About the Image

‌In 1974, Sir Roger Penrose discovered that one can tile the plane in an aperiodic manner using only a handful of tiles. Six, in fact, though he later winnowed it down to two. As Peter Lu and Paul Steinhardt illustrate (Science, 2007), this was known in the Islamic world since the 1200s. (Show at left is Panel 28 of the Topkapi scroll, which uses five tiles in place of Penrose's "kites and darts.")

About the Image

‌

‌In 1974, Sir Roger Penrose discovered that one can tile the plane in an aperiodic manner using only a handful of tiles. Six, in fact, though he later winnowed it down to two. As Peter Lu and Paul Steinhardt illustrate (Science, 2007), this was known in the Islamic world since the 1200s. Shown above is Panel 52 of the Topkapi scroll, which uses five tiles in place of Penrose's "kites and darts." (The fifth, a pentagon, doesn't appear in this window.)