The purpose of these is to provide more treasures to find.

Each naughty picture requires four pieces.
2 pictures added to chest-pool after each abilty.  (8 pieces)
Corresponding town has 4 pieces.
And each dungeon contains 4 pieces, but for multiple pictures, but no dungeon (is likely to) contain all the pieces of any single set.
After acquiring pieces, the player needs to manually put them together, choosing where to place them next to each other. All pieces are seen at once.
The pictures on the pieces are small and look similar, as black-and-white lineart, so the player needs to pay attention to the shapes and where the lines connect ebtween pieces.
When a picture is correctly assembled, it changes into a full-color version, which can then be viewed at full-size.