Whoa, thank you! Very impressive and a lot of effort 
Somewhere it has to have some imperfection.
Yes, I think the trick is to hide the imperfection over a large area or to make everything a bit random so the mind just assumes perfection ;-). Similarly architects will draw jiggly lines to make them appear more straight then they are.
Thanks to your definition you posted earlier, I got an idea how to add a helix to my dot distributor ( the one posted here: "perfect" grid in 3 dimensions - #9 by Konrad). and the results are looking promising but to early to call it:
