On the topological directional entropy

In this paper we study the topological directional entropy of Z 2 -actions generated by one-dimensional linear cellular automata and the shift map σ acting on compact metric space Z m Z . We give a formula, which can be efficiently and rightly computed by means of the coefficients of the local rule f , for the topological directional entropy of Z 2 -action generated by the pair ( T f [ − r , r ] , σ ) in the direction θ ( θ ∈ [ 0 , π ] ). We also generalize the results obtained by Akın [H. Akin, The topological entropy of invertible cellular automata, J. Comput. Appl. Math. 213 (2) (2008) 501–508] to the topological entropy of any invertible one-dimensional linear cellular automata.