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It looks more like moulding clay than origami folding I remember form a kid. Part way through you can see the basic form take shape and get pressed down into the samurai. Cool stuff!
For those in the bay area, there is a great origami store in japan town called the paper tree which I highly recommend. Last time I was there they had some truly amazing pieces on display including many of Lang's insects and sculptures as well as a ryujin 3.5 designed by satoshi kamiya.
You've hit upon some of my favorite pieces. Any of Lang's opus pieces are amazing (I really like the rock climber that sticks out of a piece of paper).

Satoshi Kamiya's works are also pretty darn amazing (the wizard, the dragons, etc.).

Lang really brought out the science in origami (he's en ex-rocket scientist turned origami pro), and wrote software for calculating the fold patterns and extraction points from paper for pulling out points of manipulation (like limbs, etc.)

This is incredible!

The steps this craft has taken to evolve over time would be so interesting to watch *cough* unfold.

Start with basic shapes. Then work towards branching element. Later form that into body shapes. Make the detail start forming from the rough structure. Continuously refine from there. It feels like watching a lifeform or fractal grow in realtime.

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This is humbling.

While from a purely technical standpoint I fully understand it's doable, the dedication and skill required is, well, rather striking.

I am currently studying 3D computer graphics.

Interesting (to me) that if you pause the video at 38 seconds you see a mesh of triangles... which are the same building blocks the computer uses to create 3d objects as well.

Prof Erik Demaine of MIT pioneers the field of computational origami. I do not know the details of his research. But there are practical applications like fitting large space probes into narrow rockets. Or making machines that flex without explicit hinges.
Well you can see what I see too. Funny origami artist who use paper clips to make origami from a single paper :) It look more like paper craft artist but not origami. Im thinking here to develope a robot hand so my 3D file will be done in an hour and I will be Origami Artist too.
How does one design such a thing? Is it software or "on paper" or with piecewise prototyping?
I think its a combination of software and prototyping from what I've read about origami artists. (software like Treemaker [0] for making crease patterns etc)

(Not an expert though)

Oragami is amazing, in part, because it's a reversible process unlike painting or sculpture. There's a certain beauty to purely non-destructive creation.
It's not really regular origami if you have to use water and a drier to "shape" your model in the process. I was expecting using only one's hands.
great observation. this sculpture of a samurai folded from a single sheet of paper indeed is not "normal" oragami.
For people looking at more of the mathematical side of how origamis are shaped and built, I recommend a wonderful book by Robert Lang: "Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami"

This really covers a lot of ground on computational origami.