The Telegraph has a report on new findings from study of the mathematics of medieval islamic tiling patterns. The work by Peter J. Lu and Paul J. Steinhardt was published in “Science” this week. They discovered that the creators of tile mosaics in ancient mosques and palaces had the ability to produce non-repeating patterns known as quasi-crystalline patterns.  In the western world, these were brought to to light by Sir Roger Penrose in 1973, with the discovery of so-called Penrose tilings.

Quasi-crystalline patterns can expand to tessellate  a surface (cover it without gaps) in all directions, infinitely but without repeating. Most tessellations are based on repeating patterns. The authors of the study highlighted the use of “girih” tiles - sets of shapes based on 5-point symmetry. These can be laid in regular patterns, but the arrangements chosen  were quasi-crystalline ones - showing an understanding of the maths required to generate this kind of tessellation.