I'm not understanding your point - which may be completely on me - but your example here - why would the "child" universe require more memory than the parent has available?
On my computer, I can write 2D simulations, or 1D. Or even 4D or 5D. The simulated universe doesn't have to have any relation to the host one.
That's magical thinking. I was referring to the total simulated state space, which does not depend on the number of dimensions or any other parameter of the simulation.
Not sure that sentence means anything. Of course the dimensionality has everything to do with the state space. It grows, by definition, geometrically with the number of dimensions.
If your state space is 16 bits, then you can create a 4x4 2-dimensional space or a 2x2x2x2 4-dimensional space, but the total space is still 16 bits. You cannot simulate a 32-bit state space on a machine with only 16 bits of memory, regardless of how many dimensions the simulated space has.
Ok a precision argument I understand. But the number of states will grow geometrically. And also, we use multiple words to create larger numbers all the time in simulation. I'm not sure how important this is at all.
I'm not talking about 32 bits of precision; I'm talking about 32 bits of data. If you only have 16 bits then the number of unique states you can represent is 65536, and it does not matter how you divide that up into dimensions.