One of the most recognised patterns from the Al Atterine Madrasah (medieval university), this dual level pattern features ten-pointed stars on both the micro (outwardly visible) and macro (structural) level.

The central motif was taught by my teacher Adam Williamson in his online courses during the early days of Covid lockdowns.

Expanding outwards from this central structure, I analysed the full pattern to create this piece. It is now featured on the cover of "Sufi Lines", by Mohammed Ali Vakil and on the title page of Adam Williamson’s book, "Profound Patterns"
- Gillian Turnham

This pattern is from the ceiling of the western portico of the Mosque/University of the Mamluk Sultan of Egypt, Cyprus and Syria: Al Ashraf Barsaby (ruled 1422 – 1438).

Whilst most patterns in the Islamic world can be found in multiple sites, this one is unique to this location. The ceiling is currently in need of restoration and the worn, disintegrating texture inspired my recreation of the design for this commission, the original of which is housed in a private collection.
- Gillian Turnham

Contained within each symmetry system are one or more harmonically proportioned rectangles, commonly used for creating repeatable pattern units for larger-scale designs. This piece explores the process of deriving the harmonic rectangle from the initial circle divisions, by way of constructing regular polygons. For example, we can divide a circle into six (or twelve) through the same method we use to construct a regular hexagon. We can then derive the harmonic rectangle by drawing lines connecting specified circle divisions at the circumference.

Each of these harmonic rectangles (a square is considered here to be a specific kind of rectangle) can be scaled up or down according to its own proportional rhythm. The final (left side) column demonstrates these scaling rhythms.
- Gillian Turnham

This composition tells the story of a long and arduous analysis I undertook of a portico pattern from the Jameh Mosque in Isfahan (depicted in blue).

The central star has fourteen points, a symmetry system incompatible with almost any other, yet presentd here in conversation with both eleven- and nine-pointed stars. I was finally able to resolve the structural analysis after encountering a rosette version of the same pattern developed by my teacher and friend Ameet Hindocha. It is depicted here in bronze. This piece has been rendered on traditional wasli paper handmade in India.
- Gillian Turnham

This design is emblematic of the Alhambra palace in southern Spain (built by the Nasrid rulers of Al Andalus between 1238 and 1358). It is found carved into the plaster (yeso) walls in several locations throughout the complex.

The design incorporates the seedpod of the Magnolia tree, a key feature of the paradisal gardens surrounding the palace. This piece was executed in the first weeks of Covid lockdowns using materials I had on hand: pencil and sketchbook.
- Gillian Turnham

The Alcazar triptych marks the starting point of this body of work. These analyses were conducted on-site at the Royal Alcazar of Seville, whilst living in Seville, Spain. Here, we see three of the most iconic palatial patterns grow from their initial “mother circle” all the way to the finished ceramic wall mosaics (known in Andalucia as alicatados, a Spanish-Arabic term referring to the process of cutting each tile shape from larger, glazed ceramic tiles).
- Gillian Turnham

These two patterns are taken from a mosaic floor in Bayt Al Kritliyyah (currently the Gayer Anderson Museum) in Cairo, Egypt. The outer two columns feature a pattern from the tenfold family (created by dividing a circle into ten equal parts) while the central column features a pattern from the twelvefold family (created by dividing a circle into twelve equal parts). Each symmetry family has one or more harmonically proportioned rectangles into which patterns can be naturally arranged. In this piece, I have established a mathematical union between the “root two” rectangle of the tenfold family and the longer, thinner “root three” rectangle of the twelvefold family, resulting in three columns of perfectly equal length.
- Gillian Turnham

The Alcazar triptych marks the starting point of this body of work. These analyses were conducted on-site at the Royal Alcazar of Seville, whilst living in Seville, Spain. Here, we see three of the most iconic palatial patterns grow from their initial “mother circle” all the way to the finished ceramic wall mosaics (known in Andalucia as alicatados, a Spanish-Arabic term referring to the process of cutting each tile shape from larger, glazed ceramic tiles).
- Gillian Turnham

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This unusual fifteenfold / twelvefold rosette pattern features on a wooden door panel from Cairo, housed now in The Louvre museum. I analysed this pattern from a photo detail from David Wade’s extensive photo archive, utilising the theoretical methodology developed in Anthony Lee’s unpublished notebooks on the mathematical structure of rosette patterns.
- Gillian Turnham

This piece demonstrates one method of constructing an approximate regular heptagon using ruler and compass (it is mathematically impossible to construct a perfect heptagon using only ruler and compass. Interestingly though, it is possible through the technique of neusis which introduces a moveable set length, and through paper-folding). This particular construction combines the circle, triangle, and square in order to arrive at the measurement for one side of a regular heptagon. This measurement is found where the equilateral triangle (formed using the length of one side of the square) cuts the original circle. This measurement can then be transferred around the circle to define the full heptagon.

With approximate polygon constructions, the compass radius often needs to be adjusted a millimetre or so in order to establish equal divisions. They are, however, still useful from a practical perspective, as well as being philosophically potent. - Gillian Turnham

The Alcazar triptych marks the starting point of this body of work. These analyses were conducted on-site at the Royal Alcazar of Seville, whilst living in Seville, Spain. Here, we see three of the most iconic palatial patterns grow from their initial “mother circle” all the way to the finished ceramic wall mosaics (known in Andalucia as alicatados, a Spanish-Arabic term referring to the process of cutting each tile shape from larger, glazed ceramic tiles).
- Gillian Turnham

This piece explores the relationship between a classic tenfold pattern common to Mamluk Egypt, and the iconic “pili gereh” pattern from the Jameh mosque in Yazd, Iran.

Whilst outwardly diverse, both of these patterns spring from the same mathematical grid structure. Working outwards from the centre, the constructions evolve in both directions toward their completed forms. Both patterns are united by an interstitial regular fivefold polygon (a pentagon to the left and a pentagram to the right), and by the usage of the “kite” polygon, highlighted in dark blue to the top-right of center. In the lefthand pattern, the kite is used as a clear and independent design motif, sometimes referred to as a free kite. This design innovation appears to have originated in pre-Mongol Persia but was utilised prolifically and to great effect by the Mamluks.

In the Yazd iteration, the kite shape is imbedded more deeply within the structure of the pattern, yet almost completely defines the outer appearance of the classic turquoise pili tiles (which some believe to be a stylized kufic rendering of the name of the Prophet ﷺ). Special thanks to my teacher Alan Adams, who identified the link between these two patterns.

- Gillian Turnham