It's fascinating to watch, even on video. I've never gotten a chance to watch a samurai sword being made in person.
I'm sorry for getting the number of folds wrong, I was just putting an upper bound there. I was too lazy to write a quick program to figure out the powers of two.
I have seen somebody make a damascine (sp?) blade. That has to do with folding and layers also, but they use two types of metals and it is done as much for appearance as for usefulness.
They don't use "folding" as much as pounding the layer flat, cutting it in half with a chisel, and then "forge-welding" which looked to me to just putting the two pieces of hot layers on top of each other.
The positions of the cuts and which way the layers control the final appearance, and there are a large number of patterns, some only known to a single smith (or so I was told, I suppose that any pattern could be figured out if somebody wanted to badly enough).
I have no idea if this makes the blade stronger or better, but it makes it very beautiful.
Unfortunately at the time I didn't have the money to buy one of the blades, and I keep promising myself each year that I will buy one at the big arts fest we have each year, but I can never justify the money (we're talking around $1,000 for a basic folding pocket knife here). I can buy my weight in Leathermans for that! And yes, I missed the 2009 Leatherman Wave edition, but I doubt I would have had the cash for that either.