Using the thinned Royal Icing and a pastry bag equipped with a #2 or #3 tip , pipe a square outline around the cookie and then fill in with more thinned icing. Allow to dry for several hours or overnight.
Divide remaining icing into separate bowls and tint to desired colors. Using a #1 or #2 tip - pipe a series of little squares in three colors as shown starting with the center square. Then go back and "squiggle" over your lines to give the effect of yarn. Squiggle a border around the whole thing and you're done!