It is a very beautiful application of number theory, topology and geometry. These three fields perhaps are my personal three favourite streams of mathematics, the most fundamental, simple and very tightly interrelated. I am a visual thinker and these kinds of diagrams are representations of the network maps that appear in my mind when I think about numbers.

Thanks to @voluntary for pointing me to this post.

@pedrosgali I would be particularly interested to see a sequence of these number patterns for special number sequences also, Fibonacci, Primes, and so forth. The number 9 is particularly interesting, because its multiples also all sum to 9 due to the decimal system. By selecting clock patterns based on these multiples you can show other patterns as well. Part of what makes the pretty patterns in the middle is also to do with aliasing across the grid of pixels you are using, this acts as a moire type filter.