Here are some quasi-periodic designs of five-fold rotational symmetry. They relate to the Penrose tiling and use the method of “quasiperiodic patterns of 5-fold symmetry …“. For all three images the wave packages for the anamorphic mappings X(x,y) and Y(x,y) use the basic waves cos(x) and sin(x). This gives us mirror symmetry.
Note that this images are very large. You can zoom in and scroll around to explore them. They are different only because I used different input images.
Using a black and red bug on a yellow flower gave this:
A clematis made that:
And a red day-lily resulted in:
At first sight these images resemble same 19th century wallpapers.