Four-Dimensional Cellular Automata
and
The Game of Life
Abstract
Almost three decades ago, the mathematician John Conway discovered a rule
that caused a semitotalistic cellular automaton to produce interesting
stable patterns. Thus was born Conway's "Game of Life." It is actually
more of a simulation than a game since there are no players involved, but
if we follow the game analogy, then it is played on a grid of squares, each
square having eight adjacent neighbors. A cell occupying a square is born,
lives, or dies based on the number of living neighbors it has. Even though
this was a simple game with no real practical applications, it caused a
significant amount of research to be done in the area of cellular automata.
This greatly furthered the science which today is used in such areas as
image processing and data compression.
Since the debut of Conway's two-dimensional game, other games of life have
been developed. For example, a triangular game of life where each triangle
has twelve neighbors, a spherical game of life where each sphere also has
twelve neighbors, and a cubic or three-dimensional game of life where each
cube has twenty-six neighbors. Rules have also been found for these games
that produce similarly interesting patterns.
The research done in yet another game of life, Four-Dimensional Life, is
presented. Previous to this work, no rules were known to exist in the 4D
Game of Life to produce the most interesting of all patterns the glider,
which is a collection of living cells that cycles through a repeating
pattern while moving through the grid space of the game. The application
developed to do this research and automatically search for these patterns
is also presented.
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