Posted tagged ‘Geometry’

Bathsheba Grossman

October 16, 2008

I’ve just found a great site and some great artwork. It encompasses a large idea I had of producing some of my own designs in some kind of 3d form, as well as the theories on which my research is based. It also relates back to the image in one of my earlier posts where I mentioned the ideas of Donald (H.S.M) Coxeter and showed how a hypercube could be evolved to a higher dimension of shape.

600 Cell by Bathsheba Grossman

600 cell – http://www.bathsheba.com/math/600cell/

Snub 24 cell by Bathsheba Grossman

Snub 24 Cell – http://www.bathsheba.com/math/snub24cell/

Grossman also mentions the subject areas that I am interested in exploring in my research and which will link to geometry.

Grossman says:

I’m an artist exploring the region between art and mathematics, and this is my gallery and storefront. My work is about life in three dimensions: working with symmetry and balance, getting from a zero point to infinity, and always finding beauty in geometry.

That’s to say, I like to think about shapes, and occasionally I think up a new one, and usually they come out very symmetrical.

http://www.bathsheba.com/artist/

I highly recommend visiting the site http://www.bathsheba.com/. Grossman explains that her motivations for creating the metal based sculptures are far from commercial and she simply prices her work in order to make it available to anyone and not just those with large amounts of money. She also explains her working process, conveys her working space through images and descriptions and allows visitors to her site use of her 3d-print images for furthering their own practice in creating similar work.

Grossman tells us of her efforts to find a suitable solution for creating her work and does so in a very open manner. The site is written and maintained in her own words and not through a third party. All these elements combine to give a very friendly perception of her personality and her work and just a strangely comforting good vibe about her intentions.

Regardless of all this, I think the work is remarkable. The 3d forms allow for different angles and views of the pieces, each time making them look a little different, and also for the effect of light and dimness to show the deeper cutouts and interlacing of sections. This adds to the look and feel of the sculptures and the complexity makes them look like inverted mazes that you’d want to shrink yourselves into in order to explore.

Hmm perhaps a maze is something I can work with? Will develop this idea later me thinks.

Word into Art – Dubai 2008 (pt 2)

October 16, 2008

Continuing from the previous post, I have a few more artists I’d like to comment on. Here is ‘Allah’ by Samir Al Sayegh:

Allah by Samir Al Sayegh

This work actually reminds me of a kameez (traditional Pakistani shirt) I used to have. The print was almost identical and in black and white (which are the colours I have favoured in my own work in the past – see link to Examples of my work on the right).

So what I like about this is the fact that you can’t tell straight off that it is produced with the word ‘Allah’ which means God in Arabic, repeated all over but rotated in places to create a pattern. The word is written in a stylised Arabic text, making it look blocky and geometric.

Artist and poet Samir al-Sayegh has been exploring the possibilities of Arabic calligraphy for many years. In this black-and-white composition he has turned the word ‘Allah’ into geometric shapes.

http://virtualgallery.birzeit.edu/p/ps?url=exhibition/BMsacred/tour012

Word into Art – Dubai 2008 (pt 1)

October 13, 2008

I was reminded of an exhibition I went to whilst in Dubai earlier this year. It was the Word into Art exhibition that had been on in the British Museum back in 2006. I was very glad to have been able to catch the one in Dubai and I was not disappointed when I got there.

I’ve shown some of the images below of the artworks that I found of interest and to my liking.

Kamal Boullata

Ana Al-Haqq - I am the Truth by Kamal Boullata

http://virtualgallery.birzeit.edu/media/photos/vw_115629/Kamal+Boulata+3?w=225

Nur ala nur by Kamal Boullata

http://virtualgallery.birzeit.edu/p/ps?url=exhibition/BMsacred/tour011

Read more on this piece here

I like the way the symmetrical layout and break down of larger square, with rotated smaller squares, has been combined with the kufic arabic calligraphy. The subject matter is the meaning of Nur – light in arabic. It is very symbolic and has many connotations in spirituality and religion – not just Islam but Christianity too.

