The beginnings of these studies

This site began with the intent that it would look at the geometry behind the traditional carved plaster naqsh work that is so much a feature of the traditional architecture of the Qatar peninsula. Other notes I made some time ago seem to have taken precedence and much time and effort has been expended in setting those down rather than continuing with the original intent. This page is intended to encourage me towards working again in this area, and starts with a note made some time ago specifically relating to the setting out of naqsh panels in Qatar.

The domestic architecture of the peninsula was simple due both to the lack of disposable income as well as the strict religious beliefs of those coming to live there. Decoration, where it existed, was originally simply scratched into walls and was always geometrical in nature. With time a more intricate form of carved plaster naqsh was developed and that, mainly, should be the focus of this page.

My intention is to begin by looking at the simpler patterns, which really means the older ones which date from the early and middle parts of the last century. The more complex patterns now see in the naqsh patterns used on new and renovated buildings are generally more complex in their designs.

There is more information set out on one of the Gulf architecture pages looking at naqsh work in Qatar. Because of this, be aware tht there may be duplication, or conflict…

The point of this is to suggest that although geometrical patterns formed the basis for all the naqsh work, it appears that there was no great concern to make this work entirely accurate. Most of the examples shown here will illustrate this. My thesis would be that although the simple tools available to them would allow interesting and accurate designs to be set out and fashioned, there was a lack of understanding of simple geometry, little concern, a wish to have the design imperfect, a time constraint or some other reason – or a combination, of course – which impelled artisans to create works with significant departures from an accuracy of layout or execution. This page intends to look at these issues.

go to top of page

Trial and error

Mention has been made in a number of places about trial and error in the setting out of Islamic patterns. In Qatar, the geometric patterns used to create naqsh panels did not use particularly accurate geometry, and this created many panels with considerable visual energy which would not have been the result had the geometry been set out accurately. An example of this practice is shown here and illustrates a character of execution which modern artisans feel unable to replicate, needing to make their patterns accurate both by training and inclination.

While many divisions are relatively easy to establish, some are impossible to construct accurately and require guesswork or an iterative testing to produce an accurate – or relatively accurate – division. Take, for instance, the dividing of a circle into nineteen parts.

The easiest way to create an unusual number of divisions would be to set out an easy geometry and then make incremental guesses for the number required. If the divisions are constructed on a circle, then stepping around it with a pair of dividers will eventually find an approximation of the required number. Here, for instance, in order to divide a circle into nineteen parts, a circle has first been divided into six by stepping round the circumference of the circle with dividers set at the same diameter as the circle. Within one of the areas coloured blue it is evident that it must be divided into a little more than three parts in order to create nineteen divisions. So, setting dividers at a little less than a third of the distance between the first sub-divisions, a process of iteration with amendments to the setting of the dividers will eventually have produced the necessary dimension for a relatively accurate approximation of the distance required to divide the circle into nineteen parts.

go to top of page

A simple lozenge or slot pattern

Here is a relatively common pattern found in Islamic designs, often in the form of a background. It has similarities with patterns found in Qatari naqsh. Based on a lozenge shape that repeats infinitely in two directions, it is constrained only, as in this case, by a relatively arbitrary selection of frame. It can be seen as a linear pattern or, here coloured, as a slightly more interesting pattern.

Yet the pattern is based on, or derived from, a square. Here I have shown three adjacent squares at a different scale in order to make the construction a little more apparent. But I have also drawn the contained circle as this form is argued to create the base planar surface for the design of the unit pattern.

In order to construct the lozenges, first take a square, here tinted blue, and draw diagonals from its corners. Through its centre, a horizontal and vertical line are taken to its perimeter, subdividing the square into four smaller squares. These squares are further divided by diagonals. Next, lines are taken from the corners to the central points of each of the sides of the square, creating the square illustrated in the centre. Each of the small squares is then subdivided horizontally and vertically into three by joining and extending lines through the intersections of the diagonals, creating the square at the right of the diagram.

The first part of this illustration shows, rather than the square, the circle on which the lozenge has been established. The second part shows how the lozenge has been created from the diagonal construction lines. Obviously the lozenge might be arranged either horizontally or vertically. In the third part of the illustration I have added four stars that bound the lozenge, though these stars would be parts of the surrounding lozenges in an extension of the pattern.

