Eisenstein Snowflakes

The Eisenstein integers are a ring of complex numbers that cover the Gaussian plane in a triangular lattice. Each number is the sum of a regular integer and an integral multiple of ω, the positive third root of unity. Eisenstein integers share many properties of the regular integers, including well-defined prime numbers and GCDs. This Demonstration shows the so-called totients of a given Eisenstein integer—that is, the integers below the number that share no factors with that number. It is simply a happy holiday coincidence that the resulting patterns resemble snowflakes.