Do we need an 8k display?

Or is a 4k display good enough? I'm not sure I have the tools to work this out mathematically but we can start with some basics. I'm also not sure about the effects of distance vs resolution.

Tree leaves in a canopy are going to be our example.

An HD display is 1920x1080. Displaying a 15ft wide canopy on an HD display results in 94mil/pixel (15*12*1000/1920) across the width.

A 4" leaf on a 77" display (67.11 inches wide) would occupy 1.49" of display. On an HD screen this is 15.9pixels. (Every inch on the display corresponds to 2.68 scene inches.) If this were rotated 45 degrees it increases this to 22.4 pixels.

That's enough to leave the edges a little jaggy or blurry (if one is to be picky about it). It's not bad though.

A 4k display reduces this to about 47mil/pixel (about 1.2mm/pixel). Up close a leaf in 1mm blocks would be obviously weird but even at 5ft (I'm looking at a leaf) many of those features are lost. I think at 10 or 15ft 1mm resolution is about all you could get with typical human eyesight.

But I am curious if this is true if they were moving (e.g. in a breeze). I have seen 8k footage of a tree moving in a breeze and it seemed to be quite better in 8k than in 4k. To my knowledge this was at the same fps which was surprising as I would expect frame rate to have a much more substantial impact on motion blur than resolution. I suppose it is possible they were using a different codec!

At 8k (7680x4320) this is reduces to 23mil/pixel and a 4" leaf would receive 63pixels (still 1.49" on screen) and that's pretty good. I doubt you would receive much improvement beyond that unless you were very close to the screen (which you wouldn't be).