A deconstructed rug. Yarn. Backing. Silk fibres perhaps. No, the simplest and most effective way to give a room a border or a decorative floor feature is simply with paint.
While parusing one of my favourite design blogs to read - Style Files, I read a post about the beautiful Greek home of designer Paola Navone where she has taken to the floors with a brush (or maybe roller) and laid her carpet with minimal tactility but maximum appeal.
Further through the blog I saw a link for Royal Design Studio - they sell stencils online so you can decorate your floor...or wall... with intricate detail or simple pattern.
Clean white rectangle or Morrocan mock tiling...Stenciled or free form...
Paola Novone's home in the Cyclades Islands
A view of the Agean Sea
white on white on white on grey
Or on floor boards
Lovely lace from the Royal Design Studio
bigger scale pattern