Five & Tenfold Islamic Geometric Patterns
Home of the #tutorialtuesday #fivefoldfun activities from September to November 2020 but great to work through any time at your own pace.
If you enjoy the free resources, any size donation welcome to help sustain my work!
This page collects together the YouTube tutorials enriched by tips, encourgament, referernces, link & recommendations to help you work your way through this family of patterns with a series of activities. Suitable for those of you have some or a little drawing experience.
Activity 1 - Watch Vintage & Modern Compasses & Kit Overview and make sure you have quality tools ready for next week.
We’ll be easing into these activities slowly as I’d love for everyone to get to know and have the right kit before we are knee deep in constructions and the problems & inaccuracies from school compasses or kit not up to the task. This isn’t to say, that the perfect kit fixes all your problems, nope, not at all… it just lessens them!
This first video is an overview of Vintage & Modern Compasses so you can know what to look for. Your reslience & perserverence is always important, but will be tested quite a bit if you do not use quality tools. My detailed recommendations are available via the materials & equipment page. Whilst you are there, do check info and links for paper, pencils, pens & rulers, erasers & sharpeners too –I’ve lots to say on them all! Many are Amazon afflicted links, so I earn a little commission at no cost to you for making these recommendations. Every little helps!
Two Constructions to Divide a Circle into Five & Ten - Using a Compass & Straight Edge
Activity 2 - Draw these constructions each a number of times and do so varying your kit, using 2mm lead, pen or mechanical, pencil, ruling pen(!) with whichever quality compasses you have.
You may now have a better idea of the different tools & the many combinations that follow. But what is your preference? Perhaps you're already decided, or happy to play with a few combinations. You may like something now and change your mind for a different drawing later! Therefore find what best works for you whilst you build up familiarity, confidence & accuracy with these constructions. The radius doesn't have to be defined for these drawings, but make sure you don’t pick the biggest radius for your compass, as you may struggle when you have to increase that radius twice for the first construction. Saying that, new geometers do start larger (e.g. 9cm to 11cm on A3 paper) and try smaller for your further drawings. Repeat as many times as you need and ENJOY!
The Sheikh Zayed Grand Mosque Fivefold Motif - A Geometric PentaBlossom
Activity 3 - Watch the new video “UPDATED #8 - Sheikh Zayed Grand Mosque Fivefold Motif - A Geometric PentaBlossom - Islamic Geometry” and draw, outline paint your versions of this motif.
Our first pattern is an oldie but a goodie – one of my main goals was to improve existing tutorials. This pattern was given the one minute animation treatment three years ago as part of a good run of #tutorialtuesdays. The animation with its chirpy music didn’t show a hint of the difficulties involved in drawing 5 & 10 divisions. So the comments section on YouTube often seemed the home of the frustrated geometer. So as every in a timely fashion, I’m fixing that now. So we have the initial construction, followed by two different ways I added detail and colour to the weave. I know it’s super tempting to recreate what you see like for like, but if you can, resist, you will really get more out of the creative process if you have to think about colour, combinations and placement. If you’re not confident with colour, keep it simple with no more then three colours, play with them, get to know how they behave on a test paper with differing amounts of water… you learn so much, how they behave and how they dry, also find the level of dilution that you like most. And if you don’t love it, paint another, the first informs the second and so on and you learn so much when the pressure is off… regardless of how you do it, enjoy every line, curve and brush stroke…
Week 4 - The Tenfold Rosette
Activity 4 - Watch either the existing tutorial #13 - Tenfold Rosette 3 Ways Tutorial - Drawing & Painting Islamic Geometric Pattern or new tutorial Drawing & Painting the Tenfold Islamic Geometric Rosette in a Pentagon to construct this rosette pattern that so many of us love. Draw, trace, transfer, tile or weave as you wish - between these two videos you can see a lot of techniques and outcomes.
If you are a beginner, dividing a circle into 5 and then 10 is a notoriously a very difficult construction. It’s one of the main reasons why I’ve built up to these two video about tools and construction. Good eyesight, brilliant lighting, excellent hand eye coordination, sharp and quality tools, precision in every move all count towards minimising the errors and in accuracy. If any of them is rushed or lacking, you won’t get it right. So be kind to yourself if it doesn’t work out first time, have a break, draw something else and then regroup and try again, perseverance is key and several attempts are sometimes needed!
It’d be fair to say this is the archetypal Islamic Geometric Rosette that has perfection built in throughout. Look at the perfect regular pentagrams, five pointed stars in between the petals, In all other rosette patterns they aren’t regular; they are optimal for their situation, but never regular, not in twelvefold, or eightfold or any other fold! Dividing a circle in to five and ten isn’t intuitive or easy. Yet the outcomes, the shape, their relationship & their proportions are ones that resonate with so much geometry in nature and our universe. More of this in the coming week’s patterns.
The first video, ideal for beginners, starts from scratch, including dividing a circle in to 5 & 10 and our first meeting with the fivefold rectangle which will come up repeatedly in the coming weeks. Then constructing the rosette as a single motif and at this stage, this can’t be tiled (tessellated). To do this, I return to my favourite tools, tracing paper & a spoon! Tessellating the rosette correctly requires a specific tile, the rhombus, which then allows you to stitch the pattern together seamlessly. I also wanted to add how I weave a pattern, so another technique to try out if you wish.
