Embedding Bratteli-Vershik systems in cellular automata [article]

Marcus Pivato, Reem Yassawi
2007 arXiv   pre-print
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'
more » ... ap 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.
arXiv:0710.3608v1 fatcat:hs3qjnfhzrhodo26zjopj6rq6m