Before revision:  The Wang shift \Omega _{12 subshift X_0 of the Jeandel-Rao tilings \Omega_0 .
After revision:  The Wang shift \Omega _{12 subshift X_0 of \Omega_0 such that any tiling in X_0 can be decomposed uniquely into 19 distinct patches of sizes ranging from 45 to 112 that are equivalent to a set of self-similar and aperiodic 19 Wang tiles. We think that this gives an almost complete description of the substitutive structure of Jeandel-Rao tilings \Omega_0 .