cyclic group Rorschach test butterfly fractals self-similarity or symmetry fr
For example, the group underlying mirror symmetry is the cyclic group of two elements, 




Z


/

2

Z



{\displaystyle \mathbb {Z} /2\mathbb {Z} }

. A Rorschach test is a figure invariant by this symmetry, as well as a butterfly, and animal bodies more generally (at least on the surface). Waves on the sea surface possess translation symmetry: moving one's viewpoint by the distance between wave crests does not change one's view of the sea. Furthermore, fractals possess (usually approximate) self-similarity.
