MediaHound

Yes.
And shoots emerge from the base. When an older shoot starts getting tall, it sheds it's leaves - the place where additional new pups will emerge is on the older pups, between an old leaf about to die and where the stem is starting.
The new pups' orientation is not the same as the mother plant. This makes very old clumps look disorganized (not that it bothers me). It would be really beautiful if the pups faced the same direction as the mother plant, but they would quickly run out of room to grow.
And this shows that it's a myth that the plant grows facing the sun.

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