Abstract For every positive integer n, we introduce a set {T}ₙ made of (n+3) ² Wang tiles (unit squares with labeled edges). We represent a tiling by translates of these tiles as a configuration Z² {T}ₙ. A configuration is valid if the common edge of adjacent tiles has the same label. For every n 1, we show that the Wang shift ₙ, defined as the set of valid configurations over the tiles {T}ₙ, is self-similar, aperiodic and minimal for the shift action. We say that \{ ₙ\}₍ ₁ is a family of metallic mean Wang shifts, since the inflation factor of the self-similarity of ₙ is the positive root of the polynomial x²-nx-1. This root is sometimes called the n -th metallic mean, and in particular, the golden mean when n=1, and the silver mean when n=2. When n=1, the set of Wang tiles {T}₁ is equivalent to the Ammann aperiodic set of 16 Wang tiles.
Sébastien Labbé (Wed,) studied this question.