There's an exhibition of Turkish slit kilims at the <i>Weaving Arts Museum and Resarch Institute</i> site http://www.weavingartmuseum.org/slittap.html
http://www.weavingartmuseum.org/slittap.html It includes pieces ranging from quite complete to quite fragmentary, and all stages in between, so it might be a useful way to explore your own reactions to pieces that are less than complete. The most fragmentary one is

Steve Price