Directed rectangle-visibility graphs have unbounded dimension

Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets. One visibility representation in the plane that has been studied is one in which the vertices of the graph map to closed isothetic rectangles and the edges are expressed by horizontal or vertical visibility between the rectangles. Two rectangles are only considered to be visible to one another if there is a nonzero width horizontal or vertical band of sight between them. A graph that can be represented in this way is called a rectangle-visibility graph.