Convert numbers to a vector space represented by their prime factors:

  2 => [1 0 0 0...]
  3 => [0 1 0 0...]
  4 => [1 0 0 0...]

And map that high dimensional space back down to two dimensions (using some technique I haven't dug into yet). Colors are assigned by some scheme, later images help to illustrate how the particular clusterings happen like one where primes are rendered in white.