I have taken interest in Conway's Game of Life and want to know if you guys can help me with a mathematical problem :) That is what this website is for right?
You need to be familiar with the rules of his game before answering this question I suppose.
Simply put, I want to figure out how many generation repetitions are possible on a give X by X game board.
Let me make a simplified example. We will use a number from 0-9 to represent each generation. Now let's say that we run the program and it calculates generation after generation. After 10 generations we have this historical data of the generations calculated: 5,3,8,6,1,9,4,5,2,6. This data contains no stagnation yet. Let's continue: 5,3,8,6,1,9,4,5,2,6,7,8,7,8,7,8,7,8. No this data contains stagnation that involves 2 generations repeating. Here is data that involves 3 generations repeating: 6,4,2,7,4,6,7,4,6,7,4,6. And 4 generations repeating: 3,6,3,8,9,2,0,5,2,9,0,5,2,9,0,5,2,9.
In a real 8 by 8 matrix we can represent the whole matrix using 8 integers holding an integer from 0-255 each representing one row of the matrix. Like this: {230,100,034,010,178,234,098,111} One of these represents one number in my simplified answer. So if I make an example using this form for a stagnation of 2 then it looks like this (notice that I only change the second row): {230,100,034,010,178,234,098,111} {230,101,034,010,178,234,098,111} {230,100,034,010,178,234,098,111} {230,101,034,010,178,234,098,111}
So again, is it possible to figure out what is the maximum stagnation period possible on a X by X game board?
I am not sure what tags should be associated with this question. Feel free to suggest some.