Posted tagged ‘tessellation’

Pyramids

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:

Pyramids!

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.

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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.