@j.p.s: Err, nope, we're indeed reducing the actual amount of colors? (Given the usual non-HDR grayscale image, from 256 to 16).
Code:
Forma_Gray.png PNG 1440x1920 1440x1920+0+0 8-bit Gray 256c 414736B 0.000u 0:00.000
Forma_Dithered_o8x.png PNG 1440x1920 1440x1920+0+0 8-bit Gray 16c 91074B 0.000u 0:00.000
(i.e., reduce the *actual* amount of colors, while, ideally, making the *perceived* result not so bad. My use of 'effective' might have been confusing?).
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Unfortunately, we can't do what you're requesting, as I mentioned elsewhere (or here, earlier): the hardware dithering is done on a work buffer that won't make it back to the framebuffer, so we can't capture it to try it elsewhere

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If you meant the dithering applied by Calibre, on the other hand, here goes.
(Again, it's easy, it's IM's 8x8 ordered dither, I'm the one who ported it everywhere I cared about ;p).
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If you have shell access,
FBInk can do that (IM's 8x8 ordered dither and/or the device's HW dithering) automatically for anything you throw at it

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