Graph with black & white nodes

At time t=0 each node of a graph is initially colored white or black. At times t=1,2,3,... all the nodes are simultaneously given a color according to the following rule: if node X has more white neighbors than black ones, then node X becomes white; if node X has more black neighbors than white ones, then node X becomes black; otherwise node X doesn't change color.
Prove: after a final number of steps the graph reaches a stable state or a period of length 2.
Stable state example:
W---W
Period 2 example:
W---B
(W=white, B=black)

I noded off reading that.

I didnt understand anything either. Maybe it would make more sense to me if it was written in german 😛

Originally posted by crazyblue
I didnt understand anything either. Maybe it would make more sense to me if it was written in german 😛

It sounds like a variation of the game of 'life' invented about 30 years ago, except that one was done on a spreadsheet matrix and had rules about reproduction, death and such. Intricate patterns that move and others that flip flop in place and others that die out completely appear.

some go on forever

Originally posted by sonhouse
It sounds like a variation of the game of 'life' invented about 30 years ago, except that one was done on a spreadsheet matrix and had rules about reproduction, death and such. Intricate patterns that move and others that flip flop in place and others that die out completely appear.

The Sugarscape?