  We discuss some numerical invariants of multidimensional shifts of finite
type (SFTs) which are associated with the growth rates of the number of
admissible finite configurations. Extending an unpublished example of
Tsirelson, we show that growth complexities of the form $\exp(n^\alpha)$ are
possible for non-integer $\alpha$'s. In terminology of Carvalho, such subshifts
have entropy dimension $\alpha$. The class of possible $\alpha$'s are
identified in terms of arithmetical classes of real numbers of Weihrauch and
Zheng.
