This cactus is called Indian fig. Unless you look closely, it appears not to have any spines...but when you look close up, each aureole (those little "dots" on the pads) has very short glochids (hairy barbed spines) protruding from them. This cactus is in the same family as prickly pear cactus (opuntia), but it's not indigineous to the Sonoran desert, they are native to the Chihuahuan desert. Very nice photo, Joan.

Thanks! - for the compliment AND the info. I thought this cactus looked different than others I have seen but couldn't quite figure it out. I found a bunch of them around an old house near the Rillito River - all sprouting these "buds" - maybe someone transplanted them years ago. Very interesting.