Posers and Puzzles

Posers and Puzzles

  1. Joined
    25 Aug '06
    Moves
    0
    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. Standard membercelticcountry
    Copyright ©2001-2006
    Eastbourne
    Joined
    20 Sep '04
    Moves
    16434
    03 Sep '06 10:51
    I noded off reading that.
  3. Joined
    29 Apr '05
    Moves
    827
    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. Standard membersonhouse
    Fast and Curious
    slatington, pa, usa
    Joined
    28 Dec '04
    Moves
    52874
    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. Standard membercelticcountry
    Copyright ©2001-2006
    Eastbourne
    Joined
    20 Sep '04
    Moves
    16434
    03 Sep '06 14:00
    some go on forever
  6. Standard memberPalynka
    Upward Spiral
    Halfway
    Joined
    02 Aug '04
    Moves
    8702
    03 Sep '06 18:43
    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?
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