A bit about the artist:

“Kamal Boullata :- PALESTINE
Born in Jerusalem in 1942. Works and lives in Washington, Morroco and Paris.
Boullata recalls sitting for hours on end as a small boy in front of the Dome of the Rock, engrossed in sketching its innumerable and unfathomable geometric patterns and calligraphic engravings. Those patterns he saw as a child still echo endlessly throughout his adult work. I keep reminding my self that Jerusalem is not behind me, it is constantly ahead of me. From an interview with the Artist”

http://www.daratalfunun.org/main/resourc/exhibit/bollata/bollata.html

Ahmed Moustafa

Moustafa uses traditional calligraphy to form the artwork and uses the old and classical decorative technique of repeating more text over the first layer but mirrored upside down. Therefore you are required to turn the work upside down in order to read the next line.

Where two oceans meet by Ahmed Moustafa

http://www.fenoon.com/portfolio/pages/0001p1.html

Sometimes the text is a mirrored version but flipped horizontally to add an almost mish mash type effect. The technique is used slightly differently below and looks particularly effective in this piece which produces a great symetrical design using the arabic names of Allah (God) – which represent his attributes as named in the holy Qur’an:

The attributes of divine perfection by Ahmed Moustafa

For more info on this piece click here: http://virtualgallery.birzeit.edu/p/ps?url=exhibition/BMsacred/tour008

Identifying a line of inquiry – which one?

October 11, 2008

On my way to uni on Wednesday I decided that maybe it would be a good idea to formulate my ideas and project aims and objectives as best I could. I started writing notes most of the journey and, as it had been about a week since I had fully concentrated on summing up my project in such a way, I think it helped to make it more structured in my head. I was able to sum up the links a bit better than before. This is what I came up with in relation to the two key words ‘Shapes’ and ‘Space’ being components of a possible working title:

The first two words are key as they sum up the elements that the areas of research I will be looking at are anchored by. In other words you can always relate the subject areas, I am interested in, back to one of these words if not both.

We usually think of shapes as pre-defined areas of outlined space that have specific names. We’ll grow up knowing that these named shapes have properties that allow the shapes to be classed within certain gropus of shapes too. So a square is made of of 4 right angles at each corner and 4 sides. A triangle with three sides and of various angles and combinations of these.

But can a shape alway be defined? And should it be defined? And how about those shapes which have properties or characteristics that are overlooked? And which characteristics should we look more closely at because they’ve been overlooked in the past?

The second key word is space. My use of the word implies many senses of space including the mathematical and the scientific (these I believe overlap in some sense), as well as the physical, perceptual and conceptual. I cannot restrict my meaning at this point. I have no reason to restrict until I have conducted more research and found a reason to do so.

What about white space? Is it real? Does it mean something to everyone? What is it’s role? Is it intentional? Should it be identified in more places?

An area of study that connects to this idea of space around shapes (and here I wonder – is this space not then a shape too?) is that of Geometry. These shapes are formed from vertices (easier to think of as dots in an invisible grid of any size). These vertices may then be connected with a line from one to another. these lines will be joint in such a way to form a shape. Various shapes are then placed together to form a larger formation. They could arguably be described as a system of shapes. This system could be called a pattern. these patterns can then become quite complex and due to their placement, repetition and possibly the ability to tesselate them – they can be endless and seem to go on for infinity.

One of my biggest aims in my project is to look into the history of Geometry – how it was developed and how it has been used over the centuries (more specifically in art work).

Then there is the branching off of Geometry in nature. I think this is a highly important and interesting subject to delve into. Not only because it entails many mysteries and brings into question the secrets of the Universe. But also because there is a tie with religion and sprirituality which is something that I can relate to on a personal level. Believing in God means that when I see the beauty of nature and proofs of perfection in nature (such as the way the body works and the structures and symmetry in plants and flowers to name a couple) I link it to Divine Creation. This is another aspect I would like to look into further. Especially as belief in this isn’t restricted to just one religion.

