Seems I have been alternating a lot this TaD between doing something with my hands and doing something with GIMP.
I took an image from my TaD of 19-February-2011 and performed some simple operations to it: (1) selected and copied half the image, (2) flipped the image vertically or horizontally (depending on whether my selection was vertical or horizontal), and (3) repeated step (1) & (2) for the other dimension.
I also rotated the image 30 or 45 in some cases before applying the above steps.
This produced some pretty kaleidoscope effects (and no mirror required - although, to be fair, it think it would have been easier to use mirrors).