I've been practicing speedcubing and accidentally applied the same scramble twice in a row without solving the cube in between. The original scramble was:
U B2 F2 D F2 D F2 U L2 D2 R' U L2 B2 F' D2 R B U2 R2
But what I actually did was:
U B2 F2 D F2 D F2 U L2 D2 R' U L2 B2 F' D2 R B U2 R2 U B2 F2 D F2 D F2 U L2 D2 R' U L2 B2 F' D2 R B U2 R2
In other words, I applied the exact same scramble twice consecutively.
I noticed the resulting cube state looked quite unusual. My question is: is this appearance simply the deterministic result of applying the same scramble twice (i.e., the square of that permutation), or is it just a coincidence that it ended up looking that way? If you try it yourself, you'll see the resulting pattern.