Posted tagged ‘Geometry’

Not so quick update

April 26, 2010

As I imagined things are becoming quite manic now. There are deadlines and things to remember all over the place. But, alas, this is the way of anything that has a specific pressured end such as the project.

Now I have a couple of books I’d like to mention which I was supposed to have done some time ago. Actually one of them I might have already mentioned…but I’m not sure so I’ll mention it anyway (you know, just in case).

The first is ‘Polyhedron Models’ by Magnus J Wenninger. It  contains some very striking,  but kinda complicated models of…yep you guessed it – polyhedrons. For those who don’t know what these are have a look at some of the images below. They look a little similar to the model I made a while back (Icosahedron).

A polyhedron (plural polyhedra or polyhedrons) is a geometric solid in three dimensions with flat faces and straight edges.


Page 21 from M J Wenninger's Polyedron Models

Page 21 from M J Wenninger's Polyedron Models

Polyhedron Models illustrates how the shapes look when flat and then once constructed to their full 3D form. However, I think most of these are beyond my capability to attempt (at the moment at least) but there are some simple ones at the beginning of the book and seem less scary as the associated mathematical formulas aren’t so daunting either. Not to mention some of the names. And you’ve just got to love some of the names – e.g. Quasirhombicuboctahedron which looks something like this:


Quasirhombicuboctahedron - from pg 132 of M J Wenninger's Polyheron Models

And the rhombitruncatedicosidodecahedron:


Rhombitruncatedicosidodecahedron - from pg 30 of M J Wenninger's Polyhedron Models

I did a search on the author and found some fascinating imagea of his coloured paper creations:

3D models of 4D polytopes

3D models of 4D polytopes - by Magnus J Wenninger

Polyhedron from set number 5 - by Magnus J Wenninger

Polyhedron from set number 5 - by Magnus J Wenninger. This one would probably look brilliant if carved from stone, although I can't imagine how it could be done.

Oh and it says on this site that he is a monk. I wonder how much that has played into or influenced his interest in this kind of geometry. Have a look at his web site for more stunning photographs and more on his writing too.

On to the second book. This one is ‘Geometric Concepts in Islamic Art’ by Issam El-Said and Ayșe Parman. Now I heard about this book some time ago but kinda forgot about it then realised it wasn’t newly available and then recently decided to just get a second-hand copy via the net. But it’s totally worth it. If I had this book maybe a yr and a half ago I think I might have done a lot more pattern work. It was Richard Henry (teacher for the pattern-making workshop) who recommended this book to me not so long ago and I can see that it is an immensely useful, practical and encouragingly inspiring one to have. Yes a lot of superlatives but they were all intentional.

Now Issam El-Said died at the age of 50 in 1988 before he was able to finish his PhD. But in the time that he was practising his art and already doing much research into the area of geometry he managed to create some beautiful pieces and publish very informative and educational writing. His work (both academic and artistic) is still valued today and this book is only one example.

Geometric Concepts in Islamic Art by Issam El-Said and Ayșe Parman

Geometric Concepts in Islamic Art by Issam El-Said and Ayșe Parman

Hardback cover of Geometric Concepts in Islamic Art

Hardback cover of Geometric Concepts in Islamic Art by Issam El-Said and Ayșe Parman

The cover itself (hardback version) has gold calligraphy on the front (under the paper cover) which is a nice touch. And then inside there are photographs of geometric patterns from real architectural sources around the world. Besides these photos are diagrams of how those patterns have been constructed. Like really simple ways to construct them!

Geometric Concepts in Islamic Art - pg 47

Page 47 from Geometric concepts in Islamic Art

Geometric Concepts in Islamic Art pg 91

Page 91 from Geometric Concepts in Islamic Art

I’ve realised that with some patterns there are a couple of ways to approach them, one being to create the foundation grid and build that up with a few layers of sub grids. This is mostly useful for when the grids might be used in multiple ways to create a pattern of maybe semi-regular tiling rather than just regular tiling. Well that’s the impression I got anyway. But the construction diagrams in this book cut a lot of the process out and show you how to get  to the final main pattern in the quickest way possible.

Unfortunately, I won’t have much time before the end of the project to try out more of these patterns.

