I've been struggling for a while with the Between Worlds Android game, and have not yet solved it. I've only noticed a couple vague properties that hold in localized cases.
To operate the puzzle, select the square, pentagon, or hexagon and move the lever. The spheres and rings on the right will move by some unknown conditions.
I would provide a summary of what I've done, but every example has at least two counterexamples. The only consistent pattern I've noticed is that, when a pair of pieces are in alignment, selecting the button counterclockwise of the circle that's in alignment doesn't move it out of place - but it doesn't hold in all cases, and I'm uncertain as to why.
What is the logical pattern behind this puzzle? How do I solve it?