Green feather-like formations in tap water - what is it? (with pictures)
I have had a biologist out taking some samples of the water. She examined them in a microscope, and identified the algae as blue-green algae/cyanobacteria. She could not identify the species further.

She said the reason probably was that my pipes where exposed to sunlight, and also that the pibes with hot and cold water ran too close to each other, creating a nice lukewarm temperature for the algae to thrive in. 

I'm of course going to change the pipes :)