So you've got two modes of reproduction with Allium. Allium like this typically follows a biennial habit, so this years garlic will split into cloves around the fall, in preparation for sending up a flowering stalk next spring/ summer. The cloves are vegetative propagules; just another way to get more garlic other than seeds. Hence you can just plant a clove and get a garlic next year, or, you can plant seed and also get garlic.
Now for your actually question, I believe the segmentation is probably exogenous, technically yes, however, I am by no means an expert in Allium morphology (although I have done graduate coarse work in plant morph, and worked in a plant morph lab), so don't quote me. However, it wouldn't appear like you are describing. Think of the ring at the base of a clove of garlic as a bunch of 'stems'. The branching would originate there.
This is amazing info to me. I've been growing garlic at a hobby level for ages and never knew how the bulbs develop. Thank you for sending me down a garlic education rabbit hole!
Here is another mildy interesting fact, in Swedish we group onions and garlic together by using the word "lök" with a color and different spacing to differentiate them:
"lök" - onion
"gul lök" - onion or yellow onion
"rödlök" - red onion
"vitlök" - garlic
We never talk about "vit lök", it doesn't really exist as a concept in Swedish, but we have more types of "lök"...
"gräslök" directly translates to "grass onion", but the proper translation is "chives"
Garlic, onions, chives, and leeks (plus shallots, spring onions / scallions, and ramsons) are actually very closely related, being part of the same allium genus. That's the same level of closeness as dogs to wolves, for example my example is bad, see AlotOfReading below
Exactly the same in Finnish also. I wonder if these words came from Swedish into Finnish, even though our languages share different ancestors. I imagine all these onions came a lot after the base Swedish / Finnish was already established.
There's a particular variety of Chinese garlic that grows as a singular bulb. It originates in the Yunnan province, I think. I remember my mother growing it back when I was a child. It's really nice!
Someone correct me if I'm wrong, but a garlic plant grows some form of a "seed" head, that will have miniature round bulbs in it if they aren't clipped off that, it's my understanding, when they are planted they'll grow like this in the first year and into a normal garlic bulb year two. I've never experimented enough to know if I'm correct, but if my info is correct I'd guess either one of those got mixed in by mistake, or if your planting in the same spot as the year prior one might've just fallen off.
It might be! That was one of the varieties I planted this year, though the cloves I put in the ground looked like normal shaped cloves, just scaled up a bit.
I'm actually second-guessing my elephant garlic thought... I planted my first clove this year and it took a month and a half to sprout!!! I thought it had died due to heat, but I finally saw its thumb-sized sprout coming up a couple days ago. My normal garlic only takes a week or so to sprout over here in AZ. The elephant garlic seed leaves look more like an iris or tulip coming up. That one commenter was probably on point, saying the bulb was too young to start segmenting into cloves. That was news to me and I'm over the moon about it! Thank you so much for posting about this in the first place!!!