Notice the cephalium, the white globular thing on the top with all the red hairs. This is not a graft, but a reproductive structure. This group of cacti, after a certain age or maybe some certain environmental trigger, stop growing the normal stem region and instead grow a structure solely devoted to budding flowers. All of the brown projections you see here (view LARGE) are the remains of former inflorescences.
My acknowledgments to Dr. Ed Leuck at Centenary College of Louisiana, whom these specimens belong to.