Geometry allows for the representation of space in 2d, 3d and even 4d and beyond:

Science.ca - Donald (H. S. M.) Coxeter, Pure and Applied Mathematics

4. Hypercube: If you pull a cube into the fourth dimension you get a hypercube. Eight cubes make a hypercube. The figure you see here cannot exist in the real world, which only has three-dimensional space. It is a projection of a four-dimensional object onto two dimensions, just as the cube before it is a projection from three-dimensional space to the two-dimensional flat surface of the paper.

5. Regular polytope: If you keep pulling the hypercube into higher and higher dimensions you get a polytope. Coxeter is famous for his work on regular polytopes. When they involve coordinates made of complex numbers they are called complex polytopes.

http://www.science.ca/scientists/scientistprofile.php?pID=5&pg=1

These main topics then branch off into other areas but are still anchored by the main theme of shapes, space and I guess now geometry too. By always having my main question along the lines of ‘ the place of geometry in the world around us’ I will have something to refer back to. Is that what I am looking at? Am I any closer to finding the answer? Am I looking into something that is relevant or have a veered off too far down a small cobbled street?

Outcomes for project: My background has been predominantly in expressing some form of communication and his has been mostly interactive. I would like to continue this by producing work that compels the user/viewer to become involved with it. I believe that the most interactively creative works are those that captivate the viewer and involve them within a process. This can be in many forms such as when using sensors to trigger some kind of behaviour or change in the work (lighting, sounds etc). This could be on an abstract level too where triggering thoughts and movements in people and influencing these is enough of a form of interaction. Only that this can be more difficult to measure.

However, my interpretation of an interactive work would be using multimedia as a possible option. My work has always been either viewable of a computer screen (short video clips), graphics, websites. Or viewable on some form of small physical and traditional media such as paper or canvas. I would really like to create some sort of installation to take my experience and work to the next level or beyond for this project. This installation would be my blank slate. Possibly like a box or container that allows a person to fully submerge themselves within it – literally or mentally. The key is for it to be thought provoking. I would want the person to question their surroundings, the purpose of the installation and investigate it too. Possibly manipulate their thoughts by pre-determining the factors the could influence their senses and perceptions related to the space around them.

And that is the end of my notes from my journey to Uni. Yes I am one of those people who can write loads of notes whilst travelling on the tube/bus/camel 🙂

We had a sort of informal feedback session after one of the Critical Framework lecture where we were required to write in one sentence what our project was about. I knew it would be a bit crazy to even attempt this so I decided to use the key words to form almost a sentence. I came up with ‘Shapes and space – the place of these and geometry in the world around us’ using my notes from the journey in. It could be the closest I’ve got to a working title yet so I just let that be discussed in the group.

After some discussion with Andy (course leader) and some feedback and questions from fellow students it would seem that perhaps I should narrow my field of research down a tad bit so that I can concentrate on finding the niche in which my project would excel. Something no one else is questioning, expressing or even addressing. Or maybe they will have but I’ll be doing it from a different angle? a unique p.o.v?

Only time will tell.

Mirror mosaics

October 10, 2008

I was just doing a quick search to see what kind of artwork is produced by artists in the style or influences of Islamic art. One artist’s work I’ve just seen is Monir Farmanfarmaian

Hexagon - Monir Farmanfarmaian

If you look closely you’ll notice that there are small pieces of mirror that have been placed together to form cubes, which combined with the reflective properties of the materials used give the overall piece a unique effect emphasising the 3d aspect of the shapes formed. I’m quite taken by Farmanfarmaian’s other peices too. These can be viewed from this page: universes-in-universe.org – Monir Farmanfarmaian

Here’s another one I really like:

Cubes within cubes by Monir Farmanfarmaian

The tessellation of small mirror pieces works wonders in this peice. At some point I’d like to see how mirrors could be used to effect lighting, and how this in turn could effect someone’s perception of a space. Hmmm…a million ideas forming again and I can’t get them all down -one second they are there the next they are replaced by another!!! Oh well if they’re of any use then they’ll come back. Hopefully.