Back to El-Said – here’s a link to web site ( in which you can read up about his history and achievements as well as find examples of his art work. Here’s one of my favourites (note the combination of Arabic calligraphy and geometry):

Allah, Mohammed (Hexagon) detail Limited edition etching 30x30cm by Issam El-Said

Allah, Mohammed (Hexagon) detail Limited edition etching 30x30cm by Issam El-Said. Image from:

Change of topic now. I’d like to mention the plug my work got on the Eastern Soul blog: It’s nice to have your work appreciated 🙂

The Eastern Soul blog has been created in order to showcase artists and individuals involved in the creative arts who have added a bit of their own Eastern touch. There should be some interesting features on the blog in the coming months…

And finally on to my project developments. These aren’t going as fast as I’l like them to be. I’ve finished the pattern I was working on recently – it looks quite nice on paper and I’m about to move onto making a mirror card prototype of a sculpture using it (God willing). Here’s an image illustrating the stages of creating it:

various stages of creating 12 point star pattern using Daud Sutton's Islamic Design.

Various stages of creating a 12 point star pattern using an example from Daud Sutton's 'Islamic Design'.

I’m now trying to digitise this pattern but have faced a few errors and need to think of an alternative approach to my current one. However, I’ve been mucking about with what I have so far and for those of you who like a bit of colour:

Pat7_Splash courtesy of Sara Choudhrey :)


And finally, we have the date for our symposium (in which all students have to do a 5 min presentation of their project) which is to be on May 5th.

The areas we have been told to cover include:

– Project overview
– Key developments during your time on the course
– Key contextual discoveries
– Post MA developments

I feel comfortable with the topics in general although the 3rd one might be a bit lengthy. We’ll need to include imagery and can either present in person or through a video/podcast. Unfortunately, I will be away the week it is due so will have less time to prepare it the way I would like to. I may have to stick to a good old powerpoint presentation – eww. Maybe I’ll try something in Flash. We’ll see.


March 5, 2010

I’ve been experimenting using some good old reflective card to create 3D shapes that could mirror well as collective components to a larger shape.

I started off with just the outer shell and got a bit carried away with this initial shape and how it worked with my reflective pattern sheet:

This is a head-on view looking into the pyramid shell, the inside is reflective the outside just white

This is the pyramid before adding the back panel. The pattern is mirrored in interesting ways. The top bit looks like a scary eye!

Pyramid - top, angled view. Placement of the top of the triangle means the pattern is better tessellated and therefore works better in creating an infinite pattern within the pyramid

Invisible pyramid - reflective panel added to outer wall

This one is my favourite because with the addition of the outer reflectivity an illusion is created whereby only the edges of the 3D shape is visible. The rest of the shape looks like it’s semi-transparent and showing the underlying pattern when it is actually a reflection of the pattern around all sides including the inside. I really like this aspect and would love to play around with it some more if I get the time.

Moving on, I started making smaller pyramids to fit inside the large shell to try and recreate a tesselated look without a 2D pattern.  Here’s how I constructed it:

Construction process for reflective pyramids structure

And here’s a better view of the final structure – a sort of open-ended pyramid filled with smaller pyramids which were also open-ended:


It’s nothing major and only a small tester model but on a large-scale I think it could look really good. I noticed that with there being gaps between some of the edges it wasn’t such a bad thing as it allowed light to come in through the back and illuminate the inner space and so allowing the reflections,  symmetry and geometry to show more clearly. It’s especially nice to look closely as if being enclosed by the reflected walls and getting an impression you could be encompassed by this structure. If it was life-size, sitting inside would be quite entrancing I think.

In a way it would be really good to be able to create many different pieces that reflect the developments in my research but that would be like setting up a massive exhibition of my own! (Maybe one day)

We still don’t know for sure how much space we get for our individual work in the end of year MA show. I’m hoping to get a proto-type completed soon so that I can not only know for myself what scale would work best but also use the proto-type to indicate scale and usability to others.

Material matter

December 15, 2009

Here is some very interesting, beautiful and inspiring work from various artists around the world. You’ll notice their work is very hands on and they utilise materials which require skills of labour not just thought and planning.

Firstly, this link was sent to me by Isaac (fellow student from MA:  The following images are just a few of the pieces created by Cal Lane who I believe is still based out in Putnam Valley, New York, United States.

