Cross Grave - Variations

Hi everyone!

Following my Cross Grave post, Cupcake, another folder, did a variation on the cross model that turned out very well. ^_^ He kindly allowed me to show you guys his model, which changes the dimensions of the original cross (7 x 5) to a smaller one (4 x 3). The model become smaller and easier to fold, but most importantly, it shows how a versatile folder can change a design if he plans it well enough.

Click here to see cupcake's model in his flickr account (I had the picture but somehow it doesn't show up)

Very nicely done! Judging from the picture, I thought he used a 15 x 15 grid for this model (but he told me that it was really 16 x 16 ^_^) ; a very interesting feature of this type of "pop-out" origami is that any square grid can be used. Theoretically, the paper can be extended without bound on all four sides, but the model, jutting out from the centre and thus not needing the edges and corners, will remain intact. This is what gives "pop-out" origami an unlimited (at least, in my opinion) potential for the combination of models.

Now for a little exercise: how many squares does this cross take up from the paper? Try it out if you're interested!

As to how Cupcake managed to make his cross, it probably went something like this: please refer to the pictures in my last post, and scroll down to the second picture from the top. In that step, instead of forming two 2 x 1 x 1 building blocks each two squares away from the central square, he folded two 1 x 1 x 1 building blocks each one square away from the central square.
He then proceeded on with the rest of the steps until his cross reached a certain height. Folders may want to try this model out, and more adventurous ones (with very thin paper available) may want to extend the method to make a cross with dimensions 10 x 7! (figure out how I arrived at those two magical figures yourself ^_^)

I hope this post has managed to convince you guys that it is possible to create variations of models with enough planning! Then again, if any of you guys have folded any of my models, please let me know, and I may feature it on this blog!

Thank you very much Cupcake for folding my models! ^_^



Origami as Pure as Snow
Shonen

Cross Grave

My second post in a month!! Cheers guys! Thanks for your support! =D
D.Gray-man rocks more than Bleach now ^_^


I mentioned in the last post that knowing how to superimpose or combine sub-models to form new designs is very important. The model that will be shown in this post is formed by a combination of building blocks of various dimensions and placed strategically around the model to give the planned end result.

Behold, the Cross!



Dang, somehow I just can't get the lighting right ^_^

Next, I'll be showing pictorial instructions to making this model, but you have to be familiar with how to make building blocks of varying dimensions. Here's a little tip to help you control the height of a building block: create a buidling block of height 1, then treat the paper as though it were flat and form an identical building block at exactly the same spot using the same creases. Keep repeating this step and eventually the building block will reach the desired height.

The italicized sentence is extremely important in the combination of sub-models; experienced folders in this form of "pop-out" origami can skip it, but the technique described in the sentence can help beginners to combine sub-models efficiently.

Start with a 32 x 32 grid. Choose a central square which will eventually become the square on the highest point on the cross (refer to the previous photo). As there is no central square (the grid size is even), choose one that is as central as it can be. Next, form 2 identical 2 x 1 x 1 building blocks such that they are on opposite sides of the central square and there are two squares between the central square and each of the building blocks (as to how the dimensions of the building block are to be interpreted, refer to my last post). The result so far:



Next, treat the paper as if it were flat and construct a 1 x 1 x 1 building block whose topmost surface is the central square. As we are treating the paper as if it were flat, do not be disturbed by any places which are thicker when folding.

At this stage, it should look something like this:



Treating the paper as if it were flat, form another 1 x 1 x 1 building block at the exact same spot.



You'd be wondering what these three prongs are for, but you'll see in the next step!

Do that step yet again, i.e. treating the paper as if it were flat, form another 1 x 1 x 1 building block at the exact same spot.



See now? ^_^

The disadvantage of treating the paper as if it were flat is that the paper is not flat, and the layers build up and prove to be a nuisance sometimes, as in this case, where the paper is so thick that I cannot press the layers down flat into the required shape for fear of damaging the structure.

The remaining steps are just performing the previous step again...



... and again and again until the cross reaches a height of your choice. I felt that a height of 7 was the best in this case, but the height can be varied to your wishes.



This is what the paper looked like once I finished folding. My friends from Origami Singapore had recommended "Elephanthide Paper" to me, but true to its name, it refused to submit to creases easily... In this model, the paper near the "joints" puffed up like a spring because of extra thickness there, and the extra paper at the base also piled up because of all the layers of paper accumulated there. Only one way to sort things out... wet-folding!

I restrained the puffed-up parts with rubber bands (I just had to run out of them at that critical moment) and put the cross under the tap for a few seconds, shook off the extra water and laid it on the floor to dry with heavy books (thank goodness for the World Book series) pinning down all those layers at the edges. I left the entire set-up overnight, and removed the rubber bands in the morning to get the final result.

