Geometric designs in the game of "Life".

Byrne, Willaim                              Martin Luther King H.S.
                                            536-8680
                           

Objective:

To predict and discover patterns generated in the game of "Life".

Apparatus Needed

Large checkerboards (one per two students) and flat counters or 
checkers of three different colors.

Recommended Strategy:

The game of "Life" is a fantastic solitaire pastime because of its 
analogy to the rise, fall and alteration of societies of living 
organisms.  The dramatic patterns can be seen using a computer.  The 
game was invented by John Conway, a University of Cambridge 
mathematician, in 1967. 

To play the game, start with a configuration of counters near the 
center of the board.  The rules of the games are as follows:  
(1) Survivals: every counter with two or three neighbors survives for 
the next generation.  (2)Deaths: Each counter with four or more 
neighbors dies (is removed) from overpopulation.  Every counter with 
one neighbor or none dies from isolation.  (3)Births:  Every empty 
cell adjacent to exactly three neighbors- no more, no fewer -  is a 
birth cell.  A counter is placed on it for the next generation.

The following procedure can be use to play the game.  (1) Start with a 
pattern of white counters.  (2) Locate all counters that will die.  
Place a red counter on top of each one.  (3) Locate all vacant cells 
where a birth will occur. (It is important to understand that births 
and deaths occur simultaneously and only white counters contribute to 
births).  Place a blue counter on each birth cell. Next remove all 
deaths (piles of two) and replace blue counters with white "adult" 
counters. This is the next generation. 

One must be very careful in checking for births and deaths; mistakes 
are easy to make.  Start with all possible arrangements of three 
counters.  (There are five distinct ways.) Some patterns die out in a 
few generations, while some become stable- no births or deaths- while 
some simple patterns go on for several hundred generations before 
dying or becoming stable.