As clued by the flavor text, this puzzle has to do with factoring primes in the complex plane. The image is a 250x250 section of the first quadrant in the complex plane beginning at (0, 0) in the bottom left corner. Each black dot represents a Gaussian prime (a prime number in the ring of Gaussian integers), and each colored dot represents a composite number with exactly two factors.
For each color (red through purple), the composite numbers are factored, and their factors are connected pairwise in the plane by a line as follows:
Taken in order, these letters spell out the solution,