A characterization of $p$-automatic sequences as columns of linear   cellular automata
  We show that a sequence over a finite field $\mathbb F_q$ of characteristic $p$ is $p$-automatic if and only if it occurs as a column of the spacetime diagram, with eventually periodic initial conditions, of a linear cellular automaton with memory over $\mathbb F_q$. As a consequence, the subshift generated by a length-$p$ substitution can be realized as a topological factor of a linear cellular automaton. 
Eric Rowland and Reem Yassawi
math.DS cs.FL nlin.CG