Escher and Islamic Geometric Design

Escher and Islamic Geometric Design Eric Broug The top row of sketches shows three fourfold tessellations, the bottom row shows three sixfold tessellations The craftsmen who created the great variety of Islamic geometric design in art and architecture were not mathematicians. They didn’t calculate angles. Instead they used a few basic tools to make all their compositions, from the relatively simple to the very complex. Their most important tool was a pair of compasses with which they could draw circles and arcs. The other tool was a simple ruler with which they could draw straight lines. Every Islamic geometric design is created by lines, circles and arcs. Craftsmen would seek and create intersections using these three elements. Choosing which intersections to use (and which not to use) creates the immense variety of patterns that can be seen across the Islamic world. They didn’t draw an entire composition with these tools but instead drew a small pattern or part of a pattern that they could repeat to create a composition. This principle of drawing a small pattern in, for example, a hexagon or a square is at the root of almost all Islamic geometrical compositions. What we can do with this one small pattern is repeat it to cover a larger area. In other words, it can be tessellated to make a composition. A simple eightpointed star can be designed in a square. This square can be tessellated and a composition is created. When it is tessellated, the square in which the star appeared is no longer needed and is invisible and the cross shapes that now sit between the stars have appeared. This principle can apply to small patterns in squares but also to small 20 escher meets islamic art 242_001 BnwrkEscherNL-57.indd 20-21 patterns in hexagons, triangles, diamond shapes and many other polygons. One of M.C. Escher’s sketches shows that this was also the way he structured many of his compositions. In his sketch he has a top row of drawings showing tessellations where squares, diamonds and rectangles are arranged to cover a surface area. The bottom row shows drawings where triangles, hexagons and lozenge shapes are arranged to cover a surface area. A pattern or part of a pattern in a square, hexagon or any other polygon can be called a ‘repeat unit’. Repeat units can have many diferent shapes and can create many diferent grids. The sketch by Escher shown earlier shows six such grids. The most simple grid is a grid of squares. Many patterns in Islamic geometric design can be made using a repeat unit that is tessellated in a grid of squares. Using a simple grid doesn’t mean that the composition is therefore less complex. This depends entirely on the content of the repeat unit. A composition that can be found in the Alhambra Palace was created in a grid of squares. The craftsmen would draw a small pattern and then tessellate it. The pattern was drawn using only a pair of compasses and a ruler. Eightpointed star set in a square Eightpointed star tessellated Pattern 1. Made using a grid of squares One of the main practical beneit of using a grid is that a craftsman can modify the size of the repeat unit to take into account the size of the composition. All the compositions in the Alhambra had to cover a speciic surface area; the craftsman had to create Escher and Islamic Geometric Design 21 11-06-13 20:45 1 8 2 3 7 Step 1: The starting point for many Islamic geometric patterns: a circle in a square, divided into eight equal sections Step 2: Draw two squares inside the circle 6 4 5 An eightpointed star surrounded by eight petal shapes his composition knowing that it had to be of a speciic height and width. It had to it. A grid makes this possible. It allows the craftsmen to determine the size of the repeat unit before he commits himself to making the composition. Another composition that can be found in the Alhambra Palace can be created in a grid of hexagons. This pattern can also be drawn using just a pair of compasses and a ruler. The vast majority of patterns in the Alhambra can be created in either of these two grids; a grid of squares or a grid of hexagons. They are also the most common grids in Islamic geometric design in general. One of the observational skills that Escher demonstrated in his sketches from the Alhambra was that he was able to identify which grids were used for which compositions. There are diferent ways to do this. One of the easiest ways is to identify the type of star pattern that is used. This can be best done by counting the ‘petals’ that surround a central star. The thousands of diferent geometric compositions that have been created by craftsmen over the centuries can generally be categorised according to what kind of star patterns feature. There are compositions with eightpointed stars, tenpointed stars, twelvepointed stars etc. These stars give clues to what kind of grid was used by a craftsmen to make a composition. A sixpointed star its in a hexagon. Similarly, an eightpointed star its in a square. In the case of compositions where there are no star patterns with surrounding petals to count, a diferent approach needs 22 escher meets islamic art 242_001 BnwrkEscherNL-57.indd 22-23 Pattern 2. Made using a grid of hexagons Step 3: Draw two pairs of parallel lines that pass through the intersections indicated with red squares Step 4: Draw an X shape as indicated Step 5: Draw four lines that connect with corners of the square and the X shape from the previous step Step 6: Draw four lines as indicated Step 7: Draw four lines. Consider them as two V-shapes on their side. Look carefully at the intersections they connect with Step 8: All the construction lines have now been drawn. Take a diferent colour pen or pencil and trace the sections of lines as indicated Step 9: Trace the sections of lines as indicated Step 10: All lines have now been drawn. The design is now complete and can be tessellated in a grid of squares to create Pattern 2 on page Triangular system, ink, pencil, watercolour, 1952 to be used. Escher’s compositions also do not feature star patterns. The best way to identify what grid was used to structure the composition is to look how recurring elements can be seen to be grouped together and spatially related to each other. There are many Escher compositions in which this method of identiication can be tested. If we take his composition with red ish, yellow bats and blue lizards we can see that each creature can be seen to be grouped in threes. Alternatively, we can focus only on the blue lizards and they can be seen to make a structure of hexagons. Alternatively again, the red ish and yellow bats can be seen to create a grid of alternating yellow and red triangles. The presence of triangles and hexagons are evidence that this composition was created in a grid of hexagons or triangles. Escher’s complex compositions typically ofer diferent visual possibilities. Diferent elements will draw attention at diferent