With such simple rules, it seems difficult to believe that complicated
patterns could emerge from the Game of Life, or any other set of rules
for cellular automata. However, it turns out that the outcome of a
particular starting configuration has a far from predictable final state.
While each automaton does follows the same simple set of rules in
Life, those rules call for it to interact with its eight surrounding automata.
When considering that for every one cell, there are eight possible
interactions that determine the next state, it begins to become evident
why an outcome would be difficult to foresee without stepping through
all of the periods on the way to reaching the final state.
For example, consider a traffic
jam. The simplest explanation for a
slow down would be a traffic accident or a slow-moving vehicle that
restricts the flow of other cars. However, many times traffic jams have
no
easy explanation. In reality, the cars cause each other to move slowly
because more are trying to move in the same direction than the capacity
of the road. Much like in the Game of Life, the movement of one car is
affected by the movement of the cars surrounding it. Those cars are in
turn affected by cars around them, and so forth. Thus, a seemingly
simple phenomenon snowballs into a complicated mess and each
lane change, acceleration, or deceleration adds unpredictably to the
intertwined confusion.
The unpredictability of the
final state in the Game of Life is what
allows it to have many applications of a non-trivial nature. When creating
the game, Conway carefully considered the rules in order that the game
have a delicate balance between having all of the cells die out and
having them replicate endlessly. His result is such that it is thus far
impossible to come up with an algorithm to accurately predict the final
configuration given the initial conditions of the board without going
through the intermediate states. This idea will come up again when
discussing the computational possibilities with the Game of Life, but
is
also useful in an area where computers often fall short: generating
pseudo-random numbers. By assigning values to the configurations,
the intricate patterns of Life can be used to generate numbers with a
high degree of randomness.
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