Take the 2-minute tour ×  What is the behavior of Conway's game
of life 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 ne