The existence of substitutions with a non-empty continuous spectrum, or even without discrete spectrum at all, has been somehow a surprise for physicists after they began using substitutions, inspired by the Fibonacci sequence, in relation with quasicrystals. The paper under review will, I guess, be also suprising: the authors explore a more subtle use of substitutions to construct tiling dynamical systems without discrete spectrum. Roughly speaking, they make use of a technique of \textit{S. Mozes} [J. Anal. Math. 53, 139-186 (1989; Zbl 0745.52013)], and of the particular substitution (which might look simple at first glance!): \[ \begin{aligned} 0 &\longrightarrow 0\;1\;0\;1\\ 1 &\longrightarrow 1\;1\;1\;0.\end{aligned} \] {}.