As you play through the game, Professor Tetra will eventually inform you of being able to access the "Alt World". The Alt World is a repeat of all of the stages in the standard world, but with a twist. These puzzles are done a bit differently. All the puzzles in the standard world are duplicated so you can get Pokémon here if you haven't yet got them in the main world. Each stage also has its own set of challenges and Picrite rewards for completing them.
However, while the Pokémon in each area is the same between worlds, the placement and order of them varies.