Define a non-periodic set (in this case using primes):
$P=\{p_1,p_2,...,p_k\},$ where $p_k$ is the $k^{th}$ prime.
I found an average, $A,$ which is the quantity $\sum P$ divided by $k.$ Then I took a copy of the distributions and reflected each of the values about the average, $A.$ After that I superimposed the two distributions. I know that all the resultant distributions have reflection symmetry about $A.$ ($A$ is not part of the distribution it's just used to calculate the reflections).
I'm interested in the spacings between points of the distributions and if they are similar to the pattern of eigenvalue spacings resulting from a random matrix?
Here is the resultant distribution I calculated from the first 6 primes.
Here's another distribution that I think exhibits Universality (Universality is a distribution pattern seen in the Riemann Zeta nontrivial zeros, the two dimensional pattern of retina spacings in chicken eyes, and many other places):
Article describing Universality:
https://www.quantamagazine.org/in-mysterious-pattern-math-and-nature-converge-20130205/
Do the two distributions I gave, exhibit the property of Universality, like the distribution of eigenvalues coming from a random matrix does?
How do you figure out if a distribution of points exhibits the property of Universality? If someone could point me to a mathematical definition of Universality that would help as well.
Related graphic depicting three notions of distributions:
