Plant Identification help needed.

After yesterday's post, I thought I would show you photos of the leaf of this plant by the back door.

I love the leaves. They remind me of the Mandlebrot set. (If you follow that link, scroll down past alot of the maths to see what a mandlebrot set looks like...very like my leaves!)

Somehow, they look like this when they are small (even newly grown wee small ones look like this, but I haven't a picture.)

and also when they are bigger.

this one was growing further up the plant.
The leaves can get very huge! and still look the same.

They grow very tall with grass like flowerheads. But it dangles like cornsilk with little tiny tags/seeds that rustle in the wind. It looks lovely with the sun behind it!
It grows very fast, and inspite of it being chopped back to the ground each year, it comes back just as vigorously.

Any clues? If not, maybe I will wait and ask again when I can take a photo of the flower/seedhead.