  Many dynamical systems can be naturally represented as `Bratteli-Vershik' (or
`adic') systems, which provide an appealing combinatorial description of their
dynamics. If an adic system X satisfies two technical conditions (`focus' and
`bounded width') then we show how to represent X using a two-dimensional
subshift of finite type Y; each `row' in a Y-admissible configuration
corresponds to an infinite path in the Bratteli diagram of X, and the vertical
shift on Y corresponds to the `successor' map of X. Any Y-admissible
configuration can then be recoded as the spacetime diagram of a one-dimensional
cellular automaton F; in this way X is `embedded' in F (i.e. X is conjugate to
a subsystem of F). With this technique, we can embed many odometers, Toeplitz
systems, and constant-length substitution systems in one-dimensional cellular
automata.
