You can do some sort of lazy evaluation. I took the example you gave with the 4x4 grid (by the way you have a typo: "we shall take a 3x3 Life grid"), and ran it forwards, and it converges to all empty squares in 4 steps. See this doc for calculations.

Even if it doesn't converge, you can add another symbol to the system and continue playing the game with it. You can think of the symbol as a function. In my document x = compute_cell(x=2,y=2,t=2)