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WereKitten said:

But it's not exactly the same as with overlapping transparent textures. The "moire effect" you get in real life when you overlap two chainlink fences is magnified by the optical diffraction in the overlapped pattern corners, the same phenomenon that brings you fringes of light and dark around the border of real shadows.

Stand in front of a window, close one eye, raise you hand between your eyes and the light at 10-15 inches from your face and "pinch the air" between your index and thumb, trying to get them as close as you can without them touching. You'll see the light between them decreasing critically when they're really close but still separated. You might even observe some dark fringes in that light slice, if you help yourself with your other hand to keep the fingers steady.

In the same way when you look at some moire patterns in real life you get "dark blots" in the corners that are actually "optically thicker" than the overlapped grids (obviously that light is not lost, it is diffracted on a wider angle,  just less evident to the eye). There might also be biological effects in there, due to how our eye responds to very fine separation between two light spots or dark spots, but I'm ignorant on the subject.

If you want to simulate/render that, I suppose that you either simulate light wavefronts in spherical harmonics, or compute optical ray curving due to interference in ray tracing.

I think it has more to do with biological effects. They eye has it's own edge enhancement build in. There are lots of optical illusions floating about to demonstrate that. Physical optical diffraction doesn't happen until you get down to the wavelength of light, 300-700 nm, not really possible with fingers :) http://bowiestie.wordpress.com/2010/02/18/moire-pattern-gifs/ no diffraction there.

Even more off-topic (sorry cgi) but optical illusions are just too cool :) (right-click view for the full effect)