Emergent Property Problem

Emergent properties are everywhere in physics.
Some of the biggest ones:
Chemistry is the emergent property of Quantum Mechanics.
Biology is the emergent property of Chemistry.
Psychology is the emergent property of Biology.
Sociology is the emergent property of Psychology.

I think Quantum Mechanics (and Relativity) is also an emergent property of a Cellular Automaton Quantum Computer (CAQC) operating at Planck scale. If so how we can find out its operation rules?

How about we try to understand the general mathematical problem first?

The problem is this:
We are given the high level (macro scale) rules of an emergent property and asked, what are the low level (micro scale) rules which created those high level rules?
(Also the reverse of this problem is another big problem.)

Could we figure out rules of Quantum Mechanics, only from rules of Chemistry (and vice versa)?

When we try to solve a complex problem, obviously we should try to start with a simpler version of it, whenever possible.

There are many methods for Computational Fluid Dynamics (CFD) simulations. If we were given 2D fluid simulation videos of certain resolution and duration for each different method, could we analyze those videos using a computer software to find out which video is produced by which method? At what resolution and what duration the problem becomes solvable/unsolvable for certain? Moreover, at what resolution and what duration we can or cannot figure out the specific rules for each method?

How about an even simpler version of the problem:
What if we used two-dimensional cellular automaton (2D CA)?
Imagine we run any 2D CA algorithm using X*Y cells and for N time steps to create a grayscale video.
Also imagine, if each grayscale pixel in the video calculated as sum or average of M by M cells, like a tile.
At what video resolution and what video duration, we can or cannot figure out the full rule set of the 2D CA algorithm?

How about an even simpler version of the problem:
What if we used one-dimensional cellular automaton (1D CA)?
Imagine we run any 1D CA algorithm using X cells and for N time steps to create a grayscale video.
Also imagine, if each grayscale pixel in the video calculated as sum or average of M cells, like a tile.
At what video resolution and what video duration, we can or cannot figure out the full rule set of the 1D CA algorithm?

(And the reverse problem is this:
Assume the grayscale video described above for 1D/2D CA, shows the operation of another CA (which is the emergent property).
Given the rule set of any 1D/2D CA, predict the rule set of its emergent property CA for any given tile size.)

Also what if the problem for either direction has a constraint?
For example, what if we already know, the unknown 1D/2D CA we trying to figure out, is a Reversible CA?

https://en.wikipedia.org/wiki/Cellular_automaton
https://en.wikipedia.org/wiki/Elementary_cellular_automaton
https://en.wikipedia.org/wiki/Reversible_cellular_automaton