“Geometry is an inexhaustible well of formal beauty with which to fill our bucket; but before the draught is fit for use it should be examined, analysed and filtered through the consciousness of the artist.”
Claude Bragdon, from Projective Ornament (1915)
I have always dabbled with geometry in my design work. Grids, repetition, natural pattern and the influence of science and maths were reoccurring themes in my work but it was only when I attended a course on Geometry and the Order of Nature with Tom Bree at the Prince’s School of Traditional Arts in London in 2014 that my interest in the subject became an all-consuming passion. Connecting this newfound intellectual and creative stimulus with the toolset of practical image-making techniques I’d built up through my teaching role at Camberwell College of Arts opened up an overwhelming range of possibilities which I’m still trawling the depths of. Not only is the development of geometric structures endlessly fascinating, but I can express each of these patterns using a range of processes and media.
I tend to simultaneously work on multiple projects which feed into each other. Here I’d like to share the fruits of one open-ended project which has allowed me to explore the structural possibilities of geometry within a visual and process-led framework. It has also allowed me to tap into an ancient tradition of design and explore it with the tools available today and the possibilities they offer.
Origins of the tile printing project
The initial inspiration for the project came from one of the appendices in Daud Sutton’s incredibly informative book Islamic Design, published by Wooden Books. Here he suggests constructing tiles based on a tenfold grid generated from a circle divided into 10 equal sectors. These tiles could then be configured in countless ways to create many intricate pattern variations. This family of patterns can be seen at sites all over the Islamic world from a range of time periods, however the Persians had a particular affinity for tenfold patterns and some of the most eloquent examples of their use can be found in Iran.
As I researched this family of symmetry further I soon came across Peter Lu and Paul Steinhardt’s 2007 paper which proposed that ancient craftsmen may have used a set of 5 tiles based on decagonal symmetry to piece together large and intricate patterns which retained accuracy over large areas. Further digging led me to earlier research into this approach by Jay Bonner and E.H.Hankin. The image below of panel 28 from the Topkapi Scroll provides a strong basis for this suggestion. You can see the main pattern in black lines, and the red lines outline a large scale version of the same pattern. The dotted red lines show the tiling polygons that relate to the pattern. These are what Lu and Steinhardt referred to as ‘girih tiles’.
Looking at the qualities of these tiles in more detail, they all have internal angles which are multiples of 36º, or one tenth of a circle. The sides of each tile are the same length and the interlaced lines meet at the centre of each side with the same angle. This allows the tiles to be joined together to cover a flat plane and for the interlacing lines to always connect.
Below you can see a larger configuration of the tiles, next with interlaced lines added and finally with the polygonal subgrid removed to reveal the final pattern.
First prototype of the tiles
The first tile prototypes I created were cut from plywood using a lasercutter at Camberwell College of Arts. Access to the facilities and knowledge of my colleagues there has been an invaluable part of the development of this project.
Playing with the tiles and exploring the different configurations wormed its way into my subconscious and I awoke one night with the striking thought that I should try printing from the tiles. I’ve always been drawn to printmaking as a methodical, hands-on approach to image-making and it seemed the perfect way to extend the modular method of creating geometric patterns that the tiles offered.
Printing from the tiles
One of the most appealing qualities of printmaking is it’s analogue nature. The tactility of the paper, the imperfections and variations that arise naturally out of the process give life to images. In contrast to digital methods, it’s a slow and methodical process but the time involved is valuable thinking time. As with drawing geometric patterns by hand, the printing process involves a lot of repetition but the active meditative state this creates, allows you to develop a deeper insight into what you are doing and why. Printmaking is an immersive process which encourages thinking through doing.
The time built into the process also invites step by step refinements in technique. I wasn’t entirely happy with how the borders of the tiles in the first prints were so visible and disrupted the continuity of the interlaced lines. Even though the lasercutter removes a minimal amount of material along the cut edge, there is still enough lost to stop the tiles quite touching each other smoothly. This led me back to the shapes that are created by the connecting lines rather than by the tiles that contain them. I identified the 8 main shapes that provided the basis of this vocabulary. There are, of course, more shapes that can arise from experimenting with these forms but this is the basic set of shapes which offer vast possibilities for pattern creation. It is a simple vocabulary but the language is complex.
