Game of Life meets Chaos Theory












3












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I was wondering if anyone had any examples of Chaos Theory in John Conway's Game of Life, i.e. a position which is stable, but change just one cell and the population becomes extinct.






reference-request







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  • $begingroup$
    There is a big discussion on mathoverflow: mathoverflow.net/questions/132687/…
    $endgroup$
    – rhsquared
    43 mins ago










  • $begingroup$
    I can't put this as an answer because it is the very opposite of chaos: with 4 cells forming a square block, this is stable. If you remove any one cell, the original shape immediately heals.
    $endgroup$
    – Weather Vane
    11 mins ago
















3












$begingroup$


I was wondering if anyone had any examples of Chaos Theory in John Conway's Game of Life, i.e. a position which is stable, but change just one cell and the population becomes extinct.






reference-request







share|improve this question









$endgroup$












  • $begingroup$
    There is a big discussion on mathoverflow: mathoverflow.net/questions/132687/…
    $endgroup$
    – rhsquared
    43 mins ago










  • $begingroup$
    I can't put this as an answer because it is the very opposite of chaos: with 4 cells forming a square block, this is stable. If you remove any one cell, the original shape immediately heals.
    $endgroup$
    – Weather Vane
    11 mins ago














3












3








3





$begingroup$


I was wondering if anyone had any examples of Chaos Theory in John Conway's Game of Life, i.e. a position which is stable, but change just one cell and the population becomes extinct.






reference-request







share|improve this question









$endgroup$




I was wondering if anyone had any examples of Chaos Theory in John Conway's Game of Life, i.e. a position which is stable, but change just one cell and the population becomes extinct.






reference-request




reference-request






share|improve this question













share|improve this question











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asked 1 hour ago









JonMark PerryJonMark Perry

21.1k64199




21.1k64199












  • $begingroup$
    There is a big discussion on mathoverflow: mathoverflow.net/questions/132687/…
    $endgroup$
    – rhsquared
    43 mins ago










  • $begingroup$
    I can't put this as an answer because it is the very opposite of chaos: with 4 cells forming a square block, this is stable. If you remove any one cell, the original shape immediately heals.
    $endgroup$
    – Weather Vane
    11 mins ago


















  • $begingroup$
    There is a big discussion on mathoverflow: mathoverflow.net/questions/132687/…
    $endgroup$
    – rhsquared
    43 mins ago










  • $begingroup$
    I can't put this as an answer because it is the very opposite of chaos: with 4 cells forming a square block, this is stable. If you remove any one cell, the original shape immediately heals.
    $endgroup$
    – Weather Vane
    11 mins ago
















$begingroup$
There is a big discussion on mathoverflow: mathoverflow.net/questions/132687/…
$endgroup$
– rhsquared
43 mins ago




$begingroup$
There is a big discussion on mathoverflow: mathoverflow.net/questions/132687/…
$endgroup$
– rhsquared
43 mins ago












$begingroup$
I can't put this as an answer because it is the very opposite of chaos: with 4 cells forming a square block, this is stable. If you remove any one cell, the original shape immediately heals.
$endgroup$
– Weather Vane
11 mins ago




$begingroup$
I can't put this as an answer because it is the very opposite of chaos: with 4 cells forming a square block, this is stable. If you remove any one cell, the original shape immediately heals.
$endgroup$
– Weather Vane
11 mins ago










2 Answers
2






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$begingroup$

One of the simplest still-lifes is the "beehive":



. # # .

# . . #

. # # .


If you remove the cell at one end, it will eat itself over the next few generations and nothing will remain.



I suspect there is a position with the properties that (1) its population remains nonzero but bounded, (2) if you change one cell you can make it go extinct, and (3) if you change one cell you can make it grow without limit (via glider guns or the like), but that would be much more difficult to construct.






share|improve this answer











$endgroup$





















    1












    $begingroup$

    There is this configuration which is stable:



    .#.    
    
#.#  
    
.#.


    If you take any of them, it will die.






    share|improve this answer









    $endgroup$














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      2 Answers
      2






      active

      oldest

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      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

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      2












      $begingroup$

      One of the simplest still-lifes is the "beehive":



      . # # .
      
# . . #
      
. # # .


      If you remove the cell at one end, it will eat itself over the next few generations and nothing will remain.



      I suspect there is a position with the properties that (1) its population remains nonzero but bounded, (2) if you change one cell you can make it go extinct, and (3) if you change one cell you can make it grow without limit (via glider guns or the like), but that would be much more difficult to construct.






      share|improve this answer











      $endgroup$


















        2












        $begingroup$

        One of the simplest still-lifes is the "beehive":



        . # # .
        
# . . #
        
. # # .


        If you remove the cell at one end, it will eat itself over the next few generations and nothing will remain.



        I suspect there is a position with the properties that (1) its population remains nonzero but bounded, (2) if you change one cell you can make it go extinct, and (3) if you change one cell you can make it grow without limit (via glider guns or the like), but that would be much more difficult to construct.






        share|improve this answer











        $endgroup$
















          2












          2








          2





          $begingroup$

          One of the simplest still-lifes is the "beehive":



          . # # .
          
# . . #
          
. # # .


          If you remove the cell at one end, it will eat itself over the next few generations and nothing will remain.



          I suspect there is a position with the properties that (1) its population remains nonzero but bounded, (2) if you change one cell you can make it go extinct, and (3) if you change one cell you can make it grow without limit (via glider guns or the like), but that would be much more difficult to construct.






          share|improve this answer











          $endgroup$



          One of the simplest still-lifes is the "beehive":



          . # # .
          
# . . #
          
. # # .


          If you remove the cell at one end, it will eat itself over the next few generations and nothing will remain.



          I suspect there is a position with the properties that (1) its population remains nonzero but bounded, (2) if you change one cell you can make it go extinct, and (3) if you change one cell you can make it grow without limit (via glider guns or the like), but that would be much more difficult to construct.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 40 mins ago

























          answered 47 mins ago









          Gareth McCaughan♦Gareth McCaughan

          68.8k3174270




          68.8k3174270























              1












              $begingroup$

              There is this configuration which is stable:



              .#.    
              
#.#  
              
.#.


              If you take any of them, it will die.






              share|improve this answer









              $endgroup$


















                1












                $begingroup$

                There is this configuration which is stable:



                .#.    
                
#.#  
                
.#.


                If you take any of them, it will die.






                share|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  There is this configuration which is stable:



                  .#.    
                  
#.#  
                  
.#.


                  If you take any of them, it will die.






                  share|improve this answer









                  $endgroup$



                  There is this configuration which is stable:



                  .#.    
                  
#.#  
                  
.#.


                  If you take any of them, it will die.







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 35 mins ago









                  rhsquaredrhsquared

                  8,31031949




                  8,31031949






























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