The second video was a happy suggestion that I was glad I was able to add in as something new/related to the week’s rosette. It is more challenging and involves drawing a fuller repeat of the rosette in a pentagon. This pentagon is the final outcome and can’t be tiled. The satisfaction levels of this pattern and its variation are high, as it seems often so tricky to get started, so enjoy the variations and see what you can create from these two tutorials. Remember to enjoy every stage of the process helping you to build up those hours of experience!
Week 5 - Umm Al Girih Tutorial 1 - A Five/Tenfold Pattern Two Ways
Activity 5 - Watch Umm Al Girih Tutorial 1 - A Five/Tenfold Pattern Two Ways to construct the pattern in a fivefold rectangle and then trace, transfer & tile the two outcomes of this video: the Rectangular & Circular tilings. Weave & or embellish as you wish.
The patterns in this and the other videos in the Umm Al Girih subseries will use 5 shapes from the Umm Al Girih family, meaning mother of patterns in Farsi (Persian). It’s an extensive vocabulary of shapes which create endless five & tenfold patterns. I’ll show you how these 5 shapes will lead to different patterns, each with their rectangular & circular variations. They can of course be tiled & constructed in a huge variety of ways.
Although these patterns can predominantly be found in Iran, Central Asia, Afghanistan & Uzbekistan and travelling further east to Mughal India, as ever there are examples elsewhere, I can think of a Mamluk frontispiece from Egypt straight away!
Their names in Farsi/Persian are often names from objects around us, foliage & flowers, animals & household objects, celestial bodies or their geometric qualities:
Shamsah meaning Sun
Toranj Kond meaning Obtuse Citron
Panj Kond meaning Obtuse Five (sided shape)
Sormadan meaning Kohl Bottle
Tabl meaning Drum
Farsi vocabulary overlaps with words in Arabic and Urdu and other languages in the region
The Construction Method
This may be deemed as traditional because we take a quarter of the pattern drawn within the fivefold rectangle, with diagonally opposite corners divided into 5. By drawing concentric proportional circles & further lines we draw the pattern using the intersections created. This style of construction allows us to obtain the two tiling s of this pattern – the rectangular & circular with great ease- whilst showing how they and the two outcomes relate to one another.
This fivefold rectangle with further lines & circles will lead to more complex patterns from this family of 5 shapes in the other videos in this series. Consider also the rectangle for other families of symmetry then consider how each can be extended and added to, to create more and more complexity. Huge potential!
My Practical Ways to show/connect the Two Outcomes
I am a big fan of tracing paper and using it to get the two full patterns has been really valuable to me drawing & painting and making connections with the patterns I see in architecture. Although I’ve seen this minimal triangle used a lot to explain the tilings, it was always digitally in books or resources online. I don’t think I’d ever see anyone use tracing paper this way so I was pleased to find a practical solution that highlights the relationship between two related patterns so clearly.
My Research and Sources have been invaluable. I didn’t understand a lot of this content when I first read and saw them, but I didn’t let that put me off and I carried on regardless. I returned to them again and some aspects made sense, whilst others were and still are beyond my knowledge & experience. I’m happy to not know everything now and love being a lifelong learner so these are resources & links I have used time & time again:
A must have for all fans of Islamic Geometric Pattern: Islamic Design by Daud Sutton
Online resources & links shared generously by Ali Reza Sarvdalir on the Drawing Islamic Geometric Designs Facebook group. A few of my paintings have his name and then 1 to 4 on them, because of a series of constructions he shared many years ago. If you are on Telegram, his channel is full to the brim of resources.
Persian Variations paper by Jean Marc Castera. A fascinating read that goes off in a different direction, but so very valuable.
Emails with Hamed Rahnama from www.girihpuzzles.com for the puzzles and insight into shape names.
Brian Wichmans’s www.tilingsearch.org website with links to PDFs of Tony J Lee’s notebooks from the 60 to 80s. If you search for patterns with pentagons and 10 points stars you can find an array of patterns, many of which link to the next website.
David Wade’s www.patterninislamicart.com website which has a scan of the 1980s publication The Design and Execution of Drawings in Iranian Tilework, Mahmood Maher al-Naqsh
Week 6 - Umm Al Girih Tutorial 2 - A Five/Tenfold Pattern Two Ways
Activity 6 - Watch Umm Al Girih Tutorial 2 - A Five/Tenfold Pattern Two Ways to construct the pattern in a fivefold rectangle and then trace, transfer & tile the two outcomes of this video: the Rectangular & Circular tilings. Weave & or embellish as you wish.
As an extra challenge, see if you can fully construct a fuller rectangular or circular tiling! There is certainly enough information in the five fold rectangle shown. If combined with a layout (see week 4’s video: Drawing & Painting the Tenfold Islamic Geometric Rosette in a Pentagon it may be something you can do!
