Though called asparagus fern, this weed ( yes it is a weed , but cultivated for ornamental purposes!) belongs to the lilly family. It is a drooping bushy plant and hence the name - fox tail.
It has stiff branches and tiny scale like leaves. I had a foxtail for years and never saw the flowers, till I spotted these tiny white flowers and berries in the plant that was in my SIL's garden.
The flowers are white or slightly pinkish. And it has red berries.
When planted in the ground it can be invasive and are ideal for pots and hanging baskets.
Common name: Asparagus Fern, Sprenger Asparagus, Foxtail Asparagus