  We introduce and study the notion of a directional complexity and entropy for
maps of degree 1 on the circle. For piecewise affine Markov maps we use
symbolic dynamics to relate this complexity to the symbolic complexity. We
apply a combinatorial machinery to obtain exact formulas for the directional
entropy, to find the maximal directional entropy, and to show that it equals
the topological entropy of the map. Keywords: Rotation interval, Space-time
window, Directional complexity, Directional entropy;
