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Reading about how grid distribution when performing supersampling is suboptimal got me wondering: are there any displays that arrange their pixels in pattern other than regular grid? Wikipedia mentions that

The use of non-uniform grids is an active research area, attempting to bypass the traditional Nyquist limit.

...which is pretty much what using non-grid sampling in supersampling does. But this only links to a paper back from 2000, which isn't exactly new when it comes to quickly developing things like displays.

Another interesting point I've found is this picture:

Photo of various monitors with individual light-emitting elements visible Pengo, CC BY-SA 3.0, via Wikimedia Commons

Apparently, TV CRT pixel grid seems to have its columns offset considerably, but is this a result of how beam is controlled (so fluorescent lines are actually uninterrupted)? Would it have a regular pixel grid if hooked to computer's video output?

Another related question I came across while researching this is Why are pixels square? - but it talks just about shape of pixels, not their arrangement.

Giacomo1968
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Though AFAIK, displays have regular patterns, there are some less common patterns, such as PenTile RGBG.

By Matthew Rollings at English Wikipedia, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=14914205

You might also find the pattern of pixel colors in sensors of interest, but again, they are not irregular, just in a different pattern.

To avoid color moiré effects, it would be interesting to see if a screen or sensor could be made with non-repeating Penrose tiling. The pixel ratio could be kept constant, yet there would be no large-scale straight-line patterns.

BTW, the Autochrome Lumière color photography process relied on truly random color pixels, with no pattern to the display.