Senbazuru from a single uncut square

Today, likely for the first time in the history of origami, I folded a Senbazuru (literally "a thousand crane") from a single uncut square. Well not in the real world of course, but in the virtual computer space, using again our Orihime algorithm. In this article, I will share with you the story behind it.

Traditionally, it is believed that whoever folded a thousand orizuru can get wishes granted. Even today there are many commercial origami packs designed precisely for that purpose. As we enter the era of super-complex origami, it is tempting to achieve the same thing, but with a single uncut paper. That in itself is not difficult in concept, but it was never actually carried out for obvious reasons.

Back in 2015, I was interested in all kinds of different variations of the traditional orizuru, including the idea of an uncut Senbazuru. I wasn't aware of the second edition of Lang's Origami Design Secrets back then, so I didn't know anything about Lang's proposed method of folding the Senbazuru. Instead, I independently developed a different pattern for the "crane on a plane" subject, which turned out to be tighter than Lang's proposed pattern. Each tile is a 10 × 10 grid, which is shown in the following figure.

The CP for one zuru.

I also made an actual 3 × 3 model based on this pattern, which is like the uncut version of the "Seigaiha" found in Hiden Senbazuru Orikata. The folding sequence is very long and tricky, and it took me four days just to fold this model back then. Because of that, I never seriously considered going any further, knowing for sure that even 100 zuru will drive me nuts, let alone 1000.

Seigaiha without cuts.

Recently, because I've greatly improved the folding capability of the Orihime algorithm implemented in Oriedita, a few people bring up the possibility of folding this thing in the computer, and I know immediately this is finally my chance to make it happen. However, the complete Senbazuru CP contains more than a million creases (in my final CP, there are 1,187,392 lines to be exact), which is a completely different level of a monster than the Ryujin CP. A quick estimate shows that with the data structure I used for the Ryujin, it will take more than 200GB of memory to fold it, which is very impractical. Even after I subsequently developed a more efficient data structure, it will still take about 100GB, and of course, that's way beyond the ram of my laptop.

Fortunately, it is possible to launch Oriedita with much greater memory settings than the physical ram, and as it goes beyond the physical ram, it automatically switches to harddrive storage. With the speed of SSD, even such monster CP can be folded in a reasonable amount of time.

But before that, I need to draw the CP file first. My ideal version of the Senbazuru is not by simply arranging the zuru in a 32 × 32 formation (since that would be 1024 of them, which is more than a thousand), or by omitting 6 of them at each corner (several people, including Lang, have proposed this formation, but I don't like the empty space in the finished model), but by making 8 of them double-sized in the 8 directions. That way in will be exactly one thousand of them without any empty space.

However, by such design, I cannot just simply copy-and-paste the same pattern over and over to create the file, but since the whole CP is so large, manually editing the CP is equally infeasible in Oriedita since the processing time will be like forever for each operation I make. Therefore, I wrote another JavaScript program just for assembling the CP file from smaller components. The final CP is 83MB in size and can be downloaded here.

Complete CP of Senbazuru.

Finally, after a few more optimizations to the algorithm, after 4 hours and 10 mintues of runtime and 128GB memory settings, I successfully folded the Senbazuru. As for the wish I made, that's a secret obviously.

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