Here is an example of the breaking of rotational symmetry into a discrete symmetry - you might have seen it in your own sink! These are photos of water flowing down vertically and being distorted into a horizontal direction. The first photo shows rotational symmetry. The following photo shows a distortion by which the water is spread out into 14 discrete beams.
These photos have been published in
Hancock, M.J. and Bush, J.W.M., 2002. Fluid pipes, J. Fluid Mech., 466, 285-304.
See also Fluid Polygons and Polyhedra.