# Graph with black & white nodes

David113
Posers and Puzzles 01 Sep '06 19:31
1. 01 Sep '06 19:31
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)
2. celticcountry
03 Sep '06 10:51
3. 03 Sep '06 11:28
I didnt understand anything either. Maybe it would make more sense to me if it was written in german 😛
4. sonhouse
Fast and Curious
03 Sep '06 13:51
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.
5. celticcountry