Exotic Image Formation in Strong Gravitational Lensing by Clusters of
  Galaxies -- III: Statistics with HUDF
  We study the image formation near point singularities (swallowtail and
umbilics) in the simulated strongly lensed images of Hubble Ultra Deep Field
(HUDF) by the Hubble Frontier Fields (HFF) clusters. In this work, we only
consider nearly half of the brightest (a total of 5271) sources in the HUDF
region. For every HFF cluster, we constructed 11 realizations of strongly
lensed HUDF with an arbitrary translation of the cluster centre within the
central region of HUDF and an arbitrary rotation. In each of these
realizations, we visually identify the characteristic/exotic image formation
corresponding to the different point singularities. We find that our current
results are consistent with our earlier results based on different approaches.
We also study time delay in these exotic image formations and compare it with
typical five-image geometries. We find that the typical time delay in exotic
image formations is an order of magnitude smaller than the typical time delay
in a generic five-image geometry.