This first diagram illustrates the extended pattern showing how the lozenges fit together, alternating their direction through 90° on an orthogonal grid or matrix. As happens with many geometric patterns formed of two shapes, the eye tends to see one or the other shape, rather than the overall two-dimensional patterning. Here the eye moves between seeing the lozenges and stars.

The next two diagrams use the same geometric construction as the lozenges above, but the pattern is orthogonal. I have included the two patterns as they are one of the patterns found in Qatari naqsh work, usually as background or within a complete pattern. The two patterns are essentially the same, the only difference being the points at which the corners of the rectangles are selected.

This lowest sketch, based on the exact geometry of the study above, illustrates something of the character of a naqsh panel with an attempt to give a three-dimensional effect with a drop shadow. A simple effect such as this would have been relatively easy to carry out on either wet or dry naqsh. The pattern is found on the other side of the Gulf where the workers are likely to have originated and is a relatively common pattern in traditional buildings in Qatar.

At first glance these two photographs appear to illustrate an application of the pattern, but will not have required any use of the circle to lay it out. You can see that the pattern has the addition of a small square to create more of an even balance between solid and void, the recessed carvings having the proportion of 5:1. The photograph from which these two details were taken was made in an old majlis at Wakra in the late nineteen-seventies. In the upper photograph you can see a typical naqsh panel with the pattern taking up the whole of the panel as a ground. In the lower photograph you can see how the setting out lines were scratched on the dry or drying plaster in order to define the areas for carving out.

There are two points to note in the above photograph. The first is that the setting out lines are made along the centre of the area to be left untouched, when you might have anticipated that the craftsman would mark out the edges of the pattern, leaving much of the setting out lines hidden. The second is that the carving is relatively deep and has straight sides. On external work it was not necessary to have such deep carving in order for the sun or light to make its effect apparent.

This note began with a suggestion that the argument shapes might or might not be based on circles, was semantic. I have gone through this brief exercise in order to illustrate how a shape is formed by following lines of a pre-constructed pattern. The note on decagonal and quasi-crystalline tiling above showed that artisans used a number of standardised shapes with which to produce geometrical patterns. While only a compass and straight edge are necessary to produce many of the shapes used by designers, it is apparent that they would have used a simplistic system rather than construct all patterns from scratch. My own experience is in seeing artisans using primitive compasses, wooden set squares and chalk. The ancient Egyptians commonly used knotted ropes to form right angles; knots set at three, four and five units apart along a rope would enable a right angle to be readily formed, this being the basis of the simplest Pythagorean right angled triangle.

I have illustrated the construction of a square above, but there are a number of other ways of constructing squares, some of which might be more suited to the production of a lozenge.

Here, to the right, is an alternative way of constructing a square upon a given line. All the necessary construction lines are there but I have added the adjacent squares, circles and diagonals in order to show the relationship with the diagrams above.

The lower illustration has been added as a reminder of the relationship between the lozenge patterns and the square and circle. The illustration clearly shows the importance of the square in establishing the pattern of the lozenges. It is clear that there is a different relationship between the four lozenges in the corners of the squares and the four on the periphery of the circle.

So, the argument about the generator of patterns being square or circle may be semantic, but it is apparent that the circle, or at least compasses, are necessary in order to generate patterns found in Islamic geometric designs. Nevertheless, it would be a rational progression for artisans to use formers constructed to a variety of angles and lengths with which to construct those patterns.

go to top of page

A simple circular pattern

This pattern is also of a relatively common form of naqsh found in Qatar. The construction is simple in that the design is established on the basis of an orthogonal grid of circles set one radius apart, the pattern being four circles wide by two circles high, creating a grid of eight by four rosettes. Because of this duality it has a rather static appearance, one that would be improved were there to be an odd number of circles in the columns and, particularly, the rows. You may notice that the pattern has almost an art nouveau appearance.

This first diagram illustrates in simple red lines the basic geometry of the pattern above. A grid of equally spaced horizontal and vertical lines is first established, either by using compasses and straight edge or, more likely, a right angled set square and dividers. In fact, when compasses are mentioned with regard to the laying out of naqsh work, it should be understood that the work is usually effected with the aid of a pair of dividers and, nowadays, a pencil. Then, with their radius set to the distance between the lines, a series of circles are drawn out with their centres on each junction of the horizontal and vertical lines.

