Penrose, the quasicrystal and the Alhambra

The mixture of symmetry and asymmetry

In 1974, the mathematician and physicist Roger Penrose developed the eponymous Penrose tiling, which can be made up of narrow and wide rhombuses, for example. The patterns that can be laid with it are symmetrical in some parts, but not when seen as a whole. They are also comparable to the quasicrystals that the physicist Daniel Shechtman discovered in metal alloys almost 10 years later. The crystalline structures that he discovered could not be moved in parallel like a real crystal because they were not symmetrical and congruent, which is why he called these crystals „quasi-crystals“. It then emerged through Peter Lu‘s work on the architecture of Islam that the patterns and ornaments developed using the Girih tiles were the artistic equivalent of quasi-crystals. This is because some parts of these patterns are also symmetrical, but not when viewed as a whole. It seems that artists already knew about these structures more than 500 years ago!

For the observer, the fascination lies in precisely this mixture of symmetry and asymmetry, because purely symmetrical patterns are calming but can quickly become boring. The quasi-crystalline structures of Islamic and Moorish architecture with their hidden asymmetry are captivating, hold the viewer‘s attention and magically attract the eye with their extraordinary aesthetics and beauty. In addition to at least thirteen regular patterns, Girih patterns can also be found in the Alhambra.

Why not go in search of them!