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For every positive integer $n$, we introduce a set $\mathcal{T}_n$ made of$(n+3)^2$ Wang tiles (unit squares with labeled edges). We represent a tilingby translates of these tiles as a configuration $\mathbb{Z}^2\to\mathcal{T}_n$.A configuration is valid if the common edge of adjacent tiles have the samelabel. For every $n\geq1$, we show that the Wang shift $\Omega_n$ defined asthe set of valid configurations over the tiles $\mathcal{T}_n$ is self-similar,aperiodic and minimal for the shift action. We say that $\{\Omega_n\}_{n\geq1}$is a family of metallic mean Wang shifts since the inflation factor of theself-similarity of $\Omega_n$ is the positive root of the polynomial$x^2-nx-1$. This root is sometimes called the $n$-th metallic mean, and inparticular, the golden mean when $n=1$ and the silver mean when $n=2$. When$n=1$, the set of Wang tiles $\mathcal{T}_1$ is equivalent to the Ammannaperiodic set of 16 Wang tiles.

Metallic mean Wang shifts I: self-similarity, aperiodicity and minimality