Please do excuse this observation, as I am not a mathamatician - just a Scottish Lawyer who (for some mad reason) loves fractals and prime numbers.
Why is it, when I play around with simple images of Ulams Spiral at high resolution on my IPad, I get odd interference pattern. Are the pixels picking up a more hidden pattern? It does not seem to happen with high res random patterns. If you play about with images from the internet, you will see what I mean. I do hope I am not wasting anyone's time. I love patterns in nature. The undernoted image is of poor quality, but you will get the general idea.
I do apologise as I did not explain myself very well. Also, I only have a rather ancient IPad and live up a mountain with poor signal. In addition, I have no formal training in mathematics - just a rather curious interest. I was googling images of Ulams Spiral, as I was trying to work out why it is that you often get a prime number after a super perfect aliquot number. It is as if nature is saying OK, that last number completely makes sense, lots of divisors, tidy, symmetrical loves itself, even, shapely then.......BANG here is a number which makes no sense at all. No divisors other than 1 and itself. Nature appears to work like this. Anyhow, to get onto my point. If you expand and contract a good quality Ulam Spiral with your finger on the screen, you do get a Moire Pattern (which I think the previous reader is referring to). Now that might be due to how the even numbers relate to the pixels on the screen, but I don't know. Have a look anyway at
http://dmitrybrant.com/images/38m_2318966.png
for instance and expand and contract it. Let me know what you think.