Gaussians Primes

On this second episode of “what has Epsilon done for the past years”, we’re gonna talk about… Prime Numbers. Code is available here.

The primes does have this capacity to create some interesting looking things, I’ll give them that. The Gaussian integers are simply complex numbers whose real and imaginary part are integers, and whose modulus is prime. If one component of this number p is 0, then p is prime only if the other component is prime and p % 4 = 3.

We can see some primes lining up in lines, in crosses, and making all sort of weird patterns. There’s also radial symmetry going on in there. However, those patterns again disapear in some kind of noise all higher level of zoom. At the beginning it kinda looks like a weird cellular automata, doesn’t it ?

I promise, the next one isn’t going to be about primes. Maybe about complexes (complices) though.