Per Wikipedia, moiré fringes are the complex patterns that manifest as a result of interference between overlaid transparent images. Provided you don’t count people on TV with dodgy stripey shirts or ties then I first encountered them as attractive features on naive loading screens for early (1982-83) Spectrum games. Sometimes drawn by the BASIC loader. The canonical example (to my mind is this one):
Not sure, but I believe the pattern emerges as an artefact of the Spectrum’s line DRAW-ing algorithm. The progam I “wrote” just draws a straight line from the origin (bottom-left) to the right-hand side of the screen, then another to a point 2 pixels higher, etc (an opposite procedure is repeated to get the second section).
This same pattern is definitely also used on other early or graphically-limited systems though, so it is something that exists in the mathematical wilds of the real world. Its light/shade effect suggests 3D corridors, although I don’t think it was ever used as such on the Speccy. If you know differently then do tell!
As an aside, drawing CIRCLEs on top of each other with ever increasing radius also produced the good-of-the-gaps on the Speccy, though to a less impressive extent.
You can also see similar effects in real-life (as below, pinched from Wikipedia), the afore-mentioned clothing-unfit-for-TV (no example handy) or sometimes in a thumbnail image online (the pics on this post itself, most likely).
In the midnight hour she cried moiré, moiré, moiré!