The key feature of fractals as geography is that they are self-similar at different scales. That means that fractal patterns contain copies of themselves. They are, of course, smaller than the base pattern.
So if you create an enclosed space in the shape of a fractal, you're going to have some corridors or rooms that are much smaller than others. Branching off from them will be even smaller spaces, and so on.
The GM will have to set some kind of limit on how small things can get. If matter in the game world is made out of atoms in a similar way to the real world, that will set a limit, but I have played in D&D game worlds where that wasn't true. There is no intrinsic limit in fractals. They're mathematical concepts that don't worry about matter. The views of fractals that we're used to are generated on computer screens, where the screen resolution provides for a limit.
So if you're going to use fractals as dungeon maps, there will be lots of space that the characters can't readily get into. It may be populated by smaller creatures, but monsters in a dungeon that the characters can't get at have limited entertainment value. So if the campaign is to be more than a one-shot, the characters will need ways to change their own scale. There are at least two ways to approach this:
The characters could use magic to make themselves bigger and smaller. They're going to need quite a lot of it, and Dispel Magic would be a powerful attack spell against creatures from a different scale, making them either much smaller, and unable to move quickly, or much larger, and subject to being squashed by the walls around them.
A more interesting approach would be to use different levels of scale as the levels of the dungeon. At the entrance, there is just one instance of the map. You push the button, or whatever, to go to the next level, and there are many instances, and so on.
In either case, there's a potential plot arc in finding out why space in this dungeon is so strange.