Given an infinite grid of squares, some marked alive (which stay alive forever,) some marked dead at any time(like Conway's game of life) and 1 alive at the beginning, there is an algorithm. It starts with a list of the living cells, which does not change through an execution. It goes through each cell, and with a probability $p$, will choose one of the 8 surrounding cells one that is dead to make alive. Two living cells can not select the same cell. Every surrounding dead cell is equally likely to be chosen. If it is completely surrounded by living cells, it will not spread. After $t$ executions of the algorithm, on average how many cells will be alive in terms of $t$ and $p$.
(Note: If you know a better way to restate this question, please do so. I am not familiar with problems of this type and so do not know the best way to state it.)