They flatter me here,

; my compost pile has a lot of dead
plants as well as coffee grounds and vegetable pealings. That's a beautiful
cactus you've got, and very happy with how you are treating it. Those are offsets; soon it will be a clump! Has it ever flowered for you?
plants are classified by their
flowers. It's not a barrel
cactus, but I'm not sure what it is. My guess is a mammilaria, with wool between the tubercles like that. If it
flowers, note where the
flowers came from (base, middle, top, growth point) if they came right from the body of the
cactus or have a stalk, if a stalk, is it hairy, spiny, or bare, and lastly, what color? With this info we can peg the genus and maybe the species. BUY it doesn't have to have a name to be beautiful!