  We present and study C*-algebras generated by "periodic weighted creation
operators" on the Fock space associated with an automorphism $\alpha$ on a
C*-algebra $A$. These algebras can be viewed as generalized Bunce-Deddens
algebras associated with the automorphism and can be written as a certain
direct limit. We prove a crossed product presentation for such an algebra and
find a necessary and sufficient condition for it to be simple. In the case
where the automorphism is induced by an irrational rotation (on
$C(\mathbb{T})$) we compute the K-theory groups and obtain a complete
classification of these algebras.
