the user should be able to manipulate groups of shapes that are not predetermined in any way
the user may decide to flip any other group of shapes as long as they are viable:

Above are all of the different possible groups that could be flipped/rotated in the first stage of the design. In my initial example, the user chose the group highlighted in black, and thus this design was created:
but as you can imagine, the outcome could have been different in many ways depending on the choice of the user. Assuming the image above was the result of the first move, the next move has even more options--as the user manipulates the design, new possibilities emerge.