> the Game of Life supports self-replication and is Turing-complete, and therefore can support arbitrarily intelligent programs.

I think people will disagree about whether “Turing-complete” is powerful enough for supporting intelligence but let’s assume it does.

> So, will a random initial position (tend to) be filled with super-intelligent life forms, or will the chaos reign?

Even if it doesn’t, it might take only one intelligent life form for the space to (eventually) get filled with it (the game of life doesn’t heave energy constraints that make it hard to travel over long distances, so I don’t see a reason why it wouldn’t. On the other hand, maybe my assumption that all intelligent life would want to expand is wrong), and in an infinite plane, it’s likely (¿certain?) one will exist.

On the other hand it’s likely more than one exists, and they might be able to exterminate each other.