Start with the hexagonal (or triangular) lattice $\Bbb Z[\omega]$ where $\omega=\frac{-1+i\sqrt 3}{2}$ is a third root of unity, and surround each lattice point with a circle of diameter $1$, we obtain the densest circle packing in the plane. Your image consists of picking the circles with centres $-2,-1,0,1,2$ (middle row), $ \omega,\omega+1$ (row above it), $2\omega,2\omega+2$ (outer, gappy row), $-\omega,-\omega-1$ (below middle row), $-2\omega, -2\omega-2$ (lower, gappy row) from this infinte packing. Of course, the six outer points $-2, 2\omega, 2\omega+2,2,-2\omega, -2\omega-2$ are concircular - they are just two times the sixth roots of unity (so the big circle is four times as big as the small ones). Apart from these circles, the image has a few lines added, which merely correspond to the "linear" nature of the underlying grid.