Trophy Garden

After you have obtained the National Pokédex, when you go to the Pokémon Mansion in Route 212, Mr. Backlot will talk about his garden and how a specific Pokémon has come up to him. These Pokémon are typically not found in the garden and change every day. You will find both the current day's Pokémon and the previous day's Pokémon in at any one time

These aren't chosen at random but will follow sequentially in National Pokédex order and will only progress when you speak to Mr. Backlot.