A happy number is a number where starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers)
It seems like he’s trying to visualize the progression of numbers towards happy numbers as rings. It’s not very clear what further away from the center, vs what around the ring means.
I read it as little more than trying to create interesting art, rather than get at some mathematical truth.