Waxing Moon

On the left are 36 photos of the spring 2025 lunar eclipse. Each photo will be randomly flipped, flopped and rotated and then stacked together on a black canvas twice their original size.
How many unique images can this process generate?

Moon Glyph: 36 moon pictures

ProCam on iPhone12, 1 sec. exposure

1

ProCam on iPhone12, 1 sec. exposure

4

ProCam on iPhone12, 1 sec. exposure

16

ProCam on iPhone12, 1 sec. exposure

64

ProCam on iPhone12, 1 sec. exposure

256

ProCam on iPhone12, 1 sec. exposure

1024

ProCam on iPhone12, 1 sec. exposure

4096

ProCam on iPhone12, 1 sec. exposure

The total number of possible unique combination is more than the number of atoms in the universe:
1281658233130699917529529859351240982104676988558886023960606669122834317458911741861617640572769739744318484950341034337902234466651673745923212101046896633844168266030423273077853691337403126297323436641715191069377263690374710623727626081930374833806705280755124054721975812096
Email me if you are interested in prints of these images or want to go over the math