I'm waiting for someone to proofread my general instructions on the process and variations so for now, I'll just post what I did to get this image. I started by resizing the image into a square and then used the smudge tool to mess it up somewhat. These are steps 4, 5 and 6 of the soon to be posted tutorial. I used the Difference blend mode in all 3 steps.
4. Duplicate the BG layer and flip it horizontally (edit/transform/flip horizontal). Find a blend mode for this layer that you like. My favorite one to start with is Difference. Some modes will keep it looking symmetrical and some wont. Flatten (shft+ctrl+e).
5. Duplicate the BG layer and flip it vertically (edit/transform/flip vertical). Find a blend mode for this layer that you like and flatten.
6. Duplicate the BG layer and rotate it 90 degrees (edit/transform/rotate 90 CW).Find a blend mode for this layer that you like and flatten.
This is awesome, Ken. That is some flipping! I was reading through the instruction and wondered what the original was before I saw the recreate image! What a transformation! I think your use of blend mode is very effective here. Excellent thinking. TFS.