International Encyclopedia of Systems and Cybernetics

A game based on a cellular automaton whose initial state and behavioral rules are specified.

J. CASTI, who describes the "game" (1994, p.223-8), observes that it is not really a game, since there are no players; nor are any decisions to be made".

P. BAK and K. CHEN describe thus John H. CONWAY's famed game: "The game of life simulates the evolution of a colony of living organisms and mimics the generation of complexity in nature" (1991, p.32).

This may be a somewhat overextended claim. As all the elements are of the same class and all the rules apply uniformly in space and time, it would seem that the game may not be more than a tool for modelling composite systems (as opposed to integrated systems – see hereafter).

BAK and CHEN pursue: "To start the game, the pieces, or organisms are placed at random on a board composed of square sites. Each site is occupied by at most one organism and is surrounded by eight neighboring sites.To determine the status of any site at each turn, one must count the number of organisms that occupy the eight neighboring sites. If one count two live sites around an empty or occupied site, then the status of the site does not change. If one counts three live sites around a site, the live sites give birth to a new organism or sustain the life of an old organism. In all other cases, an organism will die from overcrowding or loneliness.

"The game continues according to the rules until it comes to "rest" in a simple periodic state, containing stable colonies" (Ibid).

The game may also end with the total disappearance of the colony, or when a final state is reached, in which no change is anymore possible (analogous to a "frozen state").

Other possibilities are: emission of an independent configuration, that starts to evolve in its own way, and can at times be absorbed by an "eater"; self-reproduction of the original system and, in CASTI words: "… a veritable cornucopia of strange and captivating patterns" (p.225).

As a synthesis, the basic conditions of the game are:

- a limited (or supposedly illimited) substrate in which its evolution takes place

- a specified structure of this substrate (as for example "square sites")

- an unique type of elements, all of them similar

- a given initial state

- a set of transformation rules, excluding any change in the formerly stated conditions

BAK and CHEN perturbed the game "by adding an extra "live cell" and found that "the system often sustains long transients of activity" (Ibid) … and that, when measuring "… the total number of births and deaths in the "avalanche" after each additional perturbation… the distribution was found to be a power law, indicating that the system has organized itself to a critical state.

"We also found that the distribution of live sites is a fractal that can be described by a power law. The average number of active sites within a distance r from a given active site was proportional to r to the power of 0 where 0 turned out to be about 1,7" (1991, p.33).