Shovels by Cal Lane

Patterns plasma-cut into steel shovels by Cal Lane. Image taken from

Wheelbarrow by Cal Lane

Plasma-cut steel wheelbarrow (2007) by Cal Lane. Image taken from

Cal Lane

Large piece by Cal Lane. Image taken from

Although Cal has chosen industrial purpose objects, they were redundant till she took them on for her work. So oil cans and large barrels now become her medium for art. In high contrast to the very masculine and rough materials and surfaces she works with, Cal applies very feminine and elaborate patterns, cutting them out to look as if she has just embroidered lace.

The dark colours and rusty look and effect of these materials creates another aspect to her work which reminds me of henna/mehndi. This is a natural dye which when applied and left to dry leaves a dark orange stain to the skin. This is usually applied with ornate patterns to the hands and feet on special occasions in the Indian-subcontinent and Arab nations:

Traditional Indian style Henna/mehndi applied to a hand. Image taken from

To read more about Cal Lane and how she makes these amazing pieces please visit her web site where you’ll find loads more exhibition work, background info and reviews:


Colourful blasts of geometric sculptures by Jen Stark, another discovery but this time from browsing through google images. The below are just a few sample of her vast work which also includes a couple of animations and drawings.

Spectral Zenith by Jen Stark. Image taken from

I’m not sure I need to spend much time explaining why I like them so much. But I must mention that they are made using paper. Yes, I know, they are cool simply based on the fact that they are hand and crafted to create and produce extraordinary shapes and designs.

The use of colour is great and something I feel I cannot dwell on too much for my own work just yet. But perhaps for a future project I will be gladly looking to her work for inspiration on colour coordination.

Radial Reverie by Jen Stark

Transfixed by Jen Stark

Eureka by Jen Stark

Eureka by Jen Stark - a monochromatic piece

I cannot recommend enough that you should have a look through Jen’s site at ALL her work not just some of it. You will be amazed:


And finally – I accidently came across Sahand Hesamiyan‘s work whilst browsing through some Iran based art sites.

My favourite pieces of Sahand’s are the ones I’ve chosen to display below. This is because they have been created with an underlying structure of geometric shapes that when contemplated further can be identified as those that appear in traditional Islamic patterns.

Untitled, composite and brass (2007) by Sahand Hesamiyan. Image taken from

Shams Ι (Sun Ι), Black Oxidised steel (2007) by Sahand Hesamiyan. Image taken from

Eastern Sun, composite and Aluminium (2007) by Sahand Hesamiyan. Image taken from

I got in touch with Sahand and he has very kindly replied to my enquiries about his work methodology. I sent him a few interview type questions and he directed me to this statement which he did as part of the Magic of Persia – Contemporary Art Prize 2009 of which he was a finalist:

He mentions some great points about why he has chosen to focus on a sculptural presentation of these shapes which are familiar and close to the people of Iran where he is from. Here is a point he makes which I think is very significant:

The aim is to understand geometry as sculpture, which in traditional arts have always been trapped on the surface and didn’t have the possibility of presentation in the shape of independent sculpture.

I feel as if I can really relate to his aims as we both make use of shapes and forms which are closely connected to traditional Islamic patterns and yet we present them in work which is unusual for the Islamic Art scene.  I hope I do achieve my goals as well as or close to how Sahand Hesamiyan has. I find his work very inspiring and it’s great to see that he has considered the historical relevance of his work from a cultural perspective.

Have a look through more of Sahand’s work on his web site where you’ll find a range of installation and sculptural pieces and some interesting photos of how he constructs his larger pieces:

The very Grand Mosque in Muscat, Oman

March 8, 2009

I’ve been back a week now and I thought I would have been blogging straight away but alas I’ve been completely run off my feet. Admittedly the first couple of days after I came back from holiday I felt like I should give myself time to adjust from being all relaxed and lazy into being in a super productive mode. Who was I kidding – it was just a waste of my own time and now I am paying for it.

But going to Muscat was great for inspiration. The Grand Mosque was especially beautiful and abundant in colourful and varying examples of geometric patterns. The architecture had all the usual features of a major mosque: minarets, arches, courtyards and an ornate prayer hall. It was spacious and clean and even minimalist in a way (except for the prayer hall which appeared to be a grand showpiece of the local craftsmanship), for the majority being large blocks and shapes of white stone and marble. Whilst walking around I found alcoves and crevices where patterns decorated the space with colourful tiles or simple engravings and cut-outs. As we were there in the morning and the sun was shining in all its glory, the effect of the light, forming shadows, reflections and generally brightening the whole place up, seemed almost like a dream. I am so glad we faced the 30+ degree temperature to venture over that day.

