Numbering Strategies and Cellular Automa

Looking through the NKS book, SW relies on a very clever numbering system that allows his programs to do three things simulataneously:

1. Uniquely identify a pattern
2. Tell you how the pattern reacts to all possible situations
3. Greatly simplify the process of telling the program what to do on the next step

This interaction is very important and greatly simplifies the programming involved. However, it takes a small bit of work to understand.

The numbering system uses binary numbers to do these three things at the same time. Lets take a look at a simple example where the CA looks at 2 bits and makes a response to each possible state. Here are the possible states for this, with a response to each state to the right of that state:

11 -> 0
10 -> 1
01 -> 1
00 -> 0




In the left column, the possible states increase by 1 in binary from bottom to top. In the right column, the response gives another binary number, which identifies the CA and gives its response to every possible state at the same time. Reading the right column from bottom to top, this would be strategy or rule 6. Play with it a little and you will see the how this numbering system works.

We can use this same numbering system for agent strategies.

More on how this greatly simplifies the programming in the next post.