Geometric designs in the game of "Life".
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Byrne, Willaim Martin Luther King H.S.
To predict and discover patterns generated in the game of "Life".
Large checkerboards (one per two students) and flat counters or
checkers of three different colors.
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.