The Game of Life:
Systematic experimentation.
Maths Workshop
 
Simple configuration patterns.

In order to really understand how the game works we are going to experiment with a set of certain initial configuration patterns. We're going to start with the simplest pattern and then gradually move onto the more complicated ones. Furthermore, we shall start giving names to the patterns which stand out the most to make it easier to understand what's going on.

Use the board below to complete the following exercises and write the answer to the questions in your exercise book.

Exercise 1

Describe the evolution of a society made up of just one organism. Does the society's evolution depend on where this organism is located in our mini-world?

 
Exercise 2

Describe the evolution of a society made up of two neighbours. How many different possibilities are there (in terms of their position to each other) Does the society's evolution depend on how they are positioned next to each other? Does it depend on where they are located in our mini-world?

 
Exercise 3

Possible initial configurations made up of 3 individuals are illustrated below:

Configuraciones de 3 individuos

Describe the evolution of each pattern separately and find out if their behaviour is the same when they are located on the edge or in the middle of the "world".

 
Exercise 4

Make a diagonal chain initial configuration pattern (similar to the third configuration pattern illustrated above) as long as you want and describe its evolution. Try out different lengths.

A few definitions.

Bloque estable The shape which the fourth pattern above eventually becomes will be referred to as a BLOCK from now on. It belongs to a group of configuration patterns which are known as STABLE patterns.

The fifth pattern illustrated above is the simplest of what are called flip-flops or blinkers (OSCILLATING figures of period 2). If you look closely at its behaviour you will see where its name comes from.

In exercise 4 you will have seen how the chain loses its end links in each generation regardless of its length. We can therefore say that the chain disappears at each end at the speed of light. The reason for using this expression is because it represents the fastest possible movement of any configuration pattern. Any configuration pattern which changes from one generation to the next always moves at a speed which is equal to or slower than the speed of light.

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

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