The Game of Life:
More configuration patterns of interest.
Maths Workshop
 
Other configuration patterns of interest.

In this section we are going to examine different configuration patterns of particular interest. We will introduce their names as we focus on each one so that you know which one we are referring to. Use the window below to complete the exercises which follow.

Exercise 1

Describe the evolution of the following configuration patterns:

Configuraciones interesantes

Look carefully at the behaviour of the letter H in particular and compare it to the behaviour of the same pattern but with the centre counter moved up one cell to make an arch, known as pi. As you can see, although the change is small it makes a drastic difference to the evolution of the pattern.

Exercise 2

Deslizador In this section we are going to examine some especially interesting configuration patterns called gliders. They are so called as throughout their evolution they appear in the same form in different positions.

Start by experimenting with the shape on the right. You will notice that after two generations it has moved slightly and has been reflected in a diagonal line. After two more generations it has moved back to its original form but has moved one cell down and to the right. Since the glider travels one cell every four moves we say that it travels at a speed of 1/4 of the speed of light.

Conway has shown that non of the patterns can move position at a speed quicker than half the speed of light. Try and find a pattern that moves position at this speed. (Suggestion: use shapes which are similar to the glider above).

If you haven't managed to find one try some of the patterns below which are called the featherweight spaceship, middleweight spaceship and heavyweight spaceship respectively (left to right):

Astronaves

Exercise 3

Conway has also showed that spaceships cannot have bodies longer than 6 cells without generating objects that block their motion. Try it and see.

However, overweight spaceships (with bodies longer than 6 cells) are possible as long as they are accompanied by two or more smaller ships that prevent the formation of any obstacles. Try and find a configuration pattern of this type.

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

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