I continue with the same construction method, I used for Umm Al Girih Pattern 1, we take a quarter of the pattern drawn within the fivefold rectangle, with diagonally opposite corners divided into 5. By drawing concentric proportional circles & further lines we draw the pattern using the intersections created. This style of construction allows us to obtain the two tiling s of this pattern – the rectangular & circular with great ease- whilst showing how they and the two outcomes relate to one another. If you notice a lot of my paintings & tracings have Ali Reza Sarvdalir’s name on them. It was his posts on facebook that at first flummoxed me, and then eventually they made sense and made me research wider and make connections between the different sources for this way of drawing. Always so very grateful for those who share their knowledge so freely!
Week 7 - Umm Al Girih Tutorial 3 - A Five/Tenfold Pattern Two Ways
Activity 7 - Watch Umm Al Girih Tutorial 3 - A Five/Tenfold Pattern Two Ways to construct the pattern in a fivefold rectangle and then trace, transfer & tile the two outcomes of this video: the Rectangular & Circular tilings, Weave and/or embellish as you wish. And again, as an extra challenge, see if you can fully construct a fuller rectangular or circular tiling. There is certainly enough information in the fivefold rectangle.
As we get further into this family of constructions, it occurs to me that they are certainly becoming a follow by rote style of construction, I haven’t provided the reasons as to why the circles & lines work the way they do, they are still a mystery to me (the way we were able to make predictions about the next set of steps and extrapolate different sets of patterns in the twelvefold rosette series doesn’t apply here. But as ever, if I don’t know something know, I set it aside and continue to learn and progress
The resources I have read and seen on the Umm Al Girh Patterns fall in to two categories:
A) Constructing them like we have been doing, which I have found many older resources on, particularly from Iran and especially thanks to Ali Reza Sarvdalir and his posts on Facebook, OR,
B) Creating the patterns on a grid of polygons. There are so many resources on this, but they don’t particularly help me with compass and straight edge constructions. They are fascinating, interesting and beautiful observations and properties that this fivefold set of families have. They connect to other areas of mathematics & science and have allowed some to develop the language of shapes and create new patterns, so the potential & application is huge. They also give qudos and status to the geometers of the past who had such intellectual design knowledge 500 years ago.
Here are some useful and interesting discoveries & links:
The idea that all tiling repeats in a periodic way was thought to be fixed, there didn’t exist a shape or shapes that could be tiled non-periodically. Or did there? British mathematician Sir Roger Penrose, in 1974 discovered that the kite shape we draw, the Toranj, along with an arrowhead did tile infinitely & non-periodically, something which can be seen in the Persian Architecture over 500 years ago.
There is also a connection to Quasicrystals. These are shapes that tile to fill a space, but unlike true crystals don’t have symmetrical qualities that allow a pattern to be layered exactly one on top of another. Again the idea of non-periodic tiling emerges. Following Penrose, Danny Schechtman , an Israeli Scientist, discovered that atoms in a metallic alloy, were also arranged non periodically - he had discovered quasi-crystalline structure in nature. He went on to be awarded the Nobel Prize for Chemistry for this achievement. Since then, hundreds of different quasicrystals have been discovered in nature.
Finally, another pair of important people to connect all these modern day discoveries back to the Persians are Americans, Peter J Lu and Paul J Steinhardt. They showed that the Persian patterns weren‘t merely constructed as the result of a series of lines drawn with a staight edge and compass. But that in 1200CE, they understood them to be tessellations of a special set polygons (our famous 5 girih tiles) that allowed the Persians to create increasingly complex periodic girih patterns. By the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in modern day science.
Week 8 - Umm Al Girih Tutorial 4 - A Five/Tenfold Pattern Two Ways
Activity 8 - Watch Umm Al Girih Tutorial 4 - A Five/Tenfold Pattern Two Ways to construct the pattern in a fivefold rectangle and then trace, transfer & tile the two outcomes of this video: the Rectangular & Circular tilings, Weave and/or embellish as you wish. And again, as an extra challenge, see if you can fully construct a fuller rectangular or circular tiling. There is certainly enough information in the fivefold rectangle.
Now we have a group of 4 patterns, it is so useful to compare their qualities & constructions. I'll be adding in more information about this soon, but the resources and links I have gratefully relied on are:
Resources shared by Ali Reza Sarvdalir on social media in particular his Persian Moqarnas Design group on Facebook;
Brian Wichmans’s www.tilingsearch.org website with links to PDFs of Tony J Lee’s notebooks from the 60 to 80s;
David Wade’s www.patterninislamicart.com website which has a scan of the 1980s publication The Design and Execution of Drawings in Iranian Tilework, Mahmood Maher al-Naqsh
Week 9 - Tenfold Ottoman Pattern 3 ways Tutorial - How to Draw Islamic Geometry
Activity 9 - Watch Tenfold Ottoman Pattern 3 ways Tutorial - How to Draw Islamic Geometry to construct the pattern 3 ways: As a single circular motif, the circular or rectangular tiling. The pattern can be outlined in any colour ( I used black, sepia and gold), or painted leaving white channels between the shapes which allows for more ways to paint this tricky pattern.