$ 13^{-1} \cdot \bar{x}|\bar{q}$ divisor

We consider an abstract automaton that divides by $13_{(4)}$ in the quadratic numbering system. The automaton is typical for a family of divisors having no common features. As a consequence, almost every divisor is a source of original features. An example of such a divisor is presented. Some of its features are unusual and non-obvious computational objects to be investigated. All the divisors of the family can be implemented with the B-technology.