[readerrrr]

A period of a single cell would take 35328^2 periods and (2048*2048)^2 cells of the most underlying game of life simulation.

[nitrogen]

A Life acceleration algorithm would help with that, but each cell would still require 4Tb of storage (though that storage could be shared by all cells, II think).

https://en.wikipedia.org/wiki/Hashlife

[readerrrr]

And there is not real purpose since the rules are the same for every level. Making them different and more complex would be interesting.