If there is an unusual character to this simple pattern shown above, it is that the circles are not set out along their centres, but on their outer edges. Generally when patterns are set out, the pattern lines will straddle the setting out lines. This creates a geometric coherence which usually makes the pattern easier to work out and avoid eccentric shapes or difficult junctions. In the case of this pattern, setting out to the edge of the circles establishes a greater distance between the rosettes, which has the effect of producing an overall pattern which is more even in its weight of solids to voids. The first of the two blue sketches illustrates what the pattern might look like when straddling the setting out lines, the lower sketch illustrates the pattern edging the setting out lines.

This last sketch shows a more detailed view of the two alternative groups of four rosettes, illustrating in a little more detail, the visual difference between them with a single rosette emphasised to illustrate better the subtle variation. Notice how the rosettes on the right are more clearly defined by having their pattern lines touching the setting out lines, this being the probable reason for the original design decision. When the design is carved out and shadows fall across the pattern, the distinction is enhanced.

go to top of page

Two wall panels

These next two examples of naqsh probably date back to the developments associated with fishing and pearling of the 1930s. They were photographed in Wakra in 1975 and 1982 respectively, a considerable time after the conurbation was abandoned. Both are examples of panels carved, probably, on the ground, and then placed into recesses in the wall. As such they would have represented good practice of the time, a better quality than would have been found in much of the peninsula as Wakra had a significant and coherent quality to its buildings from that time. Yet these panels are simple, a part of their beauty is, like many of them, the inaccuracy of their execution. Notice that both of the panels have been carved deeply, and that neither of the two examples is symmetrical, even though there can be no good reason for this to be so.

Unlike the simple circular pattern looked at above, this pattern has been set out with its lines centred on the setting out lines. The sketches below relate to the manner in which it was design and constructed.

The first sketch illustrates the simple geometry upon which the design was to be constructed. The establishing of horizontal and vertical alignments has not been shown as it is likely that this would not have been used on the original setting out, the work most likely being set out by eye. The pattern has been established on a grid of 7½ by 2 circles.

If the pattern had been executed as might have been anticipated, then it would have looked similar to the illustration shown here. It is evident that it would have appeared to be symmetrical about both its axes and the pattern would have been seen to be correct in its execution. However, for reasons it is difficult to guess at, this was not the case.

This sketch illustrates how the simple geometrical pattern shown above was amended at its right end. Here it is evident that the basic geometry was capable of being amended and a sensible resolution of that end carried out. However, the two circles have been placed in illogical positions suggesting that the panel was determined to be a specific width where it would have been more sensible to reduce its width to facilitate a more rational geometrical arrangement to be made.

Here it is possible to see how poorly the right end of the panel was completed. The lines for the two semi-circles have been established on the right, but the area between them and the rest of the panel have been filled in a haphazard manner, the decisions made in the top right corner being dissimilar from those in the bottom right corner.

The second panel, repeated here, is a slightly more sophisticated design than the first panel in that it has a central pattern contained within a surrounding pattern. If you look at the two panels above you will see that the way in which it has been laid out establishes a considerable movement in its design compared with the first example which is more static in appearance.

This has been accomplished, perhaps accidentally. The four circles which are the main elements of the central design are contained within a rectangular frame. Lines drawn at 45° from the corners of the frame – shown on the left hand side of this diagram – establish the central point of the outer two circles of the pattern. The six circles of equal radius which are constructed on the perimeter of the outer two pattern circles are set out from the intersection of the 45° line and those circles. This naturally tilts the internal petals created to 15° from the vertical. Each alternate circle is mirrored so that, when the internal lines of the hexagon are added, a waving line is created across the centre of the pattern, as can be seen in the photograph above.

The next elements of the pattern to be set out are the small semi-circles running round the inside of the four pattern circles – the second circle from the left in the diagram above. In order to do this, the pattern circles are divided further from six to twelve and, with centres on every alternative junction along the pattern circle – as seen on the right hand circle above – a run of six small circles are drawn. This introduces a geometric illogicality in that the semi-circles overlap. However, as the execution of this type of work allows a degree of inaccuracy, the result may not show this, as can be seen in the photograph above.

Here is a simplified sketch of the central pattern of the panel. It is illustrated as an accurate drawing in order to show how the pattern might have been envisaged. Even at this scale it is possible to see that the semi-circles are not quite accurate, though the lively character given to the piece by the reflection of the circles about a vertical axis is evident.