For those visitors who were unfamiliar with this style of decor and the history and relevance of it, there were plaques with brief explanations of why the chosen styles were used (please see gallery).

I have to say I do enjoy photography even though I’m not that familiar with all the settings that can produce better images. With my own photos I think composition works best and I like to convey the different views of a building – how it looks completely different when looking from even a step away from the previous view.

Anyway, these patterns made me realise that I want my work to be focused on a contemporary take on the everlasting traditional geometric patterns used in the Islamic world. So I just need to produce my own ones through a different medium. Not too hard right? Actually, it’s very hard just trying to decide which medium to use. But for now, with less time on my hands than I had anticipated I’m going to concentrate on making some pretty patterns of my own. Which means I need to go back to practising the traditional method I failed to complete last month.

Hidden Geometry

January 28, 2009

I attended my second class of Arabic Calligraphy using Naskh Script yesterday. I signed up for these evening classes many months ago and have been looking forward to this opportunity for well over a year. The class is run by Mustafa Jafar, author of Arabic Calligraphy: Naskh style for beginners (Paperback):

Image taken from

Mustafa is himself an artist and examples of his work can be seen at

'Light upon Light' by Mustafa Jafar

'Light upon Light' by Mustafa Jafar

Anyway so in yesterday’s class we learnt to draw the first half of the Arabic letters using a traditional reed pen (looks a bit like bamboo but cut to a sharp nib on one end) and ink.

This interest in Arabic calligraphy was a personal one as well as a relevant one in terms of my project.

I will post a more detailed entry when I have gathered more informative details about the history and development of Arabic calligraphy. However in brief  I have these notes:

From its simple and primitive early examples of the 5th and 6th century A.D., the Arabic alphabet developed rapidly after the rise of Islam in the 7th century into a beautiful form of art.

– Arabic as a written language was used by few.

– Those who did use it were professional scribes and usually worked to produce important documents for legal and state offices.

– When the Qur’an was revealed and after the death of the Prophet Muhammad (may the peace and blessings of God be upon him ) to whom it was revealed, it became necessary to record the revelations. These were written and illuminated (decorated with intricate borders etc) to emphasise the beauty of the word of God.

– It is also important to note that the Qur’an never was and never is illustrated with imagery portraying humans or animals. This is because there are strict rules about the idea of recreating/reproducing the creation of God who is the only One who can create such things. It is also in order to prevent idolatry – which people can easily fall into if they are not careful. The biggest sin in Islam is Shirk which is to obey/worship/sacrifice for anyone or instead of God.

– Arabic as a written form became  standardised some time after the early centuries of Islam’s expansion and dominance.  One form was used for secular writings (the cursive script) and the other for sacred documents such as the Qur’an.

– The style of calligraphy used for the Qur’an also developed but always to a very high standard. It was imperative that the person copying the words got them 100% right and therefore they would train for many yrs under the masters of the pen before starting their own copies. There was no room for error. The Qur’an has remained unchanged since the day it was first recorded.

The significance of calligraphy? As it is used in so many forms of Islamic art and decoration and truly does look beautiful. It plays a large part in my project research. It is significant not only because of the words within the writing (usually excerpts or verses from the Qur’an) but also because of the visual effect they produce. So even if you didn’t know the words or know that it was a verse to be read and understood you could still appreciate the aesthetics of the calligraphy.

The words themselves being the words from God mean that not only do they carry an important message for mankind but they deserve to be elevated.


In the class today with Mustafa Jafar, we learnt about the proportions of the letters. These proportions govern the size of the letters in accordance to each other and although not apparent to the viewer they produce the accuracy that leads to the perfection of the overall piece of writing. Whilst demonstrating the use of the dots within the alphabet as measurements for the letters, Mustafa used the phrase ‘hidden geometry’. A light bulb turned on in my head. I already knew about the proportions and accuracy required to make the calligraphy what it is, but I never connected it with geometry before. I wonder why? I guess I wasn’t thinking outside the box. It’s not just about lines and shapes the way I know them.

