  Colour an element of $\mathbb{Z}^d$ white if its coordinates are coprime and
black otherwise. What does this colouring look like when seen from a "uniformly
chosen" point of $\mathbb{Z}^d$? More generally, label every element of
$\mathbb{Z}^d$ by its GCD: what do the labels look like around a "uniform"
point of $\mathbb{Z}^d$? We answer these questions and generalisations of them,
provide results of graphon convergence, as well as a "local/graphon"
convergence. One can also investigate the percolative properties of the
colouring under study.
