I now want to see some images. Using a photo of a caterpillar as input image I get
I used the simplest quasiperiodic mapping functions resulting from the theory of the last post
A pixel at position (x,y) gets the color of the input image at the position(X,Y). The center of perfect 5-fold symmetry is near the lower left corner. Further out you can recognize the head of the caterpillar. At higher magnification you see more clearly how the caterpillar is “anamorphized” into a quasiperiodic image:
To see the quasiperiodicity we need the image of a larger region. Here is the result from an image of a fly on Muscary flowers:￼
Do you see the various 5-pointed stars and how they are approximately repeated at other places?
Note that these images are mirror symmetric with respect to the x-axis going through the center of perfect rotational symmetry. Actually, it is difficult to create images that are not mirror symmetric. That is quite different to rosettes.
If you want to experiment then look at my public Github repository: https://github.com/PeterStampfli/creatingSymmetries. It has the code for generating images like that and much more. Start with: warpingKaleidoscope.html. Your comments and improvements are welcome. Keep in mind that this is a moving target.