Much as you deserve a basalting, we still need you, so I won't.
Besides which, you're on to something. The original shot (with added contrast) is:

It was composed within the 5x4 frame and I did my best for it to work. Two things that mattered to me: getting the suggestion of a straight line at the top and having a single, whole, large hexagon to act as feature at the bottom. I agree that a large helium-filled balloon would have made an ideal accessory but Calumet (Iceland) were out of stock. So very hard to get a more zenithal view-point. More importantly, the more zenithal view would have made the picture quasi-featureless. Making the picture square gives a lot of importance to the round tile which I don't like but which I could not compose out. So cropping to square is out too. However, making the mirrored picture square is a good idea as it reinforces the symmetry:

The mirrored picture is thus tidied up nicely, IMO. It's got more of the psychedelic teleidoscope feel to it. Playful rather than childish, I hope. I quite like the effect overall. Any more opinions?
Besides, to comment your point, isn't finding patterns in a photograph the very basis of composition? Isn't providing potential patterns what we are meant to be doing as photographers?
Charles