Yeah, it took me a while to sadly realize this visualization tells us nothing useful about primes. otoh, it does tell us a lot about composites. Hover on 29. The pattern is completely useless - you get one wave of period 29, and the other wave of period unity.
However, hover on 28. Now you get 6 waves - of periods 1,2,4,7,14,28 - these being the divisors of 28. The intersection of these 6 waves produces those interesting floral patterns. But obviously, this whole experiment tells us much more about 28, a composite, than 29 the prime.
That's just the thing. Does anyone understand the primes, really?
We know a lot about number fields, multiplication and sieving... but the primes themselves (the "holes" left in the wake of the sieving process) are something of an epiphenomenon to all of this.