PPT Slide
The most symmetric pattern is the most boring one: a homogeneous background, without spatial differentiation, and having complete translational and rotational symmetry.
It is common to regard a kaleidoscopic pattern as having a high degree of symmetry, but it has much less symmetry than the homogeneous state.
When a spatially differentiated pattern emerges from a homogeneous state, one says that a symmetry has been broken. One of the great mysteries of natural patterns is that when a homogeneous symmetry is broken by the application of a stress, the discrete symmetry of the emergent pattern often is completely unrelated to the original homogeneous symmetry, as well as to the symmetry of the stress.