This one is easily seen to be limitperiodic: A large portion of the tiling is periodic. Thus it is a cut and project tiling. A detailed description of the corresponding cut and project scheme is contained in [Fre02].
The substitution occurs already in [GS87], see Exercise 10.1.3.
Grünbaum, B and Shephard, G.C.
Tilings and Patterns
W.H. Freeman 1987, MR0857454