You may remember Maxwell's sliding felt doors he made for his old apartment. Those used thick sheets of industrial felt. The ones pictured above use a similar thick felt material, but it's turned on its side and stacked up for a multi-layer effect:
As installed, they're actually for a screening room in a Manhattan apartment. While a screening room is a little rich for this writer, I can see these translating really well to a bedroom area to provide acoustic insulation from other spaces in a small apartment.
Image: FELT Studio