You will see in the image below that the height, width and empty space produced within and around the letters are all in proportion according to the dots. So no matter what size dots you start with you should have a certain number of dots making up the length and a certain number making up the breadth for each one:

This image is taken from: where you can also find much better explanations about the history and development of Arabic in its written form.

Therefore the use of geometry comes about using this dot as a unit for measurement and it producing a proportionally accurate letter, leading to a proportionally accurate piece of writing.

Mustafa insists that Calligraphy is a form of art, not writing. I very much agree, except where it comes to the Qur’an. In the Qur’an it is both and more.

Eye of the Tiger

January 11, 2009

I hope my titles are not misleading people to view my posts for the wrong reasons lol – I just like to make them a little interesting.

Ok so Mission started and partly accomplished. I said I wouldn’t post anything until I had created some patterns and well I can’t say I finished a whole pattern but I spent at least a couple hours just doing the base work for one.

I’m quite surprised that it took as long as it did actually – just to create the grid. I took photos using my mobile (my proper camera is somewhere in a box, somewhere in my dishevelled house) so they’re not that great but the aim was to document the process.

The bare necessities

The bare necessities

Ok so I was using large (A3) squared paper so that I would be able to keep my straight lines accurate.
I used 5cm as my radius and started drawing circles from the centre of the page outwards. This method has been demonstrated in Islamic Design: A Genius for Geometry by Daud Sutton, and is supposed to be the traditional approach to creating Islamic geometric patterns. If you’ve read my Project justification then you’ll know why this is important to me. As it isn’t my usual method I thought I’d give it a go and see where it takes me.

Ok so the circles start overlapping as seen below:

circles overlapping but spreading too

circles overlapping but spreading too

I then carried on until I had filled the whole page with the circles:


As you can see this has created a tessellated effect simply with the construction of circles. After this I wasn’t quite sure what I needed to do next. I misplaced my book 😦 and so I played it by ear – well tried to remember what I had read in the book anyway. As I’ve said before I havn’t got access to my stuff.

So then I started connecting the mid points of each circle – creating horizontal, vertical and diagonal lines – a sub grid.

This produced another set of shapes on the sub grid of lines not just the circles. I’m not sure that the vertical lines were correct but it looked ok so I carried on:

Adding lines

Adding lines

I looked closely at the page (which was a bit mesmerising) and picked out shapes that I liked the look of. I usually do this in the creation of my pattern work. Breaking down shapes using lines and particular measurements and then seeing what new shapes are created. In the close up below you can see some of these smaller shapes within shapes which were created simply by the addition of the straight lines. I would now need to consider which shapes I would choose to highlight and use in the pattern and which ones would perhaps form a subtle background to the main pattern.

The shapes!

The shapes

Ok so I think this process was useful. The main thing that I found difficult was the accuracy! Even though I made sure the compass stayed at the same radius throughout, and that the connecting lines and dots and movement from one circle to another was the right place, there were still wider spaces between shapes than there should have been. The most annoying thing I found was the compass kept slipping!!! this was highly irritating and meant I had to rub out bits here and there.

But it’s been a learning process and I need to do this a lot more so I know how to neaten up my grids and start doing different kinds of patterns. I am really looking forward to the next stages of these experiments.

Now I really need to find that book!!

Zero to Infinity – connections are made

November 24, 2008

I was invited, by a friend, to attend the Zero to Infinity event at the Dana Centre South Kensington (Thursday 20th November 2008).

A quick look at the panellists and the topic for discussion sparked some interest with me. These panellists included:

Paul Prudence, generative artist
Eleanor Robson, historian of mathematics, University of Cambridge
Marcus du Sautoy, mathematician, University of Oxford
Jane Wess, curator, Science Museum
Facilitator: Rachel Thomas, Editor, Plus magazine


From this list of names only one stood out to me and that was Marcus du Sautoy. I had recently viewed his documentary “The Story of MathsThe Language of the Universe” on the BBC (thanks for telling me about it Simon) and thought he was great at explaining math related theories in a friendly and an easy to understand way.

The four very different backgrounds of the panellists was great as it provided different views on the same subject. It was clear that different uses of the mathematical theories relating to infinite numbers, the idea of multiple infinities and whether the number zero is something real or abstract can allow for connections in different areas of practice and study.

