I believe that indeed the arrangement of pixels on a computer screen does create a varying moire effect here. Moire patterns are closely analogous to interference patterns when waves are superimposed. (For one thing, when I magnify the many-dot pattern on my screen it's easy to see that the dots are quite irregularly shaped, rather than round disks.) BUT: I'm convinced that even if the rendition of the dots were mathematically ideal (i.e., no pixels involved), one would still see varying moire patterns here. Because almost everywhere, locally the dot pattern is well approximated by a linear lattice (i.e., the dots are at the corners of a tiling of the plane by identical parallelograms). * * * An interesting experiment that shows intriguing and mysterious moire patterns goes like this: Assume a computer screen with in {1..K} by {1..L} pixel coordinates denoted (x,y). Let the RGB color cube be [0,1]^3, and assign a discrete circular rainbow color table to Z/nZ = {0..n-1} for some large n; n = 1024 works well. Say by picking equally spaced points around the circle inscribed in the hexagonal intersection of the plane R+G+B = 3/2 with [0,1]^3.) Finally, color the pixel (x,y) the color whose number is x^2 + y^2 mod n. (I first tried this in 1981, and it's probably been done independently many times before and since.) --Dan << Back in September my friend Joshua Burton sent me this email. He and I and our mutual friend Michael Larsen exchanged a few emails about the phenomenon, but we never followed up: http://www.cs.uml.edu/~jpropp/sunflowers.html (I'm sending the URL because one of the imbedded images is quite large.) I asked Josh if it was okay to share this problem with others, and he replied: "By all means, share! The first to-do, I think, is to redo the work independently of the Mma engine, to confirm that the moire patterns are real, and not artifacts of some tool-specific rounding issue. If it's real, I guess the next thing is to come up with some numerical measure of the anomalous behavior of a big sunflower, as a function of N. That, or an actual clue what's going on."

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