The image of the last post is quite bewildering. To get a calmer and simpler image I imposed mirror symmetries on the original image. A vertical mirror line results from taking the absolute value of the x-coordinate. Similarly, I take the absolute value of the y-coordinate to have a horizontal mirror. A diagonal mirror is simulated by exchanging the x- and y-coordinates if x is larger than y.
Thus I got:
Here we can see more clearly how the image details double upon going inside.