I got two puzzles for you, /sci/.
Which of the 6 figures at the buttom fit the pattern; and more importantly, why?
And here there are three versions of each shape. There is the original, then there is one cut into two where the right half is flipped 180 degrees, and one where the both halves are mirrored horizontally. |_| is the original and _|_ is the one with both mirrored, thus the answer is again upper right.
All of them do, and more importantly, because you can encode the information in the drawings as an integer, so we have a finite integer sequence which can NOT determine a unique "next term", any term is equally "plausible", asking for which one fits is subjective and irrational.
Consider the lines around the squares, and cancel the ones overlapping. First row gives us that in the middle column the NW or the NE line corresponds with the left line in the left column. The second row gives us that there is a correspondence between the upper line in the left column and the NE line in the middle, so that we now know the middle columns to be squares rotated 45 degrees clockwise.
Using the remarks above, it is easy to see that the third row gives the square in the lower left option.