The third one seems to be rule based but can be interpreted in two ways:
- The square binding prevents movement from the inner four tiles.
- The long line needs an arrow binding or it rotates.
Seeing as the first compares best to the fourth picture the most obvious choice would be the first one. Which makes me think it would be:
The shape can be displayed in a 4x4 grid in all examples. Seeing the size of the possible solution makes me believe the solution will be a 4x4 grid.
The squares in picture one are in the inner 2x2 block and move away from the center in the next images. In the third picture it would be very likely for these squares to have the position (-1,-1)(5,5). Because of this it would be logical for this to happen in the solution as the fourth picture takes the same position.
The outside half squares follow the rule; if you are not in the inner 2x2 grid then invert your position. If you are inside the 2x2 grid then hold your position for a single turn.
The last rule is that of the rotation through lack of squares in the field. When there are no squares in the field the grid rotates (either left or right) by 90 degrees and squares are created at (2,2)(3,3).
So for the actual solution the half squares would be inverted and moved to the inner 2x2 grid. The squares move to the outside and the center lines retain there position because of the presence of squares.