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." Jim Propp