Kites and Darts

Kites and Darts are a type of non-periodic tiling invented by Roger Penrose. The tiles cover the plane in an infinite variety of beautiful, non-repeating patterns. The Golden Ratio (1/2)*(1+sqrt(5)) features prominently in the tiles, in their construction and in their patterns. In the limit, the ratio of kites to darts is the golden ratio. So if you print 1000 darts you should print 1618 kites. There are seven ways the tiles can be arranged around a vertex. These seven patterns were given