Penrose Mosaic, Arab mosques and the optical paintings of Barbara Kempe
Written by David Knoll
20/07/2023
Penrose mosaic in the creator’s version. It is assembled from two rhombuses, one with a 72-degree angle and the other with 36 degrees. The picture is symmetrical but not periodic). Fragment of an ornament from an Iranian mausoleum from 1304. On the right is a reconstruction of the girihs.
In 1973, the English mathematician Roger Penrose created a special mosaic of geometric shapes known as the Penrose Mosaic. This pattern is assembled from polygonal tiles of two specific shapes (slightly different rhombuses) and can pave an infinite plane without gaps.
The resulting image resembles a kind of rhythmic ornament – a picture with translational symmetry. This type of symmetry means that in the pattern, you can select a specific piece that can be duplicated on a plane and then combine these duplicates with each other by parallel translation (without rotation and magnification).
However, the Penrose pattern does not have repeating structures but is aperiodic. Although an optical illusion, the mosaic is not chaotic: it has a rotational symmetry of the fifth order. The patterns covering the mosques in Asia, built in the Middle Ages, show easily recognisable mosaic tile patterns. They are called girihs (from the Arabic word for knot) and are a geometric ornament, characteristic of Islamic art, consisting of polygonal figures. The ancient designs of Arab mosques are accurate constructions of the Penrose mosaics.
Mosaic Differentials. Barbara Kempe. Oil on canvas. 120 x 160 cm. 2015
The same mathematical principle can be found in the optical painting of Barbara Kempe, who researches matter vibration and wave interaction of solid physical bodies. In general terms, Barbara Kempe's painting can be attributed to geometric abstraction. The mechanism of action of his paintings is similar to that used by medieval Arabs in mosques and to the classics of optical (op) art: closely spaced parallel or densely intersecting lines make the surface vibrate, revealing the relativity of two dimensions. Kempe reveals spaces that exist not according to the principle of the mutual arrangement of objects in perspective, not ‘drawn in the picture’ , but are directly expressed by the picture. Thus, his painting and graphics do not ‘depict’ any object in the visible world but refer to the fundamental principle of the existence of this world. Kempe is close to the concept of the Pythagoreans, who believed the basis of everything is number, which leads to proportion, harmony, the golden section, and symmetry.
Barbara Kempe's creative method is based on the author's conscious and controlled contact with his own mind. Kempe’s extremely laborious construction of the picture's surface is a meditative exercise, like creating a mandala from multi-coloured grains of sand. This monotonous but purposeful work opens up deep layers of the artist's consciousness. It allows him to visualise a world of abstract, pure and sterile concepts marked by human touch.
David Knoll has published widely on international modernism and in 2011 was a Center for Curatorial Leadership Fellow. From 2017-19, in addition to his role in the department, he served as Curator in Charge of the Leonard A. Lauder Research Center for Modern Art and now sits on the Advisory Committee. David holds a Ph.D. from the University of Aberdeen.