A Staircase Illuminator for Simply Connected Orthogonal Polygons

Let \( S \) be an orthogonal polygon in the plane bounded by a simple closed curve. Assume that every two boundary points of \( S \) have a common staircase illuminator whose edges are north and east. Then \( S \) contains a staircase path \( \mu_0 \) whose edges are north and east such that \( \mu_0 \) illumines every point of \( S \). Without the requirement that the illuminators share a common direction, the result fails.