  In this paper, we will study the following geometric flow, obtained by
Goldstein and Petrich while considering the evolution of a vortex patch in the
plane under Euler's equations,
  X_t = -k_s n - (1/2) k^2 T, with s being the arc-length parameter and k the
curvature. Perelman and Vega proved that this flow has a one-parameter family
of regular solutions that develop a corner-shaped singularity at finite time.
We will give a method to reproduce numerically the evolution of those
solutions, as well as the formation of the corner, showing several properties
associated to them.
