The Game of Life:
Introduction.
Maths Workshop
 
Introduction.

"Try this one," Cal suggests, giving her the R-pentomino.

"That's similar to the one I just did. You've just tilted it sideways, which makes no topological difference, and added one dot."

"Try it," he repeated.

She tried it, humoring him. But soon it was obvious that the solution was not a simple one. Her numbered patterns grew and changed , taking up more and more of the working area. The problem ceased to be merely intriguing; it became compulsive. Cal well understood this; he had been through it himself. She was oblivious to him now, her hair falling across her face in attractive disarray, teeth biting lips. "What a difference a dot makes!" she muttered.

Piers Anthony. Ox 1976.

The "Game of Life" is a fantastic solitaire game designed by the mathematician from the University of Cambridge, John Horton Conway (although it is really an example of cellular automata rather than a game). This game could be included in the so-called category of "simulation games", which includes all those games that attempt to copy real-life processes. The game we are going to look at includes very similar processes to the rise, fall and alterations of a society of living organisms.

How the game works.

The game is set in the "world" of a grid (theoretically infinite) where any one of the squares is or is not home to a person or living organism. Each square in the grid is surrounded by eight other squares which are referred to as its "neighbourhood".

The game works as follows: the player chooses the initial configuration, in other words, decides on the distribution of the people who make up the so-called first generation or generation 0. This population will evolve according to certain set rules. The aim of the game is simply to follow this evolution.

Evolution will lead the population to one of the three following situations, regardless of the initial configuration:

  • EXTINCTION: the entire population will die out after a finite number of generations.
  • STABILIZATION: after a finite number of generations the population becomes stable, either becoming rigid and immobile or oscillating endlessly between two or more patterns.
  • CONSTANT CHANGE: in this situation the population either increases indefinitely or does not clearly follow any set pattern.

At first, this game might seem a bit dull but you will certainly soon become fascinated by it once you start playing. Furthermore, as we will see throughout this unit, the game can also be considered as a starting point or means of experimentation to examine some current scientific issues. In addition to this, the method we have selected could also be used to tackle other types of problems.

How do we play?

As stated above, the game is very straightforward: first an initial configuration is chosen and then we observe its evolution.

Before long, players will start to think about which initial configuration patterns have a tendency to die out quickly and which tend to survive for longer. Then, they will start to look for configuration patterns which survive for a long time without becoming stable. Later on, they will start to look for configuration patterns which reflect particular types of behaviour etc.

Throughout this unit we will try to take you through this process step by step and point out some of the indirect consequences of certain decisions, which you may not otherwise be aware of.

Rules of play: Conway's "genetic laws"

As we have already explained, there are some set rules governing the process of evolution. These rules are varied and even Conway himself carried out along period of experimentation before choosing his rules. However, there were three requirements that all the rules had to fulfill:

  1. There should be no initial configuration pattern for which there is a simple proof that the population can grow without limit.
  2. There should be some initial patterns that "apparently" do grow without limit.
  3. There should be some simple initial patterns that grow and change over a considerable period of time before dying out or settling into a stable configuration.

To sum up: the rules should be such as to make the population's behaviour both interesting and unpredictable.

After a great deal of research Conway finally decided on the following rules which, from now on, we will refer to as "Conway's genetic laws":

  1. SURVIVALS: Every counter with 2 or 3 neighbours will survive and go on to form part of the next generation.
  2. DEATHS: Every counter with less than 2 neighbours will die from loneliness. Every counter with more than 3 neighbours will die from overpopulation.
  3. BIRTHS: If an empty cell on the grid is adjacent to exactly 3 neighbours the cell will 'give birth to' a new counter in the next generation.

Once you start playing you will notice that the population doesn't stop changing. Whether these changes seem strange or beautiful to you  they will certainly happen unexpectedly.

     
           
  José Luis Alonso Borrego.
 
Spanish Ministry of Education. Year 2001
 
 

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