25 February 2014

Origami Tulips





I have finished folding the ten beginner projects from Eric Gjerde's book, Origami Tessellations. I am yet to post 6 more though, out of which I have drafts  ready for two and for the other four I need to take photos. Taking a break from tessellation "addiction", I went on to fold this simple Origami Tulips.

I remember folding many simple Origami models in my school days like Origami ball, piano, shirt, containers, rocket, boat and so on. Among them is Origami tulip that I frequently folded tearing sheets from my school books (especially the subjects that I least liked!!). I would cut out the square from the rectangular paper and I used the remaining sheet to make stalk for the flower. 

This is a simple yet beautiful traditional Origami model.

Instructions are available on net. I had folded tulips so many times that I still remembered the steps very clearly.

For the flowers in the photo I took 4 inch square color printer paper.


24 February 2014

What is Tessellation?


I thought before continuing to post any further tessellations it's worth writing a little about Tessellations:

Tessellation is when a shape or a pattern is repeated over a plane without leaving a gap between any patterns and with no overlapping. Tessellation is also called tiling.Honeycomb is an example for tessellation in nature.

Another simple example of tessellation is floor tiles. Square tiles repeating with no gaps (Figure 1). This is an example for regular tessellation. Spread hexagons is an example of regular tessellation. There can be only three possible regular tessellations with repeating Squares, triangles and hexagons.

The other type is semi-regular tessellation or Archimedean tessellation. This type of tessellation contains two or more different regular polygons. Example, a tessellation with repeating hexagons surrounded by triangles (Figure 2).

Naming convention: A tessellation is named after the polygons it contains. If there are repeating squares, it is named as 4.4.4.4, considering a vertex, and polygons that surrounds this vertex. 4.4.4.4 is an example of regular tessellation.
A semi regular tessellation for example one which has hexagons and triangles are named as 3.6.3.6. The smaller polygon is mentioned first while naming. For example, for the below semi regular tessellation the naming cannot be 6.3.6.3.

Figure 1


Figure 2


Tessellation techniques are widely used in computer graphic designs. One example is it's application in nvidia's DirectX 11. It is used in GTX 400 series GPUs to improve performance. A much detailed and interesting article about the nvidia product and how tessellation feature is used to enhance the performance is provided in their website:

http://www.nvidia.com/object/tessellation.html


Source and reference:

http://mathforum.org/sum95/suzanne/whattess.html

Related links and further reading:

http://www.mathsisfun.com/geometry/tessellation.html
http://www.coolmath4kids.com/tesspag1.html
http://en.wikipedia.org/wiki/Tessellation
http://www.csun.edu/~lmp99402/Math_Art/Tesselations/tesselations.html




19 February 2014

Star Puff


Beginner Project No. 4


The forth project in Eric Gjerde's book - Star Puff tessellation, designed by Ralf Konrad, is based on Spread Hexagons pattern. It involves triangle twist on a completed Spread Hexagons pattern. Easy folds and didn't get messy anywhere. 

Front View of the completed Star Puff pattern:



Reference:  Origami Tessellations by Eric Gjerde


Difficulty : Intermediate


Time :  < 2 hours.

No. of Units : 1 sheet of paper


Paper size : 8.5 inch square sheet


Paper type : Color printer paper.



Back View of the tessellation:




15 February 2014

Tiled Hexagons



Beginner Project No. 3:


Tiled Hexagons is the third project, in Eric Gjerde's book, after Five and Four tessellation and Spread Hexagons. I found this relatively easy. The elementary fold or twist in this tessellation is triangle twist. This twist is easy to figure out. I had earlier done square twist while doing Kawasaki Rose. Triangle twist is simpler than that.

Below is a single triangle twist on a square sheet of paper:



I tried a single tile in this tessellation. Below is the pattern that repeats through out in this tessellation.


Back view of the single tile.


Only recommendation is to mark the Crease pattern, it might get confusing otherwise. I marked the hexagons around which the above tile is to be made. Rest is very simple. This tessellation didn't give me any problem.

Front view of the completed tessellation:


Reference:  Origami Tessellations by Eric Gjerde

Difficulty : Easy

Time : Can be finished in one hour or so.

No. of Units : 1 sheet of paper

Paper size : 8.5 inch square sheet

Paper type : Color printer paper.

No glue no scissors required for this or any other tessellations.

Back View of the tessellation:







08 February 2014

Spread Hexagons


Project No. 2 : 


Spread Hexagons tessellation designed by Eric Gjerde. This design is the first origami tessellation Eric Gjerde discovered on his own. The pattern reminds me of honey comb. Front view of this design is overlapping hexagons and back view is similar to a honey comb with repeating hexagons.

I first practiced 120 degree pleat intersection which is the basic fold throughout this tessellation. I made a single hexagon.

Front view of resulting hexagon:


Back view of the same:



I then started with 8.5 inch square sheet, made a hexagon out of this square sheet. The resulting hexagon had a side of 4.2 inch which was my starting point. One could start on a square sheet as well, without making hexagon. This step can be skipped.

First identify the center hexagon and make a 120 degree pleat intersection on all six vertices.

I took quite sometime to figure out the folds for the subsequent layers. The confusing part was to start the second layer around the central hexagon. One could mark the crease pattern given in the book. I started without it. But it's not really difficult to complete without marking crease pattern and just by following instructions given in the book.

To complete four layers, I took almost two days (may be 4 hours).

With hexagon of side 4.2 inch, I could make 4 layers (including the center hexagon which I count as first layer). For more layers, we need a bigger sheet.




The instructions in the book are very clear. I read and re-read to clearly understand.

Once I figured out the trick, it was not so difficult to complete. Thoroughly enjoyed making this tessellation. This photo is of my first attempt.

Online instructions by Eric Gjerde here:

http://www.origamitessellations.com/docs/spread-hexagon-tessellation.pdf

I used color printer paper.

Difficulty : Intermediate.

Time required : Once the folds are clear I would say this model can be easily finished within one hour for four layers.

Number of Sheets : One

Reference : Origami Tessellations by Eric Gjerde







01 February 2014

Five-And-Four Tessellation

Origami Five-And-Four tessellation by Eric Gjerde

Front View


Back View 

Reference : Origami Tessellations by Eric Gjerde

Number Of Sheets:  One

Paper Size : 8.5 inch square

Paper Type : Color printer sheet

Time required : 1.5 to 2 Hours

Difficulty : Intermediate. 

I love single sheet origami for the fact that I can start right away with one sheet of paper.

Five and four tessellation is a beginner project in Tessellations. Square of 4 units side, is tiled on square of 5 units side, hence the name. Earlier I had tried Andrea's Rose and Hydrangea. This tessellation is easiest and good for beginners.

However, I took a while to figure out 90 degree pleat intersection fold. This is the basic fold in Five-and- Four.

A very accurate folding is required. Every small fold matters a lot. 

The above photo is my second attempt. The first time,I missed the small diagonal folds. Paper got crumpled a lot while I was trying to figure out the 90 degree pleat intersection.

The instructions for 90 degree pleat intersection is available in the book. The Crease pattern is also provided for every Tessellation. 

The second time it was a lot easier and turned out more perfect.