We will recall the new family of metallic mean Wang tiles. This is a family of sets of aperiodic Wang tiles (unit squares with labeled edges) whose dynamics involves the positive root of the polynomial $x^2-nx-1$. This root is sometimes called the $n$-th metallic mean, and in particular, the golden ratio when $n=1$ and the silver ratio when $n=2$. The metallic mean Wang shifts are self-similar. The Rauzy fractal defined from the self-similarity is polygonal and forms a partition of the canonical window of a 4-to-2 cut and project scheme.