**—READ THIS FIRST—**
For some reason Tumblr seems to remove some of the quality of my image and also make it smaller, even when you click through to view it itself and zoom to 100%. I have uploaded it here instead: http://img42.imageshack.us/img42/2137/finalrender2.jpg
This is my final 3ds Max render with all 3 Solidworks iterations. I wanted to keep it simple just as i had with my iterations (which i think on average had about 150 triangles). I kept it black and white, to emphasise the importance of each model. Rather than have them get lost amongst other renders, materials and images. I also wanted to keep everything in a grid. Grids are important in mathematics, so it made sense to use something like that to arrange my iterations. Each are arranged similar, with a slight rotation on each axis.
What i like about this render the most though, is that it looks so similar to my 81 iteration renders in project 1. You can see how all my renders fit together and the way that i design. Everything seems like a family which i think is pretty cool.
One of my friends said it made them feel dizzy and question gravity!

Above are some simple sketches i started drawing, playing around with different equations. These can be seen next to each box which it corresponds too. There are some equations which have been used twice because i found different ways of visualising each pattern.

I then started bringing some of those patterns into Illustrator, trying to think about how this would be represented in 3d at the same time. I had a little trouble doing this with some of these patterns, which was a shame, but i brought a few of these into Solidworks to trial.
For the start of project 3 i began to research some patterns that interested me. Immediately i starting thinking about mathematics and patterns that have a sensed mathematical feel to them.
I found some nice images (below) to help me begin my sketches.

This was the first image that i really liked. Although it isn’t really a 2d pattern, i loved how it portrayed that sensed mathematic feel and without even reading about it you could tell a mathematical equation was used to decide where to bend and fold the materials. Sure enough, after i read up about it @ http://artabase.net/discussion/chat/20-origami, it turned out to be a form of mathematical origami. I didn’t like the curves so much, just the fact that an equation was used to create a form quite unique.

I found this image next and liked how the spikes extruding from the centre object began to get smaller as they got closer to the centre. They seem to decrease and the same percent as they get a spike closer to the centre. I thought it was great how much of a contrast this object was to the object in the photo above. Both created using mathematical equations, but creating completely different shapes. One which evokes soft, sweet emotions with its curves and gentle creases, and one which evokes fear from hundreds of spikes.

I liked this image for a few reasons. One: I liked how it was in the shape of a simple cube. Two: Because it had 2 different positions. On and off. I loved how it sort of hid its beauty just standing there and then once it was turned on lit up. Which also happened to be in a mathematical way. Thinking ahead, this gave me a nice idea to have 2 positions for my 3d print, where one view shows the surface, but once its viewed from a different angle shows something completely different; the interior maybe?

i really liked the geometry in this pattern, where the pattern didnt necessarily repeat itself, but you could definitely tell that something was deciding where those lines and circles were being drawn / cut.

A shot of the fibonacci sequence found in nature. Im starting to think that mathematical forms really can appear anywhere and look completely different.

Another version of Fibonacci in nature, although this time the shape of the geometries gradually changes over time. I think this is really neat, almost draws you in. Hurts my eyes after a while though!



After i had finished brainstorming ideas and making some sketch models i made the decision to go with layering up my model using laser cut pieces of plastic. I decided to go with cutting out the model from the square and use the negative space to create my model. The pictures above are examples of this that i found.


Above are some simple sketches i did before starting to slice up my model into sections. I wanted to have a general idea of the differnet versions i would be attempting.
1. Horizontal Sections
2. Vertical Sections
3. horizontal Negative Space Sections
4. 45 Degree Sections
5. Planar Sections
This would then give me a nice variety of iterations, which would then allow me to select the best one to pursue for my final.