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.

**Many thanks for all the answers.** A related question that I thought about is what is the situation for "noisy" versions of Conway's game of life? For example if in each round a live cell dies with probability $t$ and a dead cell gets life with probability $s$ and both $t$ and $s$ are small numbers and all these probabilities are independent.

Another example is to consider the following probabilistic variant of the rule of the game itself ($t$ is a small real number):

Any live cell with fewer than two live neighbours dies with probability $1−t$.

Any live cell with two or three live neighbours lives with probability $1−t$ on to the next generation.

Any live cell with more than three live neighbours dies with probability $1−t$.

Any dead cell with exactly three live neighbours becomes a live cell with probability $1−t$.

Following some comments below I asked about the computational power of such a noisy version [over here][2].

**Update**: Related question http://mathoverflow.net/questions/132687/is-there-any-superstable-configuration-in-the-game-of-life

  [1]: http://en.wikipedia.org/wiki/Conway's_Game_of_Life
  [2]: http://cstheory.stackexchange.com/questions/17914/does-a-noisy-version-of-conways-game-of-life-support-universal-computation