Not all lenses are good lenses, especially not the ones nature makes by accident. It also matters where the background source is relative the centre to the crappy lens.
A favourite human made example seems to be the base of a wine glass, that manages similar levels of awfulness, see third picture here for how the same basic shape can make different images of the same source: http://inspirehep.net/record/850223/plots#
A favourite human made example seems to be the base of a wine glass, that manages similar levels of awfulness, see third picture here for how the same basic shape can make different images of the same source: http://inspirehep.net/record/850223/plots#