A picture of my valiant efforts to subdue the thickness of paper:



Now for an explanation for the title of this post; Firstly, my parents thought of a tombstone the moment they saw this model (which was a little disappointing T_T), and "Cross Grave" appears in D.Gray-man!

As mark of my new anime affiliation, I will end off this post in a new way...



Origami as Pure as Snow
Shonen

(My eternal thanks to the creator of this excellent picture! ^_^)

有口福

My sincere apologies for the over-one-month gap between posts. Because of my exams, I haven't been able to fold much... Well, its the June Holidays, so I might be able to post a lot more often than usual from now on! Thank you so much for supporting this blog, even though my posts have been rather scarce! *bows* ^_^

Now, to business! Remember my last post which taught you how to fold a "Negative Building Block"? (suggestions for its name are very welcome... heheh) Well, these little sub-models are rather useless unless you can incorporate them into a new design. If you refer back to the model in "Pop-out Prosperity", you'll see that the negative building block is not used on its own in the model; instead, it is used in conjunction with the Building Block to create a "well" structure. One example of such a structure is the "口" radical in the Pop-out Prosperity model; This post will show you how to convert a negative building block into that structure.

Firstly, you have to create a negative building block.



For details on how to fold a negative buidling block, refer to my last post.

I used a 15 x 15 grid for this model instead of the 9 x 9 one used in my last post, because I needed more space to fold the "well structure" than the negative building block itself. This gives a little insight on how paper is sucked up two-dimensionally while we try to build "upwards"... I call it "The Law of Conservation of Paper" - In an isolated model, the amount of paper present is always constant. ^_^

Anyway, for the next step, treat the model at the current step as flat paper (i.e. disregard the presence of the little hole in the center of the model). This step seems to be crucial in the superimposing of certain sub-models in this form of origami. Form a 1 x 3 x 3 building block with the hole at its center.

Before we continue, I feel that we should set down a standard way of referring to the dimensions of a building block so it is easier to refer to.

A building block with dimensions x x y x z has height x, length y and breadth z.
(For problems in the direction of y and z, I will clarify in a future post.)

A view of the model in the current stage:



And you're done! My, that was fast, wasn't it? Let's take a closer look at the "well structure" in the middle:





Now, you can see that the center part of the model corresponds to the "口" radical in the Pop-out Prosperity model.

The superimposing of sub-models does give you interesting results; the important thing is to know which sub-models to use and how to merge them to form a new model.

Now for a view of the underside of the model:



Compare this to the flip-sides of the Pop-out Prosperity model and the Negative Building Block; curious folders may also want to fold a 1 x 3 x 3 building block on a separate piece of paper and compare its reverse side to the picture above.

We're done with the model, but there's one more technique to show you that will help in folding this form of origami. How do we measure how much space the model takes up? Remember that what makes this form of origami unique is that the paper around the model can be extended without bound without affecting the model (because the model itself "pops out" of the paper and does not require edges and corners) and the extended portion can be used to fit in more models so long as the models do not interfere with one another. Hence, it is important for a folder to measure the amount of space his or her model takes up so he or she knows whether another model can be fitted in, or what grid size he or she should use. The space the model takes up is measured in terms of the two-dimensional area on the paper which the model takes up, as opposed to the three-dimensional notation of a building block.

Because of the sucking up of paper inside the model, it is rather impossible to gauge the number of squares it takes up by counting from the inside. However, we can use another approach; counting from the outside! If you've folded the model already, measure the distance from any edge of the paper to one side of the model in terms of the number of squares (in this case, 4) . Do the same for the opposite side (4 again) , and add the distances together (4 + 4 = 8) . subtract that total distance from the grid size (in this case, 15, because a 15 x 15 grid was used) to get the number of squares the model takes up in that dimension (15 - 8 = 7). Repeat for the other dimension (7 again). Thus, in this case, the dimensions of the model is 7 x 7.

Theoretically, a 7 x 7 grid can be used to fold this model; yes, it can be done, all the features of the model will be inside, but the edges of the model will not be locked vertically, and the thickness of the paper will force it to open up a little, resulting in the model not looking very nice. The edges of the model depend on the flat paper surrounding it for locking, so it is best to give a bit of leeway, like a 10 x 10 grid or more ( a 9 x 9 grid would not give enough locking for stiffer paper) .

Ahhh... a long post! I hope that you have enjoyed this post, and thanks for the support!

The next post will be really cool, I'm smoothing out the details for it now, it won't be long!
I'll be cross if you don't come back for the next post! ^_^


Origami as Pure as Snow
shonen