Next I lasercut a new set made up of these 8 shapes and started making patterns and prints from them. Without the interruption of the underlying tiles, the prints came across more strongly.
For the following set of tiles, I offset the outlines of each shape to create channels between them and give a different feel to the printed image. The modular approach offers more flexibility in composition than a ruler and compass construction and more fluidity in exploring pattern variations.
So far, I’d been cutting the tiles from the acrylic in patterns so as to create zero wastage of material but with the channels, the wastage became something in it’s own right.
Expanding the vocabulary
I began to create further sets of tiles with different compatible forms. There is another vocabulary of forms that arise by applying more acute angles to the girih tiles, one which is compatible with the previous set but results in designs with a different feel, similar to speaking in a different dialect.
With valuable insights from the work of Jean-Marc Castera in his magnificent tome Arabesques, and through exploration of the 8-fold Moroccan geometric system as seen in the incredible zellij tile work in places like Fez and Marrakesh, I cut a set of these tiles.
Building up diverse vocabularies of geometric forms in this way, especially for printing, is not dissimilar to using traditional letterpress printing to set and print sentences, and it reinforces the analogy with language. Piece by piece I meticulously prepared a whole range of patterns, each divided into 2 colours.
From here I was able to immerse myself in the printing process. At the same time as engaging in a physical activity, the mind is constantly engaged in making design choices, choosing and mixing colours, experimenting with papers and embossing the designs (pressing into paper without ink). I thought these were particularly successful because they emphasise the physicality of the process and allow the textural qualities of the paper become one with the pattern.
These are just the first steps of this ongoing project; from this node in the process, the structure of the geometry, the laser cutting and the printing process all offer many possibilities for progression and variation of a basic initial idea. The set of prints available to purchase in very limited runs from the shop are the fruits of the project so far but there is an ever expanding body of ideas of where to take it from here, not least further exploration of the golden ratio proportions and self-similar qualities embedded within tenfold and eightfold patterns.
For me, concept and process are intimately connected and inform each other constantly. The interplay of digital and analogue processes, of ancient and modern understanding of nature, maths and science, creates a dialogue through which unique processes and outcomes arise, as demonstrated in nature itself, the subtleties of each process feeding into the subtleties of another to open new creative avenues. By taking an openly exploratory and practical approach to geometric art, I have found that the analogue and the digital, the traditional and the contemporary, the contemplative and the analytical, are not opposing elements but complementary ones which allow for a full and deep exploration of geometry as a creative language.
The beauty of geometry as a lexicon of design is that it is universal because it is a visual representation of the number patterns which govern the way the universe is structured. When combined with the ever-expanding possibilities in the methods of application and expression of these forms, both traditional and contemporary, it presents to the artist an inexhaustible creative resource.
If you’re still here at this point I thank you for your time and attention. I am aware that they are valuable commodities in today’s high speed world.
Many thanks and appreciation go to Daud Sutton for inspiring my initial interest in geometric pattern design with his books and for his continuing valuable personal guidance, the imparting of his expansive knowledge and his encouragement as my esteemed teacher.
In addition, the important work of Anthony J Lee, David Wade, Jean-Marc Castera, Alan Adams, Richard Henry, Jay Bonner, Mirek Majewski, Abdelhalim Ghodbane and many others who have influenced me through their involvement in the practice and discussion of geometric design, not least all the Geometry Circle participants.
Lastly, huge thanks and respect to all other geometers past and present for contributing to a tradition and practice which I feel plays an important role in enforcing our interconnectedness with nature and one another.
All images are my own and of my work unless credited otherwise.
Its just beauty
Very interesting article, the relationship between fractal geometry and Islamic tile design was what drew me into the study of that great and profound tradition.
Many thanks Ed. Yes I love the fractal possibilities of Islamic design too. In fact I am teaching a course on Dual Level patterns at PSTA in April. I hope to explore self similarity further using this printing system.
Thanks for sharing such wornderful art, I love the geometrical forms.
Wonderful article, Ameet! You made your own IG puzzles 🙂
Thanks Dawn! Endless fun with these..
Ameet, this is a super duper interesting article! I intend to study it more thoroughly! Thanks for posting it!
Cheers Susan.. I have lots of insightful fun with these.