Ibn Tulun; Drawing Lajin’s Minbar 3

Finally we arrive at the development of the main pattern of the minbar at ibn Tulun. This rosette pattern of the flanks of the minbar is a further development of the eight point rosette tiling. It is finer in scale, rosettes are smaller relative to the pattern, and more complex. It is no longer simply rosettes at the center of the octagon tiles. Even as a more intricate pattern, it is not difficult to draw.

We do need a large layout of the hidden foundation Archimedean octagon and square tiling, as shown in yellow. A new pattern layout problem with this tiling is how to define the isolated rosette in the center of the octagon and the 8 regular pattern octagons which surround it.

Drawing the entire pattern is a bit wasteful of space since it is essentially a half pattern, filling the space below the steps. Defining the pattern requires a 3 by 3 grid of the octagon square tiling.

The definition and construction of the eight rosette was dealt with in the first drawing post on Drawing Lajin’s Minbar. The underlying structure layout very rarely changes from this ideal pattern; everything follows from this ideal layout here. I will move through the details of the layout of the rosette quickly; please refer back to the earlier post for details. We will simply need to define how the isolated center rosette is connected to the ring of 8 eight fold rosettes around it.

We can go straight to the details of drawing a new and larger tiling layout. What is required here is an accurate, reasonably concise, layout of the 3 by 3 Archimedean grid of octagons and squares.

A large grid can be drawn by creating the octagon layouts one by one, adding on to the previous octagon, but accuracy often suffers when working from a center outward, locating each new polygon based on a previous octagon. It is almost always better to work from a large master circle inward. The practicality of this preferred method is limited only by the capabilities of your compass. This is the clearest argument in favor of owning a beam compass. This layout will nicely illustrate the problem of a very large range of radii.

The large master layout circle will contain the entire pattern. This complete pattern is best attempted on A3 paper or larger. Construction begins as for almost every fourfold symmetry layout.

The geometric problem is how to define three circles across the bottom with proper overlap to define the octagons we desire. It is worth keeping a notebook of the solutions to these basic problems so that you do not need to puzzle over it every two years when the same layout problem reappears. Most of these basic problems will be compiled on this site in the large post on the divided circle but it will take some time to appear.

Looking at the first figure in this series above, the green overlapping squares which define the octagons we need shows where the layout circle should lie.

Adding a pair of squares creates all of the structure we need.

A new layout circle is well defined by clear intersections. Filling these in around the pattern divides the original square into 9 full, half, and quarter squares. If we extend the layout just a half square outside of the the original layout circle, we have a 9 square grid. The squares are already divided into 8 by the layout.

When the double square is inscribed into these circles, we have a complete 3 by 3 Archimedean grid of octagons.

The minbar pattern will be created by drawing a rosette at every vertex of this Archimedean grid. For this post I will show a two by two portion of the pattern to keep the drawings at a reasonable scale. This is big enough to show all of the structure and interactions of the pattern.

The Octagonal Rosette Pattern Layout in Detail

If we look at the center of the pattern above, a familiar composition appears. Looking at the four rosettes around a square in the center, exactly the same pattern was shown at the completion of the first “Drawing Lajin’s Minbar” post. The pattern here is rotated 45° relative to the pattern on the minbar of Alâ ad din camii, in Konya. The pattern lines also extend inward to complete a new field on Lajin’s minbar but as for a 800 years of tradition to come, the underlying structure is identical.

Since the basic rosette pattern layout structure is identical, we will concentrate on what is special about the pattern found on Lajin’s minbar. This is largely centered on the new tiling

One practical issue always comes up first. “How big do I make my first circle?” It will probably be limited by your compass here.

If we draw in one rosette above, we see an interesting problem with the large master circle layouts. The initial layout circle radius used to define the Archimedean grid is about 16 times the smaller layout circle needed for the rosette definition. This range of radii is just about practical with an extension bar in a bow compass, but it is far better to have a beam compass for the job. Using a typical bow compass with its extension gives a larger radius of about 220 mm, ~ 8.5 inches. This leaves only about 13-14mm or ~½ inch for the radius of the layout circle critical to defining the symmetry of the rosette. It is good to keep that smallest layout circle at least 12-15 mm radius for accurate layouts. These layouts are a difficult job for a single 6 inch compass.

