Note that for a Life board what one means by "random" is not at all obvious. How likely are cells to start as alive? This percentage could drastically alter the behavior of the board.
There's a more general question that you seem to be implicitly asking: Is there a life configuration which will have a reasonably high probability of of expanding across most random fields? My initial conjecture is something like "no, unless the initial probability of a cell in any given spot is very low". The rough intuition here is that even if one has a functionally smart configuration in Life, it will not be able to see what is happening far away from it until it is too late. Essentially, the speed of observation and the speed of bad things happening to it occur at about the same speed.
Random
If the board is big enough, I don't know that it matters what the chance of any given cell starting alive or dead is.
Sight in Life
I'm not sure if this is possible, but I can imagine a Life Entity that generates and fires radar projectiles which also continuously generate their own projectiles firing back at the entity. (The entity has some kind of membrane that easily absorbs the returning projectiles.) If the radar particle collides with something, it is disrupted and stops sending particles back. The entity is able to observe events in the d...
Conway’s Game of Life is Turing-complete. Therefore, it is possible to create an AI in it. If you created a 3^^3 by 3^^3 Life board, setting the initial state at random, presumably somewhere an AI would be created. Would this AI somehow take over the whole game board, if given enough time?
Would this be visible from the top, as it were?
EDIT: I probably meant 3^^^3, sorry. Also, by generating at random, I meant 50% chance on. But any other chance would work too, I suspect.