It’s not easy making a connection

October 6, 2008

I’ve been trying to anchor my thoughts – they really are flying everywhere. Ok so I said i was going to look into the different types of geometry but then I became sidetracked by one kind – Islamic geometry and it’s possible symbolism. I think there are some very important relationships that can be drawn from the accuracy and detail and near perfection of the patterns that are created in Islamic and even non islamic but similar geometry.

One such relationship is that of the divine creation and the indications of this that are found in nature. It can be argued that the artists of the early Islamic art movement were trying to portray the perfection of God’s creation through the use of geometry and without the use of imagery showing any living beings (reasons for doing this will be discussed in future – or you can nudge me to tell you sooner – any feedback or questions are appreciated). This is a plausible point as symmetry and geometry can be found in nature all around us including our very own bodies.

This then closely relates to the idea of the Golden mean. The ancient Greeks placed much importance on this and here is a quick explanation from wikipedia:

In philosophy, especially that of Aristotle, the golden mean is the desirable middle between two extremes, one of excess and the other of deficiency.

To the Greek mentality, it was an attribute of beauty. Both ancients and moderns realized that “there is a close association in mathematics between beauty and truth.”

The Greeks believed there to be three concomitants of beauty: symmetry, proportion, and harmony. This triad of principles infused their life. They were very much attuned to beauty as an object of love and something that was to be imitated and reproduced in their lives, architecture, Paideia and politics. They judged life by this mentality.”

Ok so now I’ve lost track of where I was going with this. I want to quickly mention the Golden ratio also known as Phi. As seen in the image below:

The golden ratio (phi) represented as a line divided into two segments a and b, such that the entire line is to the longer a segment as the a segment is to the shorter b segment.

http://en.wikipedia.org/wiki/Golden_ratio

Ok so back to the point – I am going to concentrate on drawing a connection between the ideas presented in the theory of geometry and symmerty in nature, golden mean and ratio, the divine creation and symbolism that can be found in artistic interpretations of these ideas/theories. Am I taking on too much? well considering that I keep coming up with new topics to look into means that at least my thoughts are developing. Lets just hope they are sinking in and remain relevant to my project.

Geometry

September 25, 2008

Ok I know I said I would look into colour inversion some more but I just had too many thoughts, ideas and avenues that I also wanted to look into. They all relate to the use of shapes, space and composition in one way or another. The one at the forefront of all this is geometry and then closely behind this follows symmetry.

So…I think I will make categories of all the subjects/areas and then add to each whenever I come across something of relevance for each.

Now back to geometry. A quick definition from wikipedia:

Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the third century B.C., geometry was put into an axiomatic form by Euclid, whose treatment – Euclidean geometry – set a standard for many centuries to follow. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere, served as an important source of geometric problems during the next one and a half millennia.

http://en.wikipedia.org/wiki/Geometry

Ok so we can see there are actually different types of geometry too – but we’ll have to come back to this later. Now for a definition from Dictionary.com:

–noun, plural ‑tries.

  1. the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties of space.
  2. any specific system of this that operates in accordance with a specific set of assumptions: Euclidean geometry.
  3. the study of this branch of mathematics.
  4. a book on this study, esp. a textbook.
  5. the shape or form of a surface or solid.
  6. a design or arrangement of objects in simple rectilinear or curvilinear form.

http://dictionary.reference.com/browse/geometry

It seems to me there’s more involved in geometry than I originally thought. It’s not just about fitting shapes together to make them look pretty – Ok I knew there was some maths involved too, calculating angles – making sure that the outcome could be continued for eternity using tiling and rotated symmetry. So my next step is to look into this further. Find out where this study of lines, shapes, depths and space came from and why it links to astronomy and even spirituality! Looks like I’ve given myself even more homework to do!