<i>Ulam Spiral</i> (and see ref to Martin Gardner's famous SciAm article):<p><a href="https://en.wikipedia.org/wiki/Ulam_spiral" rel="nofollow">https://en.wikipedia.org/wiki/Ulam_spiral</a><p><i>Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations</i> - 3Blue1Brown<p><a href="https://www.youtube.com/watch?v=EK32jo7i5LQ" rel="nofollow">https://www.youtube.com/watch?v=EK32jo7i5LQ</a>
you can not only map prime numbers in a circle/spiral, but also in a triangle and get some nice knitting patterns :)<p><a href="https://tessi.github.io/walking-the-ulam-spiral/" rel="nofollow">https://tessi.github.io/walking-the-ulam-spiral/</a>
If you're plotting primes, all the coordinates where you're not plotting are non-prime - so every 2nd coordinate will be blank. As will every 3rd and every 4th, 5th, 10th, 11th. etc etc.<p>Surely that's where the pattern comes from.
I’m not a mathematician so correct me if I’m wrong, but the patterns that emerge or more the natural result of the plotting method vs revealing anything meaningful about the distribution of primes.
shameless self promotion:<p>i built an "animation framework" in JavaScript around it where you can control and animate several parameters and even record the animation<p><a href="https://primes.nickyreinert.de/" rel="nofollow">https://primes.nickyreinert.de/</a>