Extended symmetry groups of multidimensional subshifts with hierarchical structure

In this contribution, we discuss the automorphism group, i.e., the centralizer of the shift action inside the group of self-homeomorphisms of a subshift, together with the extended symmetry group (the corresponding normalizer) of certain Zd subshifts with a hierarchical structure, like bijective substitutive subshifts and the Robinson tiling.