While the central pattern and its elements look, more or less, accurately set out, this is more than can be said for the surrounding border. Apparently composed of semicircular shapes alternatively mirrored about an axis parallel with the semi-circles’ base, there are, respectively 11½ and 12½ top and bottom, and 4 and 3½ left and right – although this may not be too accurate a representation due to the inaccuracy of its layout. Whatever the number here, they bear no obvious relationship with the four circles in the centre of the panel. As you can see from the adjoining sketch, not all the semi-circles have been mirrored, and that quarter circles and vertical elements have been added, apparently at random. What is clear is that the artisan who made the panel seems to have run out of inspiration in setting out the surround – or that he made a number of decisions without thinking of their rationale within the overall geometry of the panel. The semi-circles have been marked out with a pair of compasses, but the lines scribed do not meet as might have been anticipated.

The setting out of the semi-circles may seem a little irrational as the system is different from that of the circles in the central pattern. It was probably based on the corners of the centres of the grid lines describing the semi-circles being in line with each other, as shown on the left, whereas the main circles of the pattern have these central lines being coincident, as shown on the right.

The problem with this kind of surrounding pattern is in creating a logical corner, not only one which can turn the corner sensibly but, perhaps, also one which relates to the central pattern. This panel, obviously has not resolved the problem.

Combining the central pattern and its border, here is an illustration of the actual panel, admittedly with a number of small variations, but giving a relatively accurate representation of the original. Note that although there are a number of variations from a simple arrangement of semi-circles, perhaps the oddest decision was to have had two similar semi-circles adjacent to each other on the bottom right of the panel.

These last two sketches can be compared with the sketch above as well as the original photograph of the panel. They illustrate how the pattern might have been carried out had it adhered to a more coherent geometry. The most obvious difference is in the relative proportions of void to solid. This is a reflection of the smaller number of semi-circles in the first illustration – 9 by 3 – and of the larger number of semi-circles in the second illustration – 17 by 5 – which are needed if the semi-circles are to align with the geometry of the circles in the central pattern.

It would be possible to use even numbers of semi-circles, but this would result in the need to have different treatments for two of the corners. Of these two patterns, the lower one is the one which more closely resembles a Qatari naqsh panel.

go to top of page

The design of the spiral

One of the more important features of Qatari carving was the use of the spiral in the design of naqsh panels. This has been dealt with elsewhere and this note is, more or less, a copy of a note on another page. There are two characteristics which appear to attach to the use of the spiral. Firstly, there is the visual motion brought about by use of the spinning motif and, secondly, the sense of direction relating to the use of a spiral spinning in an anti-clockwise manner. Note in this example that the main spiral is set anti-clockwise whereas the supporting two spiral sections have been established clockwise on the left and anti-clockwise on the right – the direction from which the panel would be read.

As mentioned above, these examples are looked at elsewhere, but here the intention is to concentrate more on the geometric design of spirals. Looking at the old examples such as that at the head of this section, it is apparent that a great deal of latitude was taken in setting them out accurately. Here, however, is a more modern interpretation, carved in the 1970s and based on fifteen-point geometry. I am not able to say how it was worked out. Five- and six-point geometries are easy to construct, but fifteen and thirty require the use of Neusis to trisect angles, so I have to assume this example was carried out by trial and error or by using a modern protractor to establish the angles of 24° or 12° required to set this central spiral out accurately.

This sketch illustrates how the spiral would have been set out. The central circle is divided into six by the usual method of describing a series of circles of the same diameter as the central circle and with their centres on its perimeter. The distances between these intersections would then have each been divided into five parts either, as suggested, by protractor or by trial and error, the latter a relatively easy method bearing in mind the usual degree of accuracy practised in setting out naqsh panels using a pair of simple dividers.

This suggestion is strengthened by this example of a new naqsh panel, recreated in another building in the 1980s. Here there is a similar spinning motif but, in the case, there are seventeen elements in the design. While it is possible to produce a seventeen-sided geometry, it is extremely unlikely that this would have been the case here. Much more likely is it to have been, again, the result of trial and error setting out.

