This edit was done using steps 1 through 6, Difference as the blend mode and 2 twirl layers, 1 at 100 degrees and 1 at -100 degrees. I increased the saturation a bit, did a 1% increase in shadows in SH, slight boost in contrast, and sharpened with the High Pass filter. One of the problems with this type of edit is that since there are so many colors and so much detail created, you may have to save at a low setting or resize to smaller dimensions to get it under the 200kb size limit. This was saved at 50%.
In this tutorial, I used Polar Coordinates because that's the filter that got me thinking about the process. Since then I've found that other filters and processes will also produce fun results.
1. Create a square image by either cropping or resizing with the 'Constrain Proportions' unchecked in the Image Size dialogue.
2. Apply Polar Coordinates (filter/distort/polar coordinates) making sure 'Retangular to Polar' is selected.
3. Apply Polar Coordinates again (ctrl+f) and again and again. keep doing this until the center dividing line disappears. It usually takes 10 or so applications. You should now have an image that looks sort of like 2 odd faces looking at each other.
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 won't. 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.
Now it's time to go crazy and be creative! Anything beyond this point would also apply to a standard 4-way flip. Since there are no rules for this, it's up to you to get creative. Maybe add another rotation/blend layer with a 45 degree rotation. I like to try twirling it and see what I get. Create 2 new copies of the BG layer and apply a twirl of say 100 degrees on one and -100 degrees on the other and choose a blend mode for the top layer. If your result seems a bit dark, try using shadow/highlights with a very minor increase in the shadows. Sometimes all it takes is 1%.
If your goal is to end up with a symmetrical edit, be sure to balance out any filter you apply like I did with the twirling example given above. Otherwise, apply filters and see what you get. Go wild with the saturation, contrast etc.
Variations: Instead of using 'Retangular to Polar' in step 2, try 'Polar to Retangular". Actually, many filters or tools can be used instead of Polar Coordinates in step 2. I've just been messing with twirl, wave, zigzag, zoom blur, liquify and even the smudge tool and the paint brush and all are producing cool results. If you do this, modify the number of applications in step 3 or don't use step 3 at all. It really doesn't matter because no matter what you do, you will end up with something interesting!