The Game of Life:
Other scientific implications.
Maths Workshop
 

Stable patterns, self-replicating patterns and "viruses".

One of the most important discoveries of the Game of Life was made by Wainwright, who examined the effect of adding extra cells to pre-defined stable configurations, such as the one illustrated below.

Check that this is a stable configuration by clicking on the Animate button and then follow the instructions given underneath.

In the following exercise move the pointer along the empty spaces only to avoid destroying the present structure. If you make a mistake then correct it as indicated in the instructions or click on the Init button.

Practice

Place a "virus", i.e. an individual cell, where the pointer is situated (or on any of the squares where two empty lines cross) and watch how the virus is eliminated and how the pattern soon restructures itself. 

Click on the Init button and this time place the virus on any empty square, other than one where two empty lines cross. Watch the chaotic evolution of the pattern. In fact, if the pattern was infinite this virus would cause its entire destruction. However, in our example, once again, due to problems of finitude, the pattern may not necessarily become extinct, but its existing perfect organisation is destroyed completely .

The most immediate practical application of this could be the design of circuits, which are capable of self-repair. It could also have important implications on cell growth in embryos, the replication of DNA molecules, the operation of nerve nets, genetic changes in evolving populations and so on. 

Now try and construct some stable patterns in the following window, using the ones you are already familiar with as a starting point. Then, investigate what happens to each pattern if you add a virus to it.


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

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