Up to now we have never encounter "true fractality" in the hierarchical cascade of "atoms" (to the greek sense) the matter is made ok: atoms are not like molecules. nucleus and electrons are not like atoms. protons and neutrons are different. Quarks and gluons are a lot different to them.
And there are really quantum units of things that you can't subdivide. And the gravity plays to large distance rather than to short distance where electrostatic forces for instance rules a lot more. So your small "universe" could not be made of electric charges and photons and so on, for instance, and would be organised with subparticules and force making it totally different to our.
Besides, From molecules and below the hierarchy is very tight, why our macroscopic world is a lot more loose. But at the same time, uncertainty principle make the notion of distances and positions more and more blurry at the very small scales. So your small universe would be constrained by all this.