I began by taking an perfectly square crop of a large part of the original.
For this particular image I did a horizontal flip, followed by a vertical flip, each time using "lighten" blending mode instead of "difference."
This was followed by a 90 degree rotation, also using lighten mode, and then a 45 degree rotation. For the 45 degree layer, I also used the transform->scale function to make that layer smaller, but still centered.
Finally, I tried to sharpen up the image with some enhancement ofthe lines by sharpening, and then used the "burn" tool to bring out the interesting little pattern in the center which was very faint.