I've seen waves with two or three catapults.
What determines how many catapults spawn in a lane? Is it based on the number of enemy keeps destroyed? Is it based on time since the keep was destroyed?
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