  We consider the curve shortening flow applied to a class of figure-eight
curves: those with dihedral symmetry, convex lobes, and a monotonicity
assumption on the curvature. We prove that when (non-conformal) linear
transformations are applied to the solution so as to keep the bounding box the
unit square, the renormalized limit converges to a quadrilateral which we call
a bowtie. Along the way we prove that suitably chosen arcs of our evolving
curves, when suitably rescaled, converge to the Grim Reaper Soliton under the
flow. Our Grim Reaper Theorem is an analogue of a theorem of S. Angenent, which
is proven in the locally convex case.
