I had mentioned this work in my previous article Senbazuru from a single uncut square, and in this article, I would talk more about the background of this design.
In the history of origami, the earliest known publication dedicated to recreational paper folding (as opposed to ceremonial folding) is Hiden Senbazuru Orikata (meaning "the secret of folding a thousand cranes") by Gido Ichien (pen named Rokouan) in 1797. The book contains 49 designs in the category of what is now known as Renzuru (connected crane), each folded from a square or rectangular sheet of paper with cuts. The book shows only the CP and the folded result of each design, with no instructions. In many of its designs, the cranes (or technically orizuru) are connected only by a tiny piece of paper and need to be folded very carefully to not tear the connection. A full list of its designs can be found on the website orizuru49.com.
One of the designs from this book is titled "Seigaiha" (meaning "the wave of the blue sea"), which is a name borrowed from one of the traditional Japanese decoration patterns. The folded result is basically 9 orizuru in a 3 × 3 formation, connected only at the tips of the heads, tails, and wings.
This, of course, is done by cutting slits on the paper (refer to the link above for instructions). Even with all the modern design techniques for super-complex models, it is still pretty much infeasible to fold to exactly this result from a single uncut square, as those places where the orizurus connect will be ridiculously thick in practice.
However, if we compromise by accepting a "base plane" to exist underneath these orizurus, the same formation is then completely feasible from a single uncut square.
In the ERM map shown above, we can see that the concept of this model is really simple. The lakes become the base plane, connected by rectangular rivers, and the circles forming the orizuru are placed in the spaces in between.
Despite its simplicity in concept, its folding is perhaps even more tricky than the original Seigaiha. In my note, I mentioned something like "96 closed sinks and 144 spread squashes", and that's only a tiny part of the process. It took me four days to fold this model, and after that, so far I've never folded it a second time.
Update
I later fully diagrammed the folding sequence of this model, and as a by-product, I did fold this model again. I highly doubt that I will ever do it once more, but who knows?
The full instruction of this model is now for sell on my Ko-fi store:
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