Assuming a 16:10 display a 4096 wide display would be 2560 lines 'tall' and have a total of 31,457,280 pixel elements (r,g,b). Each of those would include a transistor as well so another 31.5M transistors, coming out to driver logic at the edge of the screen. At 498 ppi that would be about an 8" x 5" screen.
To drive that screen at 60hz you would have to push out 31.5M * 60 bytes of pixel data (that is for 8 bits per color, higher fidelity 10 bits per color would be more. At 60hz that is a bandwidth of 1.8 GBps or 18 Gbit/sec. This is faster than the current DVI spec is rated for, although I believe dual-channel can get there.
The yield rate inversely increases the cost per good screen, so a yield rate of 50% doubles the cost, and a more likely yield of 25% quadruples the cost. This can be offset somewhat by bigger glass (more chances to succeed, semiconductor manufacturing is in many ways a game of statistics) but bigger glass may require different factory layouts (they might have to build a factory just for this type of display).
So Nvidia helped make some progress when they announced the Tegra-3 could drive 2560 x 1600 displays. That's more than halfway to your 4K display. And this will be the 'killer' display technology in the next gen 10" tablets.
If the tablets can keep up the ship rate then they will give manufacturers a better feeling about being able to sell enough even higher resolution displays to offset their costs and that is when we'll see something like this demo come out in a larger size.
All of those are a far cry from Toshiba's prototype (495 ppi) or the screen Apple uses in its iPhone and iPod touch (330 ppi).
[1] http://members.ping.de/~sven/dpi.html
[2] http://en.wikipedia.org/wiki/List_of_displays_by_pixel_densi....
"Resolution independence has been "coming soon to Mac OS X" since 2005. The dream of drawing the same interface elements at the same visible size but with more pixels was so close in 2007 that we could taste it. Then Snow Leopard arrived and the Mac's interface scalability features actually regressed. Depressing.
Meanwhile, Mac OS X's sibling operating system waltzed right into a high-resolution UI on its very first try. iOS's secret? Don't try to support arbitrary scale factors, just support one: double resolution. A 50x50-pixel square on a non-retina iPhone screen is exactly the same size as a 100x100-pixel square on a retina display. Graphics that have not been updated for the higher resolution are simply drawn with four-pixel squares in place of each low-resolution pixel. All dimensions are nice, even, integer multiples of each other. This is a perfect fit for physical screens which, of course, have an integer number of pixels. Fractional measurements necessarily require ugly compromises.
Lion has taken the hint from its younger brother. Arbitrary scalability is gone. In its place is a single check box to enable "HiDPI" display modes. (This option is still hidden away in the Quartz Debug application, so it's clearly not an end-user feature. But unlike all previous incarnations of resolution independence, this one actually works.)
After enabling HiDPI, new display modes will become available. In the screenshot above, the 720x450 mode is half native screen dimensions, and the 640x400 mode is half the (non-native) 1280x800 setting. After selecting a HiDPI mode, everything is drawn with twice as many pixels as its non-HiDPI equivalent. Here's a screenshot featuring TextEdit, our usual interface scalability workhorse.
It looks pretty good, right? The only flaws are the bitmap graphics that haven't been updated for HiDPI (look closely at the black triangles in the ruler). Unfortunately, there are a lot of these throughout the operating system and its bundled applications. But unlike in all years past, the framework is finally there for third-party developers and Apple itself to finally get their applications ready for a world in which 300-dpi desktop and laptop displays are more than just expensive curiosities."
[1] http://arstechnica.com/apple/reviews/2011/07/mac-os-x-10-7.a...
(the biggest drawback I guess is that it doesn't really do anything for people wanting a larger interface for readability reasons, having everything four times as large is a hard blow for the real estate when you really wanted 120% or something)
What the author constantly mixes up is that you need four times as many pixels, not twice. And thus we need ~400 DPI to have everything at the same size as today. But yeah, just hope that it becomes mainstream enough to be affordable, OLED to the rescue? Thanks to displayport the interconnect won't be a problem at least.