Midway through the talk we were split into two groups to participate in a short workshop first off with Marcus du Sautoy. This was a brilliant and practical demonstration to help us understand how one infinity could be larger than another. Ok there were many things floating about such as how fractions and decimal numbers could be used to check against whole number and negative numbers and this was delving into scary territory for me – maths not being my forte. So these further explorations into different types of numbers, rational and irrational, and the stark statement from Du Sautoy that there are different types of mathematics just completely lost me. At one point I had to just accept that there are many possibilities out there in the universe numbers and mathematics are perceived and manipulated to prove various theories using various methods.

Even then, Du Sautoy’s enthusiasm made the workshop enjoyable. Even though there were, well lets say, some brains participating too who were determined to prove something by asking questions that could only really lead to a debate that the rest of us wouldn’t be able to keep up with, it was quite funny to see that not everyone had the same views. And I’m pretty sure one man was actually flirting with him and using his mathematical knowledge to impress him!

Anyway so the next workshop was more of a historical look at how the number zero came into existence and its early use by the ancient Babylonians who kept records of how many different types of cattle were collected and received for the king. This part of the workshop was overseen by Eleanor Robson of Cambridge University. She explained that the Babylonians used to make marks representing different numbers on chunks of clay. This allowed for the accounts to be preserved for thousands of years. An empty space basically represented a zero. Of course their idea of the number zero was used merely for counting that something was not there but not in the same way it is now used for example for negative numbers and calculations of the abstract kind.

Twelve German Jetons - The Science Museum

We also looked at some of the shapes included in a mid 17th century wooden learning box – based on the teachings and principles of Euclid’s geometry. These were original items from the Science Museum’s collection and explained to us by curator Jane Wess. The collection included abacuses from China, Japan and the West where the base numbers for counting were all different.

Euclid's geometry - wooden box of shapes from 17th century Abacuses

Having reached the last part of the evening we heard from Paul Prudence; a generative artist and Video Jockey (VJ) whose work was displayed on the screen in the room. The display was of moving tesselated digital imagery. These images were based on geometric forms relating to the theories we had been hearing about earlier in the evening and in the workshops.

View a video of his work here:>/a>

Fast Fourier Radials - A spectrographic visualisation of sound
Fast Fourier Radials

I was in awe. He had succeeded in creating digital work based on geometric shapes and from this were produced beautiful patterns. So obviously all of this started ringing bells in my head. I was thinking to myself ‘I need to ask this guy some questions and find out what processes he is involved in, what software, which techiniques, etc etc’. I was very curious. So I waited till most people had started dispersing after the talk and told him about the MA and why his work was of particular interest to me in relation to my project. He gave me some of his business cards and encouraged me to take as many as I wanted, as he had so many and each had a different image on the back (stills from his work). They were really cool so I took six 🙂

Talysis 2
Talysis 2

I found a lot more information about Prudence’s work and recent project history on his website:

And I don’t think I could be any more amazed and slightly jealous. He uses Flash and ActionScript to write programs which then produce the patterns and some of them in real time!!! The use of algorithms and mathematics (written into the ActionScript) means that numbers can be used to produce 3d effects of shapes within certain spaces. These have boundaries in which the pattern might become curved along the outer curve of a sphere or within the inner curve and so producing both a convex and concave look with the shapes getting smaller or larger as they move along, further toward or away from the x axis. Ok I’m not sure if I explained this the right way.

Heres what he’s got in the biography section of his site which pretty much sums up his skills quite impressively:

Artist and real-time visual performer working with computational and visual feedback systems and video. Uses VVVV, Flash & processed Digital Video. Lecturer on visual music and syneasthetic art.

Researcher and writer at Dataisnature.

Freelance Interaction Designer and ActionScript Developer. Authoring chapters in a few books relating to computational design with Actionscript.

I’m glad to see a clear example of how a contemporary approach using the latest in technology and programming skills can be made the most of in order to produce something that connects all the ideas that are bought to light in the subject of geometry, shapes, and space (more specifically numbers and their connection to the theories of science and physics of the universe). I mentioned in an earlier post that it was hard to make the connections between the different subject areas as they could become very diverse and branch off into their own projects all together. But this is a great example to show that it is possible to make those connections apparent in one piece.

I feel inspired and have a positive feeling about achieving something great, as a result of this project. God willing 🙂