I played the Game of Life intensively for a while. I tried to keep things alive from all kinds of initial configurations and succeeded up to about 1000 iterations maximally. Everything died all the time.
Sometimes a change in two initial elements gave huge differences and chaos theory popped up in my mind.
Still there are initial configurations leading to eternal life, eventhough this life is not very interesting. There is no significant evolution of life forms, if this is possible in the first place.
Can we catch the evolution in some kind of mathematical formula that has the initial configuration as input, returning a yes, no, or probability of eternal life? Or does one has to run the game from every educated initial configuration?