For a kaleidoscope with six-fold rotational symmetry and using three distinct colors I made up a new kind of mirrors that exchanges colors cyclically. That means that color number one becomes color number 2 in the mirror image. Then color 2 becomes color 3 and color 3 becomes color 1. Thus the mirror image of a mirror image is not identical to the original image because it has different colors. The images of such a kaleidoscope are not periodic.
Using the methods discussed in the last post I get images like that: