>>2
First problem is aliasing/alignment artifacts. That is, even if you have lots of semantically similar components, unless they are also located in the same position in respect to the containing quadtree nodes they are going to hash into a polynomial number of different keys. Plus the same problem for
temporal alignment of processes, if I understand correctly.
Then, any computation in the Game of Life is by necessity local, I mean, you don't have anything like random access, your signals have to physically propagate across the virtual space. So it's not very efficient model to begin with, similar to Turing Machine, actually. Hashlife
might speed up this, but only if you have larger exactly repeating patterns in the entire region where the "wires" in question are located. I think. I'm not sure.
All in all I suspect that you will lose nothing except some problems if you go for "hash lambda calculus" or "hash SKI" instead.