The Game of Life is, briefly, a two-dimensional cellular automata universe governed by a simple set of birth, death and survival rules. It was invented in 1970 by the Cambridge mathematician John Conway and popularized by a series of articles in "Scientific American" by Martin Gardner. Each of the cells in the 2d universe can be in one of two states: alive or dead. Beginning with any given initial pattern of live cells, one can employ Conway's rules in order to determine the behavior of the universe over any number of generations or time steps. Whether a cell survives, dies or comes into being is determined by the number of live neighbors the cell has. Each cell has eight possible neighbors (four on its sides, four on its corners). The rules for survival, death and birth are as follows:
When one employs these rules to any given initial pattern of live cells, the results can be startling. Complex behavior consisting of various Life forms, composed of several or more living cells, often occurs. We will discuss the types of Life forms below.
Simple Life forms can generally be grouped into two categories:
still-lifes and blinkers. Still-lifes are stable forms that do not change
over successive generations unless disturbed by other live cells. The
block and the beehive are two common forms of
still-lifes. Blinkers are periodic Life forms which have predictable
behavior. The traffic light is a quite common form of
blinker that has a period of two.
The glider is a unique Life form. Technically, it is a blinker,
having a period of four. However, it is not a stationary blinker, but
one that travels a single diagonal cell ever four generations.
If a glider is capable of escaping the milieu of a changing pattern, it
travels off into the distance forever.
The eater is a still-life that is remarkable for it's capacity to
devour gliders, provided that the glider approaches it at a certain
angle.
Methuselahs are initial patterns of live cells that require a large
number of generations to stabilize. The smallest and
perhaps most famous methuselah is the R-pentomino which
takes 1103 generations before it reaches a stable (periodic) state.
The acorn is perhaps the longest lived methuselah known,
requiring over 5000 generations to reach periodicity.
Glider guns and puffer trains are two unique Life forms that
produce populations of live cells that grow without limit. The
glider gun simply continues to produce gliders, while the puffer train
travels endlessly in a horizontal direction, leaving a trail of smoke
behind it. Both were discovered by Bill Gosper of the Massachusetts
Institute of Technology. Below is a picture of the glider gun in action.
Life contains an amazing variety of still-lifes, blinkers and other, more comlex forms, which cannot be dealt with comprehensively in this context. One other particularly interesting forms are the spaceship, a structure similar to a glider that travel horizontally with a period of two.
Although the rules that Conway arrived at for Life may intially seem somewhat arbitrary, they were not arrived at by chance. Conway had a specific set of criteria which governed his search for the rules. He did not desire a set of rules that led either to chaotic, infinite growth or rapid stability. Rather, he sought after a set of rules that allowed for patterns which grow and change for some time before stabilizing. Using these criteria, he arrived at the rules that govern the Game of Life. If you experiment with different survival, death and birth, rules , you will quickly see that Conway's rules are anything but arbitrary. They delicately skirt the boundary between chaos and order.
Conway's unique universe has many implications for the new science of Artificial Life. To begin with, Conway has shown that Life forms such as glider guns can be used to create logic gates, the foundations of a Universal Turing Machine. In short, Life can act as a computer. This suggests that Life may also be able to perform the function of self-replication required of an actual living creature. Claus Emmeche, in his survey of Artificial Life, The Garden in the Machine, tells us that "...it can be shown explicitly that it is theoretically possible to implement von Neumann's complicated self- reproduction in this simple game."
Even if the Game of Life is not a medium in which actual life can be formed, the phenomena one can examine through Life are of great interest to the fields of Artificial Life and Philosophy. For example, the macroscopic structures of Life are perfect examples of emergent phenomena: behaviors that arise out of the simple interaction of microscopic parts. Furthermore, the Game of Life is a good tool with which to study such concepts as predictability and complexity.
Among many others, the following web pages are good resources on the Game of Life:
http://www.cs.jhu.edu/~callahan/lifepage.html
http://www.astro.virginia.edu/~eww6n/math/Life.html
http://members.aol.com/life1ine/life/lifepage.htm
In order to search for books one can purchase on artificial life or Conway's Game of LIfe, go to www.amazon.com.
For an excellent page on artificial life in general, go to http://alife.santafe.edu/
To return to the introductory page for the course on Artificial Life, click here.