times and looking more closely and more frequently at his compositions will give the viewer diferent visual rewards over time. This is one of the more profound visual similarities between Escher’s work and the geometric patterns that can be seen at the Alhambra. The style of geometric design at the Alhambra, where small glazed tiles with bold contrasting colours were used, meant that these compositions ofered diferent visual rewards depending on the distance between the observer and the composition. The pattern that was drawn in the step-byEscher and Islamic Geometric Design 23 11-06-13 20:45 Pattern 3 without the hexagonal grid being visible step sequence was also drawn by Escher on his trip to the Alhambra. The lower right black and white drawing shows features the familiar arrows shapes that point left and right and up and down. What is clear from this drawing and the two colour drawings on the same page was that Escher was especially interested in how shapes interact with each other. The arrow pattern shows this well: the black arrows need the white arrows to exist and vice versa. The two colour drawings show how Escher experimented with modifying the size of shapes in a composition. The original composition appears in the Alhambra. Both colour drawings show Escher altering the size of shapes without signiicantly altering their appearance. Nevertheless, when seen side by side, both drawings show compositions that are subtly diferent. If all compositions in Islamic geometric design were created with grids with just one shape, the creative potential would soon be exhausted. If the only creative opportunity for the craftsman was to decide what pattern he created in his square or hexagons, there would not be the rich diversity of patterns and compositions that we can see in Islamic geometric design. This rich diversity was in part created by combining diferent polygonal shapes to create new grids. These new grids could form the basis for new patterns. For example, a simple grid of hexagons with a repeat unit can create a pattern. The picture on the left shows the repeat units, the picture on the right shows the same composition but 24 escher meets islamic art 242_001 BnwrkEscherNL-57.indd 24-25 Pattern 3. Made by tessellating a simple sixpointed star in a hexagonal grid without the repeat units. When a triangular element is added to this grid, it becomes a grid of hexagons and triangles. The triangular shapes can be treated as new repeat units that can contain part of a pattern and they can now contribute to the creation of a new pattern. The picture on the left shows the composition with the repeat units visible, the picture on the right shows the compositions without the repeat units visible. What becomes clear that the simple addition of a small triangular repeat unit signiicantly changes the pattern. There are hundreds of such modiications that can be done to grids and repeat units. These is the creative source of Islamic geometric design. Sketch of tile work in the Alhambra, pencil, 1936 A grid of hexagons and triangles Pattern 4. Made using a grid of hexagons and triangles. The hexagons have the same content as the hexagons in pattern 3 Pattern 4 without the grid of hexagon s and triangles being visible The Nasrid craftsmen at the Alhambra Palace worked exclusively with fourfold and sixfold compositions. They did not try their hand at ivefold compositions (based on the division of a circle into ive or ten equal sections). Why this is the case is not clear. Some eras in Islamic history are especially renowned for the beauty and innovation of their Islamic geometric design. The work of the Nasrid craftsmen at the Alhambra should certainly be considered in this light. However, it seems that they found suicient creative expression in fourfold and sixfold geometric design. This is untypical. If we consider the geometric design of the Mamluks of Cairo (1250-1517) or of the Seljuks of Anatolia (1077-1307), we can see that they also sought to ind new creative expression in Islamic geometric design. They found this frequently in ivefold (and Escher and Islamic Geometric Design 25 11-06-13 20:45 tenfold geometric compositions). However, this was not the case for the Nasrid craftsmen though. Interestingly, the Marinids who had their capital in Fes, Morocco and had friendly relations with the Nasrids in the Alhambra Palace, built many madrasas where the decorative theme is evidently indebted to the style of decoration used at the Alhambra. One such madrasa, the Bu Innaniya madrasa (1350-1355), has Islamic geometric decorations all around its central courtyard. It features several tenfold star patterns that have been tessellated as if they were fourfold patterns. The craftsman who made these compositions seemingly knew how to draw tenfold star patterns but not how to tessellate them in a way that is most suitable. Tessellating a tenfold pattern is not as straightforward as tessellating a sixfold or fourfold patterns. That is why, for example, Mamluk and Seljuk craftsmen were so attracted to them: they posed unique design challenges. Escher showed some interested in ivefold geometric design but not in the context of his compositions that feature tessellation. He certainly wouldn’t have come across any examples of ivefold tessellation at the Alhambra Palace. Escher’s ivefold star pattern composition is a rare instance where he used this category of geometric design. Tessellating if ivefold geometric design is more diicult because it doesn’t work to the same rules as fourfold or sixfold design. Squares and hexagons can be repeated ad ininitum. This is not the case with pentagons. 26 escher meets islamic art 242_001 BnwrkEscherNL-57.indd 26-27 They can not be tessellated to cover an area; they overlap or they leave gaps. Over the centuries, Islamic craftsmen have found creative solutions to still be able to make large ivefold compositions. They did this mostly by creating unusually shaped repeat units. Order and Chaos II, Lithography, 1955 A ivefold composition When Escher’s work is placed next to Islamic geometric design, it is clear how he was inspired by it. The way shapes interact in a composition, the way grids are used behind the scenes to give structure and more creative freedom, the way diferent elements can give various visual rewards, they way in which colour and contrast feature in the Alhambra, these are all characteristics of Islamic geometric design that Escher subsequently used in his own work. It is interesting to wonder what would have happened if Escher had managed to make a trip to Cairo or Anatolia in Turkey. He would have seen a whole new geometric language expressed in the many ivefold and tenfold compositions that were made by Mamluk and Seljuk craftsmen, respectively. It would undoubtedly have had an impact on his work in the same way that his trip to the Alhambra had a formative impact on his work. Escher and Islamic Geometric Design 27 11-06-13 20:45