Schmidt Arrangement

This picture drawn by Katherine Stange shows what happens when we apply fractional linear transformations $z \mapsto \frac{a z + b}{c z + d}$ to the real line sitting in the complex plane, where $a,b,c,d$ are Eisenstein integers that is, complex numbers of the form $m + n \exp(2 \pi i/3)$ with $m,n$ being integers.