rectangle attractor

iterates to find the inscribed rectangle inside a convex quadrilateral, if it exists

No input arguments. Starting at any point [circled in green] on the [black] quadrilateral,
we move in straight [blue] lines inside, horizontally and then vertically,
taking left or right 90-degree turns to reflect off of the convex 4-gon
whenever we impinge on its edge. (Of course, this is different from the
way a light ray reflects from a mirror physically, which is by the law of
equal angles of incidence and reflection.) As we continue this process,
a pattern emerges, either cyclic or chaotic. [Note that the final
nine iterations are highlighted in yellow, and the stopping point is
circled in red.]