  We construct a one-parameter family of singly periodic translating solutions
to mean curvature flow that converge as the period tends to $0$ to the union of
a grim reaper surface and a plane that bisects it lengthwise. The surfaces are
semigraphical: they are properly embedded, and, after removing a discrete
collection of vertical lines, they are graphs. We also provide a nearly
complete classification of semigraphical translators.
