Cattails form their familiar seed head in their second Summer of growth.
The seed head is a marvel of packing them in, thousands of very resilient seeds that birds like to line their nests with.
During Winter these seedheads start falling about in the breeze, carried some distance when the winds blow or the birds drop them along the way
In its second year of growth a cattail might spread 20 feet and form 20 or so plants from its long thick strong rhisome
So if you start with a pretty clump of five, the progression may be along the lines of 5 in the first Summer, 100 (year 2) 2,000 (year 3) 40,000 (year 4) 800,000 (year 5) Where a pond has the space and the fertility to keep them perky
Not forgetting all those l'il seeds drifting about...
Regards, andy