  In this paper we propose a rule-independent description of applications of
cellular automata rules for one-dimensional additive cellular automata on
cylinders of finite sizes. This description is shown to be a useful tool for
for answering questions about automata's state transition diagrams (STD). The
approach is based on two transformations: one (called {\sl Baker
transformation}) acts on the $n$-dimensional Boolean cube $\frak B^n$ and the
other (called {\sl index-baker transformation}) acts on the cyclic group of
power $n$. The single diagram of Baker transformation in $\frak B^n$ contains
an important information about all automata on the cylinder of size $n$. Some
of the results yielded by this approach can be viewed as a generalization and
extension of certain results by O. Martin, A. Odlyzko, S. Wolfram.
Additionally, our approach leads to a convenient language for formulating
properties, such as possession of cycles with certain lengths and given diagram
heights, of automaton rules.
