It would appear that you now can have a 'secret base' in Ruby and Sapphire. To Get them, all you have to do is teach a Pokémon TM43 (Secret Power) and find an Indented Wall, Bush or Tree and use it there and one will be created as seen in the Pictures below:

Indent Tree

These are just like the decorating of your bedroom that you could do in GSC, which you can also do here. Once you've got one, you can give it to your friend in the 3rd Slot in the top of a Pokémon Center. In there, there will be a random trainer there who will battle you. There are Loads of Decorations That you can get to put in this Secret Base as you can see by the Picture below:

Serebii's Own Secret Base

With the many decorations...some not even programmed in the game yet but allocated space (curious) but here are the ones that are Programmed into the game and how to get their respective categories anyway.