Is a two-dimensional butterfly able to fly by symmetric flapping?

We consider whether two rigid plates (on a hinge) swinging completely symmetrically with respect to the up and down directions can produce enough lift for flight. By simulating a simple napping motion in two-dimensional space using a discrete vortex method, we found a new type of symmetry-breaking mechanism that allows for the generation of sufficient lift to realize steady-flapping flight. The most important factor in determining the behavior of the model is the nature of the flow following the second downstroke, in which the wing produces significant lift through its interaction with the separation vortices.