A word for something that is "whole unto itself"

If you take something and cut it in half, you end up with two things that are mostly identical (although perhaps smaller) pieces of the original.

I will provide a word for those pieces as well as a word for the original thing.

A word for the smaller pieces is microcosm:

[Merriam-Webster]
2 : a community or other unity that is an epitome (see EPITOME sense 2) of a larger unity
// The suburb has been the microcosm of the city.

[thesaurus entry]
something (such as a place or an event) that is seen as a small version of something much larger
// The village is a microcosm of the whole country.
// The game was a microcosm of the entire season.

The thesaurus entry also provides alternative words such as cross section.

There might be a more technical term for the original, undivided piece than I can come up with.

But one word, which can be understood analogously, is hydralike. Although it has no actual entry in main dictionaries, it's formed from the base word hydra and the suffix like. It means, as at Definitions, "resembling a hydra."

From Merriam-Webster's definition of hydra:

1 : a many-headed serpent or monster in Greek mythology that was slain by Hercules and each head of which when cut off was replaced by two others

In short, one head, when cut, becomes two identical heads.

This is an analogous idea to cutting a cloud in half and ending up with two clouds, or cutting a worm in half and ending up with two worms. Applying it to a scream or a hole is even more metaphorical, but the essential concept is the same.