Symmetries are important for design because they determine the overall appearance of an image. Rotational symmetry without mirror symmetry makes a dynamical image, whereas additional mirror symmetries give a more static appearance. Generally, an image becomes more abstract if we have more symmetry.
As rosettes are essentially Friezes wound around a central point we can use all the symmetries of Friezes for rosettes too, although they may be distorted. As an example, we now look at the distorted mirror symmetry at r=1. It imposes the condition f(1/r)=f(r) on the mapping functions, thus they are
The images are somehow bloated around r=1. This makes it difficult to create nice images. A photo of a minstrel bug gave this
and a moth morphed into that
See how the outside of the rosette is wrapped and squashed to the inside. Near the symmetry “axis” r=1 we get strong deformations and abstract designs. Far away details of the input image remain.
And now for something different: Let’s fire the anti-science fools on april 1 !