We will zoom in as the layouts progress to keep drawings at a reasonable scale for the screen. The full minbar panel is quite a bit of work.

Lajin’s minbar requires a rosette at every vertex of the underlying octagons. Those rosettes touch, tip to tip. This completely defines the layout circle for the rosette; the layout circle is one half of an octagon side.

The proportioning circles for the rosette are drawn in for ideal proportions. The smaller circle is located as shown; refer back to the earlier post for details. It defines the inner layout circle of the rosette.

We will not need the octagon drawn in for this layout but I have drawn some of them in since it is good to remember how the center of the proportioning circle is defined and because something interesting will happen later.

That inner proportioning circle defines a star polygon. It can be drawn in. This is still the special case of a rosette, a parallel arm rosette. This means that the arms of the petal are defined by the corresponding polygon, an octagon as shown below. The definition of the rosette is complete.

[Optional Information: We will see what happens when the arms of the rosette are not parallel when we look at the patterns of the doors of the minbar. Some extra steps are then required to define the proper proportion rosette. This special case skips two or three steps since we know that the end of the petal is defined by the octagon.]

Adding a rosette at each vertex is a lot of drawing, but all of the layout circles are already defined using the layout we have here.

This is where something interesting happens if we look at the octagons for the rosettes. The pattern below has a star polygon shaped hole in it. If we take away the rosette pattern lines, it is even clearer.

Looking beneath the rosettes, a new tiling of octagons and squares is developing. At each square in the Archimedean tiling a new, identical octagon and square proportional tiling arises. This smaller scale proportional tiling is not a perfect tiling, but leaves a hole in the shape of the 8 star polygon in the center of the original octagons. This is the basis of many Zellig patterns. See Jean-Marc Castéra’s Arabesques, Decorative Arts in Morocco for an exhaustive look at the family of pattern.

Back to our pattern. The next element to address is that large hole in the pattern left by the star polygon shaped space in this tiling. There is more than one way to fill this, but the pattern here uses another ideal proportion rosette. The rosettes cannot align tip to tip, so these are aligned along the inter-radii.** The space is already divided into 16 parts by the tiling and the radii are shared with the other rosettes so layout is easy.

We still have a large empty space around the center rosette, so it is filled by simple extension of the pattern lines of the existing pattern until they cross or meet. This is the most common way to complete a pattern when a “hole” exists and it usually defines what can be called a geometrically legitimate and complete pattern. As in this case below, the shapes formed are not always ideal. These new irregular hexagons are a bit large, slightly out of proportion with other elements of the pattern. A large part of the art of designing pattern is to create a shape with good proportions in size and shape and relationship in symmetry to the remaining pattern. These slightly oversized tiling result polygons are often modified further.

In this case we can add a new layout circle defined by the rosette petal tips at each position. This allows the conversion of the hexagon shape to a regular octagon by the addition of two new sides. This is very common where the angles of the irregular polygon shapes allow it to be converted to a regular polygon by adding a side or two. In later, more complex, minbar patterns we will even see this done where the resulting new polygon is only an approximation of a regular polygon but close enough to be regular in appearance.

With this “perfection” of this new shape to a regular polygon, the pattern is complete. The full minbar panel has one full octagonal ring or rosettes, four half octagonal rings and a quarter.

If we compare this to the earlier Anatolian or Zengid minbars, Lajin’s minbar has a more complex, developed, pattern. The rosettes are smaller relative to the full pattern, their relationship to each other is more complex, and the pattern has introduced new visual complexity in the rings of octagons. All of this pattern work is still dominated by strict submission to geometry. It is defined by the underlying Archimedean tiling of octagons and squares. All of the pattern proportions are fully defined by the ideal form of the eight fold rosette. The result is quite elegant.

This leaves on ly the two patterns of the doors of the minbar portal. These are both patterns dominated by tapered 12 point rosettes. Perhaps it is surprising that these too are completely defined by the proportions of the same ideal eightfold rosette of the pattern studied here.

** Talking about designs requires some names to assign to things. I believe that the assignment of “radius” and “inter-radius” was first used by AJ Lee. The arms of a rosette or points of a star polygon are defined as sitting on the radii. The divisions falling between the rosette petals or star points are called the inter-radii.