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I'm sure you're correct about the type of cactus. But, I'm equally certain these were planted as cacti are not native to North Carolina – while there was a fad of planting them in yards in the late 1970 through the 90s. My Gran had a patch in her yard from the same fad. It's also likely that this one was a potted cactus left in the tree which then overgrew the pot. I've seen other plants sunned that way and forgotten until the overgrew so much they burst through the pot. Out of camera view there was actually profuse stand of cacti growing on the other side of that strip of new road you see in the photo of the house, with the detritus of terra-cotta potsherds scattered among the cactus fronds. I didn't photograph it because the owner of the house on that side of the street stepped out into the yard; he was highly suspicious of me and my then 12-year old son and did not want me to photograph his yard or house.

I think the tree cactus was likely from someone setting a potted cactus on that flat space where a branch had been sawed off, probably to encourage it to bloom in NC's August sun and heat. Then, it was abandoned there and burst its pot.

I also had never seen a cactus growing in a tree.

It's very likely that the pot was left in the tree. Yep, Opuntias aren't native to your part of the states, they originated further South in desert and semi-desert areas. They are extremely invasive and grow all over where I live, which is why I thought of a bird spreading it around