There, I wrote that
Here's the crop, zoomed progressively from 100% (as originally posted) up to 800% where it's easy to see the individual pixels).Bear in mind that some degree of Moiré is pretty much inevitable whenever you have a small regular pattern that gradually shifts phase with respect to the pixels. At the very least there will be a periodic shift of pixel values as the pattern lines up in different ways with respect to the pixels. See HERE for illustration. Depending on where and what direction you measure, the bold pattern of ommatidia in this eye has a spacing around 3-6 pixels per cycle after resizing. The lower end of this range puts it well into the danger zone. If Gérard wants, I can post an extreme crop of his resized fly eye to show what I'm talking about.
In the last frame, I've marked with orange arrows a couple of places that should be compared. These are the dark areas on the lower portions of two ommatidia. In the original large size image (HERE), there are plenty of pixels to make these areas almost identical. But in the smaller resized image, due to differences in how the dark areas line up with individual pixels, the dark areas get represented differently. In the upper case, there is a sort of T pattern of 4 dark pixels, where in the lower case it's more of a rectangular block of not-so-dark pixels.
In a perfect world, the total amount of light coming from each pattern would be identical, so if you could not see the individual pixels, the patterns would look the same. But in the real world it doesn't work out that way. Any change of curves or levels, the total amount of light becomes different, and then the different representations show a visible Moiré pattern.