Colour an element of 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 Z^d ? Our answer to this question opens up further fields of investigation. One can generalise this problem in several directions (look from a point uniformly sampled in a subgroup, study the N-valued colouring by the gcd, etc.): we solve the generalised problems, provide results of graphon convergence, as well as a "local/graphon" convergence. One can also study the percolative properties of the colouring under study.