This is the orignal page describing the idea:
http://cranmer.home.cern.ch/cranmer/html/game_of_life.html
In the image above, you can see the original image of the rocks quickly approach either an area of stable life or total death. Then the the area of stable life attempts to find a stable shape. Normally that would be a circle, but because the life wraps around the edges (like a torus), it ends up filling the entire space. At one point, I only use 1 out of every 10 images to speed up the convergence. IT took about 700 iterations in total.
See also:
- ChaosLife? - what happens when the we adjust the rule a bit....
- SquareLife? - not square for long...
Errata:
The page linked to above quotes the super-stable point as p= 0.564261 = p*, but that is incorrect. I believe that is the value of p+: the value beyond which the board will die. Clearly from the graph, the stable life value is a little less than 0.4 I need to solve this equation, but in the images shown above, the grey value that life is attracted to is p = 0.368621826172 which seems consistent with the graph.
Note From Clint Sprott - the super-stable point is close to 1/e = 0.36787944117144233