What is the behavior of [Conway's game of life][1] when the initial position is random? -- We can ask this question on an infinite grid or on an $n$ by $n$ table (planar or on a torus). Specifically suppose that to start with every cell is alive with probability $p$ and these probabilities are statistically independent. This question was motivated by a recent talk by Béla Bollobás on bootstrap percolation.


  [1]: http://en.wikipedia.org/wiki/Conway's_Game_of_Life