We now want an image with periodic or quasi-periodic rotational symmetry that changes colors upon mirroring. Thus we need a color-changing function U(x,y) that changes the sign

U(x,-y)=-U(x,y)

for its mirror image at the x-axis. We can easily get this from the difference between packages of wave functions f(x,y) and their mirror images

U(x,y)=f(x,y)-f(x,-y).

For more details you can look at the last post. This is a result with 8-fold rotational symmetry and 2-color mirror symmetry:

The center of perfect symmetry lies outside this image. You can see local approximate 2-color mirror symmetry in many places as well as approximate 8-fold and 4-fold rotational symmetry.

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