Mention was made in the first paragraph of this note of the direction in which the spiral has been set. Note that both these motifs spin anti-clockwise. I have written elsewhere about the way in which the way in which we read writing influences the way in which we view other aspects of the visual world. In this case it seems to make sense that the Arab craftsmen would see this as advancing from right to left.

You will see immediately the relationship which the first carved naqsh panel, shown above and to the right, here, has with the lower panel illustrated here, both of them incorporating eighteen blades. This design suggests either that spirals were a common feature of carved panels, or that they were part of the design vocabulary of a single person or group whose work was, or included, carving these panels. Compared with that panel, this is missing the rectangular element at its base but is otherwise the same. Both have the counter-clockwise whirling motif constructed of eighteen blades though the surrounding running pattern is different and, along the bottom edge, further away from the centre of the circle in this example, creating a different fill pattern below the centre circle. Note, incidentally, the small differences in setting out the two panels to the left of the naqsh carving.

There are eighteen blades on the circles, which require the positioning of thirty-six points along the circumference in order to set them out. While it is very easy to construct six point geometry and not difficult to construct nine point geometry, it is likely that these whirls would also have been set out on the basis of six-point geometry and then established by trial and error to accord with this degree of accuracy. I should also point out that the centres for the curved blades are set half way between the centre of the circle and its circumference, as illustrated by the blue semi-circle in this sketch.

Generally, spiral designs were created as individual patterns, elements in arrangements suited to a range of panel shapes. Occasionally they appeared as single spirals supported by two semi-spirals as shown a little way above. In very rare cases, panels were designed to incorporate a pair of spirals, here seen revolving in the same direction with each spiral made up of eighteen blades, the panel being photographed in one of the many ruined buildings at Wakra in 1972. This type of pattern is ideally suited to a rectangular panel, the internal proportions, obviously, being in the proportion of 2:1, though the addition of the external running pattern will amend this slightly.

go to top of page

Eccentric designs

Many of the pages here make reference to the eccentric setting out of carved naqsh panels or work executed directly into walls. The reasons for this character of work is usually ascribed to a lack of concern, an ignorance of geometric method, the necessity for speedy execution, little experience and a number of other factors. But whatever the reason is, the results tend to have a significant degree of visual energy in them compared with accurate patterns. This is a natural consequence of the eccentricities of setting out, as is illustrated in this apparently simple example which somebody has partly coloured, bringing out an extremely irregular shape from what might be anticipated to be a regular pattern.

The intent of the designer appears to be that the pattern should consist of a number of semi-circles, mutually in contact. On the left, the first semi-circle on the curve touches the first on the lower straight line. On the right, the corresponding pair do not touch. Hence the irregular resultant shape.

One of the problems of setting out associated with this type of pattern relates to the decision on where to establish the surrounding geometry. In this case the semi-circle is the outside line containing the panel. This means that the lines parallel to it and within it, meet at their internal angles at less than right angles. It follows that the semi-circles established on the curve can not be full semi-circles.

On inspection of the scratched setting out marks on the naqsh, it appears that the pattern would have been relatively easy to set out. Why it should lack simple symmetry might be difficult for many to understand without thoughtful analysis. However, the point to make is that although the pattern looks simple, it is not easy to set out. In fact, it is impossible to establish logically for simple geometrical reasons.

Here an attempt has been made to suggest how the circles should have been distributed. The circles superimposed are all of the same size while those on the panel seem all to be different. In particular it is the setting out and sizing of the quadrant of the circle in the bottom right hand corner which has pushed the other circles to the left, resulting in the eccentricity picked out by somebody using a dark blue paint.

Although it is not a mistake as such, it is notable that the circular line on which the top three small circles are centred does not create the same relationship with the edge of the panel as does the horizontal line on which the bottom four circles are centred. The black lines show where the associated circles should be centred in order to create a more logical pattern. However, that would draw the upper left and right circles away from the central circle and nearer to the corner circles.

This illustration shows how the setting out of the small circles would have been impossible. The circles have been expanded so that they touch each other. On the left and right there are two groups of three contiguous circles and, along the bottom of the illustration there are four contiguous circles. The central circle has, by simple geometry, to fit exactly between the upper left and right circles. Moving it up automatically introduces space between it and those two circles. Shrinking the circles will introduce space between all of them, but those spaces will be of different sizes. Discovering this when laying out the circles may be the reason for some of the eccentricity of the pattern.

more to be written…