Automata over a binary alphabet generating free groups of even rank
  We construct automata over a binary alphabet with $2n$ states, $n\geq 2$, whose states freely generate a free group of rank $2n$. Combined with previous work, this shows that a free group of every finite rank can be generated by finite automata over a binary alphabet. We also construct free products of cyclic groups of order two via such automata. 
Benjamin Steinberg, Mariya Vorobets, Yaroslav Vorobets