Chapter 4.4, Problem 21MS

Penrose tiles. Roger Penrose constructed two tiles that can be used to cover the plane only in aperiodic ways. One tile is called a kite, one is called a dart. Show how to construct a tiling using these tiles. Notice that each tile contains both a blue and red arc. The only rule for assembling the tiles is that the ends of blue arcs must touch only the ends of other blue arcs and ends of red arcs must touch only the ends of other red arcs. Given this rule and using many copies of the kites and darts, show how to construct a tiling using these two tiles.