UCLA neuroscientist Matt Lieberman posted the 'no red pixels' image on the left. It's developed from an original by Experimental Psychologist Akiyoshi Kitaoka (right) that, despite appearances, does have some very slightly red-tinged pixels in it.
Remember internet kerfuffle that was 'the dress' ? Well, there's another optical illusion that's puzzling the internet right now. Behold: the red strawberries that aren't really red. Or more specifically, the image of the strawberries contains no 'red pixels.'
The important distinction to make here is that there is red information in the image but, despite what your eyes might be telling you, red is not the highest value for any individual pixel in the image. Hence, no 'red pixel' in the image.
As was the case with 'the dress,' it all relates to a concept called color constancy, which relates to the human brain's ability to perceive objects as the same color under different lighting. Which should immediately bring to mind a familiar photographic concept: white balance. Although there's a significant cyan cast to the whole image, your brain is able to correct for it without you having to consciously identify a neutral part of the image (as you'd need to in processing software).
As a photographer, this should make it clear just how clever auto white balance algorithms have become and also why, when color accuracy is critical, you're still better off telling the camera or leaving yourself a target to confirm what grey looks like in the available lighting.
We have Experimental Psychologist Akiyoshi Kitaoka to thank for turning this puzzle loose on the world, and neuroscientist Matt Lieberman for turning it viral. Curiously, the first image contains a few red-dominated pixels (which Lieberman's edited version doesn't), yet appears more grey than Lieberman's version.