Question about Conway's Life ?

Question

I want to know is someone know some kind of formulas used to predict the average lifetime of a Conway's world ( Cellular Automata rule 23-3. ) from the worldsize of said Conway's world.

If there are no such formula. I am currently trying to do this problem by using statistics. See this link for more info :

http://tech.groups.yahoo.com/group/cellularautomataresearch/messages

Thank you.

Answer 1

(This is a private joke folks)

Shall I ask my dog?

Answer 2

I know what Conway's Game of Life is, but how do you define a lifetime for a Conway world?

____

Answer 3

some suugestions

1 Moving average method

use the  theory of estimation of  Population Mean

Answer 4

I think there may already be literature on this subject, try checking google scholar. (as far as finding averages via statistical methods)

If not, your best bet would be to translate the game of life problem into some similar dynamic problem, and see if you can come up with a solution for that. Another approach would be a brute force method, and try to come up with a sequence. For example, start with n = 1, and try to find the average lifetime of a 1x1 world. (there are 2 possible initial states, one is already dead, the other will take 1 turn to die). Then move on to a 2x2 world, and so on. already at n=3, you have 512 different set of initial conditions, but you'll notice patterns, and you should be able to greatly decrease the number you have to try.

Also I strongly suggest you not use someone else's program, and use your own. Are you sure it counts cycles correctly? When/how does it decide when a world repeats?

Edit: Looking at all of this over again, I'm thinking the software you're using is your own. In any event, take a look at lots of smaller examples. One very easy thing to notice is that as your world gets larger, the average lifespan also grows. Or, no matter what the size of your world is, if only 1 or 2 life is placed, it will always have a life time of 1. You can make similar observations with n, n-1, n-2 observations being placed. There are many many other things you can observe... where average lifetime peaks (based on how many initial life) on a given world, or in general, it's distrubition, symmetry, etc.