Happy to oblige.
I have three Platanus occidentalis neighboring my deck/backyard. All three are volunteers, one being the offspring from the two older ones. The two older ones volunteered from a neighboring farm - those parent plants being more than a thousand feet from where these are now growing. I had no sycamores on my property when we purchased it 33 years ago.
These thin individual seeds in your photo (achenes) come from the aggregate golf ball-shaped and sized structure (syncarp) formed on the tree which hangs by a several inch long stem (peduncle).
Those seeds have a way of getting around, and into places difficult to remove them (gutters, downspouts, between deck boards, siding, etc.