A decorated version of the Hofstetter 4fold tilings. This version can be generated by a proper substitution rule. It was shown in [FH15] that this version is aperiodic, as well as limitperiodic. For more details see Hofstetters 4-fold.
[FH]
Frettlöh, D and Hofstetter, K
Inductive rotation tilings
Proc. Steklov Inst. Math.
2015,
288,
pp. 247-258,