This is fascinating. But I can't tell from the picture, is this actually an algae seaweed (such as Fucus or Chondrus species) or is it a seagrass (Zostera sp.) which is a vascular plant, not an algae, and would be more like hay when dried. Zostera is also become highly protected and might have restrictions on harvesting for mattresses unless it is washed up on a shore already. I'm interested in using this at some stage.
Jan, please excuse my bad english. By seaweed I meant seagrass (Zostera)! You are absolutely right, it dries to a hay-ish like thing. Zostera is indeed highly protected, because it is endangered, and I would strongly advise to NOT cut it from the seabed! This would be quite unpracticable, anyways...
The usual approach to harvest seagrass is to wait for the next onshore storm, and visit the beaches the next day. There will be plenty of fresh seagrass waiting there on the hard, you just need to collect it (At least in Germany, you are allowed to take anything from the beaches that is washed ashore). Typically, doing this you are doing a favor to the municipalities: they pay a lot of money to clean the beaches from that "rubbish" - to make those beaches bright and shiny again, for tourisme purpose. In Germany, the municipalities even have to depose it as "hazardous waste" on landfills... That's really a shame!
A hundred years ago, it was quite common in northern Europe to make matresses from seagrass. It was also used commonly in coastal areas to insulate houses. I heared stories of old villas from the 19th century being demolished nowadays, where the walls and floors are found totally rotten, but the seagras insulation is still as new, freshly smelling like hay.
What an amazing, underestimated material! And its free, washed upon the shores from time to time.
If you are interested (and willing to use a translator), have a look at:
Strand-Manufaktur
Seegrashandel Lübeck