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Undoubtfully the number is really large, but I'm not sure what exactly you mean by cube Planck lengths. A comparison to atoms would be more clear.

Still, it wouldn't have to. Since most arrays would have pieces with lower numbers( 2,4,8 ) you could very efficiently compress the data.

At some point you would run out of memory but it would be playable. Just like those Game of Life implementations with seemingly infinite grid.

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Planck length is a theoretical very small unit of length in physics. It is the scale of quantum foam and several orders of magnitude smaller than all those fancy particles like quarks, electrons, protons and atoms: https://en.wikipedia.org/wiki/Orders_of_magnitude_%28length%...

BTW you are right about compressing: you could store the initial state very efficiently, and probably even play the to the end without trouble.

if you store it with log2(n) you could easily store everything with a single byte. That brings the storage requirements down considerably. Though you still have huge issues with storage, not to mention input. For input you'd need 4096 combinations!

You can even do 2 numbers per byte (11 takes 4 bits).

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